Tracking maneuvering targets. Features of guidance on maneuvering targets
As a result of the primary processing of radar information, two streams of target marks arrive at the input of the autotracking algorithm:
"true targets", grouped near the actual position of the targets;
"false targets"", one of which is tied to areas of interference and reflections from local objects, and the other is evenly distributed throughout the station's field of view.
If it is decided that a certain set of marks received by each in its radar survey refers to the same trajectory, then the next task is to evaluate the parameters of this trajectory, which consists in calculating the parameters considered in Section 2.2 X 0 ,At 0 ,H 0 ,V x ,V y ,V H ,a x ,a y and a H. If there are two marks about the target as initial coordinates X 0 ,At 0 and H 0 the coordinates of the last mark are received, the components of the speed V x , V y and V H are calculated in the same way as with auto-capture of the trajectory.
If a larger number of marks are distinguished, it is possible to switch to a more complex model of target movement and smooth the trajectory parameters. Smoothing is performed in order to reduce the impact of radar target coordinate measurement errors on tracking accuracy. The most common in ACS are a linear model of target movement and successive smoothing of trajectory parameters.
The essence of the successive smoothing method is that the smoothed values of the trajectory parameters in the next k-th range are determined by the smoothed values obtained in ( k-1)-th review, and the results of the last k th observation. Regardless of the number of observations made, only the previous estimate and the result of a new observation are used in the next calculation cycle. At the same time, the requirements for the capacity of storage devices and the speed of the equipment are significantly reduced.
The final expressions for smoothing the position and velocity in the kth radar survey are as follows:
It can be seen from these formulas that the smoothed value of the coordinate is equal to the sum extrapolated to the moment k-observations of the smoothed coordinate U* KE and taken with a coefficient k deviations of the extrapolated coordinate from the measurement result.
Smoothed speed value in k th review V * U K is the sum of the smoothed speed V * U K-1 in ( k-1)-th review and taken with a coefficient k speed increment that is proportional to the deflection.
U=U K- U KE.
H
Rice. 2.5. Smoothing of target trajectory parameters.
The dotted line in Fig. 2.5 means the smoothed target trajectory calculated in the ACS computer in k th review. Due to the fact that the coefficients of the smoothed coordinates k and k lie within 0...1, the smoothed initial coordinate is in the interval U* KE ... U K, and the smoothed speed is V * U K-1... V * U K.
It is proved that for a rectilinear uniform motion of the target, the tracking errors will be minimal if the coefficients k and k are calculated according to the formulas:
(2.9)
Figure 2.6 shows the dependence k and k from review number k. It can be seen from the graphs of the figure that the coefficients asymptotically approach zero. In the limit at k This achieves the complete elimination of target tracking errors. In practice, there are always deviations of the target trajectory from a straight line.
Therefore, the values of the coefficients k and k decrease only to certain limits.
Qualitatively, the effect of smoothing on the accuracy of target tracking can be estimated using Fig. 2.7. In the area of rectilinear motion, the error of the smoothed target coordinates is less than the unsmoothed ones: segments of dotted lines are closer to the true trajectory of the target than segments of solid lines. In the maneuver section, due to the discrepancy between the true nature of the target’s movement and the hypothetical one, dynamic tracking errors occur. Now segments of solid lines more accurately determine the actual position of the target compared to segments of dashed lines.
In the air defense automated control system, when tracking non-maneuvering targets, the choice of coefficients k and k produced in various ways: they can either be recalculated from initial to some final values, or remain unchanged during the entire maintenance period. In the latter case, the optimal successive smoothing turns into the so-called exponential smoothing. Target maneuver detection can be performed visually by the operator or automatically. In both cases, the target is considered maneuvering if the measured target coordinate differs from the extrapolated one by an amount that exceeds the allowable coordinate measurement errors.
W
Rice. 2.6. Dependence of smoothing coefficients on K.
Rice. 2.7. Effect of Smoothing Trajectory Parameters on Target Tracking Accuracy
Usually, the calculation of the current (extrapolated at a given point in time) coordinates of the target is timed to the moments of issuing information to indicators, communication channels, memory zones of other algorithms, etc. The calculation of the predicted values of the target coordinates is carried out according to the formulas:
(2.10)
where t y- lead time, counted from the current moment t.
Usually t y when assessing the air situation, it is set by commanders, and when solving other data processing tasks, it is read from the permanent memory of the ACS computer.
The final stage of target tracking is the solution of the problem of correlating newly appearing marks with existing trajectories. This problem is solved by mathematical gating of airspace areas. Its essence lies in the machine verification of the fulfillment of equalities, with the help of which it is established that the mark belongs to the area under study. In this case, rectangular or circular gates are most often used. Their parameters are shown in Figure 2.8.
Let be X uh, At E - extrapolated target coordinates at some point in time t. To find out which of the marks received in the next survey belongs to this trajectory, it is necessary to check the conditions:
P
Rice. 2.8. Strobe parameters
|X 1 -X E | X pp; | Y 1 -Y E | Y pp; (2.11)
when using a circular strobe -
(X i – X E) 2 + ( Y i – Y E) 2 R str, (2.12)
where X page, Y str - dimensions of a rectangular gate;
R str - the size of the circular gate.
As a result of the enumeration of all possible pairs of "trajectory-mark" in each survey, it is established which marks continue the existing ones, and which ones initiate new traces.
From the description of target trajectory tracking algorithms, it can be seen that the processing of information about the air situation is a very laborious process that requires large amounts of RAM and computer speed of the automated control system.
The maneuver of the target in the horizontal plane is reduced to a change in course and flight speed. The influence of the maneuver of an aerial target on the first and second stages of guiding a fighter by the "Maneuver" method manifests itself in various ways.
Let us assume that guidance is carried out at the first stage, when the air target and the fighter were respectively at the points AT and BUT (Fig. 7.9.), And their meeting was possible at the point C o .
Rice. 7.9. Influence of target maneuver in the horizontal plane
to the flight path of a fighter
If the air target is at the point AT made a maneuver in the course and in time t turned to a corner w c t , then in order for the fighter to follow a tangent to the turn arc of the second stage of guidance, its course must change by the angle w and t . After the air target has completed the maneuver, a meeting with it will become possible at the point With , and the path length of the air target to the point will change to DSc.
If we imagine that the turn start point is moving along with the CC, located relative to it at the same interval and distance as the fighter at the start of the turn, then the fighter is guided to this point by the "Parallel approach" method. If the CC is at a long distance Before from a fighter, compared with which the interval I and predicted turning distance dupr can be neglected, then in general the properties of the "Maneuver" method are close to those of the "Parallel approach" method.
To a later meeting of a fighter with a target (DSc > 0) leads her lapel from the fighter (DΘ and > 0) , and turning towards the fighter leads to an earlier encounter. Therefore, the countermeasure against the maneuver of the target heading, as in the case of guidance by the "Parallel approach" method, can be the simultaneous guidance of groups of fighters on it from different sides.
As the distance to the CC decreases, the difference between the properties of the "Maneuver" method and the properties of the "Parallel rendezvous" method manifests itself more and more. During the turnaround time of the VC, the fighter needs to turn around at increasingly large angles, that is, its angular velocity w increases.
Value change w and when flying a fighter on a collision course with an air target (UR = 180°) characterizes the dependence graph of the ratio of angular velocities w and / w c from the range, expressed in fractions of the lead turn distance D/Dupr.
As can be seen from the graph, at long ranges (D / Dupr = 5÷ 10) attitude w and / w c differs slightly from unity, that is, the angular velocity of the fighter is slightly different from the angular velocity of the maneuvering target. With a decrease in range, up to about three Supr , the value of wi grows rapidly, and when the fighter approaches the turn start point (D / Dupr = 1)w and increases to infinity.
Thus, when pointing by the "Maneuver" method at a maneuvering AT, it is practically impossible to bring the fighter to the turn start point with the calculated radius.
Rice. 7.10. Dependence of the ratio of angular velocities w and / w c during target maneuver
at the first stage of guidance in relation to D / Dupr
During the guidance process at the first stage, the air target can maneuver repeatedly. So, for example, an air target at a point IN 1 can turn on a fighter, resulting in a point A1 it must be turned away from its previous course and the direction of the previously envisaged turn must be changed. As a result, the fighter's trajectory at the first stage of guidance turns from a straight line into a complex line consisting of turning arcs with a variable radius and straight line segments between them. All this complicates the flight to air combat.
The influence of the maneuver of an air target at the second stage of guiding a fighter by the "Maneuver" method will be considered using Figure 7.11.:
Rice. 7.11. Influence of air target maneuver in the horizontal plane
at the second stage of guidance by the "Maneuver" method on the flight path of a fighter
Let us assume that at some moment of the second stage of guidance, the fighter and the air target are, respectively, at the points BUT and AT and to meet the target at the point So the fighter performs a turn with a radius Ro and angular velocity w and = Vi/Rо .
If for some period of time Dt air target will change direction of flight by an angle w c × Dt , then meeting with it will become possible at the point With . To get to this point from the point BUT the fighter would need to perform a turn with a different radius R . But in advance for the time Dt he would have to additionally tighten the corner w and D × Dt .
Thus, the maneuver of an air target at the second stage of guidance leads to the appearance of an additional angular velocity of the turn of the fighter w and D . The smaller the remaining turning angle UR fighter, the greater the value w and D , and as the fighter approaches the end point of the turn w and D increases to infinity.
Thus, it is almost impossible to bring a fighter to a given position relative to a maneuvering air target at the second stage of guidance using the "Maneuver" method.
In this regard, in the case of maneuvering an air target, at the second stage, as a rule, they switch to guiding a fighter using the Chase method.
Introduction.
Chapter 1. Analysis of filters for tracking the trajectories of air targets.
§1.1. Kalman filter.
§1.2. Application of the Kalman filter to track the trajectories of the CC according to the surveillance radar data.
§ 1.3. "Alpha - Beta" and "Alpha - Beta - Gamma" filters.
§ 1.4. Statistical modeling.
§1.5. Findings.
Chapter 2. Analysis of adaptive methods for tracking the trajectories of maneuvering air targets based on maneuver detectors.
§ 2.1. Introduction.
§ 2.2. Joint detection and estimation of target maneuver based on the updating process.
§ 2.3. Adaptive algorithms for tracking maneuvering
CC using maneuver detectors.
§ 2.4. Findings.
Chapter 3. Research of known multi-model algorithms.
§3.1. Introduction.
§3.2. Bayesian adaptive approach.
§3.3. Study of the well-known MMA tracking of the trajectory of the CC for a surveillance radar.
§3.4. Findings.
Chapter 4. Development of a multi-model algorithm for tracking * trajectories of maneuvering air targets.
§4.1. Introduction.
§4.2. Estimation of the motion state vector of the CC.
§4.2.1. Formulation of the problem.
54.2.2. General approach to problem solving.
04.2.3. Linear algorithm.
§4.3. Comparison of MMA with other algorithms.
§4.4. Findings.
Recommended list of dissertations
Secondary processing of information in a two-position radar system in a Cartesian coordinate system 2004, candidate of technical sciences Sidorov, Viktor Gennadievich
Filtering estimates of spherical coordinates of objects in a two-position radar system 2004, candidate of technical sciences Grebenyuk, Alexander Sergeevich
Algorithmic Provision of Information Support for Estimating a Dynamic Situation in Multisensor Systems with Automatic Tracking of Surface Objects 2001, Doctor of Technical Sciences Beskid, Pavel Pavlovich
Development of methods for controlling the location of state aviation aircraft in the process of air traffic control in the off-route sector of the airspace 2009, Candidate of Technical Sciences Shanin, Alexey Vyacheslavovich
Development and study of a method for pointing at a maneuvering object based on a stochastic prediction of its movement 2004 PhD Truong Dang Khoa
Introduction to the thesis (part of the abstract) on the topic "Research of algorithms for tracking the trajectories of air targets"
The relevance of the dissertation topic
One of the most important tasks of civil aviation is to improve flight safety, especially during takeoff and landing. To achieve this goal, automated air traffic control systems (ATC) must have the necessary quality indicators, which to a certain extent depend on the quality of incoming radar information. In the ATC system, radar information from en-route and airfield radars is used to control the movement of air targets (AT), collision avoidance and landing approach control. When controlling the movement of the AT, it is necessary to calculate the current coordinates of each AT in order to exclude dangerous approaches of the AT. Otherwise, the pilots are given commands to correct the trajectories. In the collision avoidance mode, an estimate of extrapolated coordinates is formed, on the basis of which dangerous proximity zones are determined. Moreover, in recent years, the density of air traffic has also increased. The increase in air traffic density leads to an increase in the number of dangerous encounters. Prevention of dangerous approaches of the AE is part of the most important task of civil aviation - ensuring flight safety. When controlling the movement of the AT at the landing approach stage, the radar checks the correctness of the movement of the AT along the given trajectories.
Therefore, the issues of improving the quality of radar information constantly attract great attention. It is known that after the primary processing of radar information, the process of secondary processing of radar information (SOP) is usually carried out by programmed digital processing algorithms on a computer, and the quality of the radar information flow strongly depends on the reliability and accuracy of the processing algorithms. This task is all the more relevant if the AT maneuvers at the take-off and landing stages associated with level changes, course changes and the implementation of standard approach procedures, etc. are taken into account.
Consider the location of the elements of the airspace of the ATC area and a typical approach pattern. In civil aviation, the airspace is divided into an airway - an established airspace above the earth's surface in the form of a corridor with a width of (10 - 20) km, along which regular flights are carried out, an aerodrome area - an airspace above the aerodrome and the area adjacent to it and a restricted area - airspace in which flights of aviation of all departments are prohibited.
Air corridors, take-off and landing areas and waiting areas are organized in the area of the aerodrome. An air corridor is a part of the airspace in which the ATs are descending and gaining altitude. Take-off and landing area - airspace from the level of the airfield to the height of the second safe flight level. The dimensions of this zone are determined by the flight performance characteristics of the ATs operated at a given aerodrome, the capabilities of ATC and landing radio navigation aids, approach procedures and the specific features of the aerodrome area. As a rule, the boundaries of the take-off and landing zone are 25.30 km away from the airfield. If for some reason the pilot did not land the VC from the first approach, then the VC goes to the second circle, i.e. moves along a special route in the circle zone (see Fig. B.1). If the OC is not allowed to move along the approach route due to temporary occupancy or unavailability of the runway (runway), then the OC is directed to the holding area intended for waiting for the landing clearance in the aerodrome area. These zones are located above the aerodrome or 50 - 100 km from it (Fig. B.1). Thus, in the area of the aerodrome, the frequency of maneuvering the TC is high. This is explained by the fact that in this area there is a high density of ATs, and in order to maintain given routes and distances, they always maneuver from one zone to another.
1 - tracks; 2 - corridors of the airfield area; 3 - circle zone; 4-zone takeoff and landing;
5 - waiting areas.
In addition, to improve the safety of the TC and passengers during landing, the “box” approach scheme is currently widely used, in which the TC must plan (1-2) circles over the airfield before landing (Fig. B.2). This pattern consists of some sections of straight-line traffic and four 90-degree turns.
Rice. IN 2. Scheme of landing approach on the "box".
On the other hand, the state and development of computer technology makes it possible to apply more complex and efficient algorithms for processing radar information to improve the accuracy of estimating the coordinates and speed of the CC.
Thus, the study of algorithms for tracking the trajectories of the CC, which provide an increase in the quality of radar information, is an urgent problem.
When processing radar information, a particularly urgent task is to study processing algorithms in the areas of the maneuver of the AT, which lead to a discrepancy between the real movement of the AT and the motion model used in the algorithm. As a result, the accuracy of the estimation results deteriorates, and the received radar information becomes unreliable. Known approaches to improving the accuracy of tracking the trajectory of the TC in the sections of the maneuver are mainly based on solving the problem of detecting the beginning and end of the maneuver and the corresponding change in the parameters of the tracking filter. These approaches lead to the scheme of "alpha - beta" and "alpha - beta - gamma" filters, or a Kalman filter (KK) in combination with a maneuver detector.
It is known that in the theory of detection and estimation, the adaptive Bayesian approach can also be used to solve a priori uncertainty. When filtering in the state space, this approach lies in the fact that all possible variants of state models are taken into account, with each variant its posterior probability is calculated. Its application to solving the problem of tracking the trajectories of maneuvering ATs has been developed in recent years. In this case, the CC trajectory is described simultaneously by several models, and it is assumed that the process of transition between models is described by a simply connected Markov chain. In the literature, one option has been proposed for creating such an algorithm based on the Gaussian approximation for the a priori probability density of the state vector. Its essence is to combine the possible hypotheses of the models, and the resulting algorithm is called the "multi-model algorithm" (MMA).
The dissertation analyzes the above mentioned approaches, shows their advantages and disadvantages, and develops a new MMA. Unlike the well-known MMA, the proposed algorithm is based on the Gaussian approximation for the a posteriori probability density of the CC state vector, according to which the resulting algorithm has advantages over the known adaptive algorithms. The result of statistical modeling showed that the algorithm under study makes it possible to improve the accuracy of estimating the location of the CC in comparison with the adaptive FC and the known MMA when tracking the trajectory of the maneuvering CC. The results of the study showed that the cost of computing the first simplified FC is reduced compared to the second simplified and extended FC, at the same time, its accuracy in estimating both the coordinates and the speed of the CC increases by (30-50)% compared to "alpha - beta" and " alpha - beta - gamma" filters. Therefore, the use of the first simplified FK for tracking the trajectory of non-maneuvering ATs is more preferable.
Purpose and tasks of the work
The purpose of the dissertation work is to study and analyze algorithms for tracking trajectories of the CC, develop a new MMA and compare the obtained MMA with known adaptive algorithms. In accordance with the goal in the dissertation work, the following tasks were solved:
The study of the general theory of estimation in the state space, and its application to the filtering of the trajectories of the CC.
Analysis of "alpha - beta" and "alpha - beta - gamma" filters and a method for selecting their gains in the areas of maneuver and lack of maneuver.
Investigation of adaptive FC for tracking the trajectories of maneuvering ATs with a detector of the moment of the start of the maneuver.
Optimal estimation in the state space with an extended state vector that includes, in addition to the vector of state parameters, an as yet unknown parameter that determines all possible variants of the state model.
Research of well-known MMAs and development of a new MMA for tracking maneuvering CCs based on the description of the trajectory of CCs by several models simultaneously, which are states of a simply connected Markov chain.
Research methods
The theoretical study and creation of algorithms for tracking the trajectories of the CC are carried out on the basis of the theory of filtering conditional Markov processes in discrete time. The obtained algorithms are analyzed on the basis of statistical modeling. The scientific novelty of the work lies in the following: MMA was developed when describing the trajectory of the CC simultaneously by several models for a simply connected Markov chain.
The reliability of the obtained results of the work is confirmed by the results of statistical modeling.
Practical significance of the results of the work
An algorithm for tracking the trajectory of a maneuvering AT has been developed and studied, which improves the accuracy of tracking in maneuver sections.
Approbation of the results of work and publication
The main scientific results of the work were published in the articles of the journals "Radio Engineering", "Electronic Journal Proceedings of the MAI" and "Aerospace Instrumentation", and were reported at the 5th international conference "Digital processing and its application" (Moscow, 2003), at the international conference and exhibition "Aviation and Cosmonautics 2003" (MAI 2003). Scope and structure of work
The dissertation work consists of an introduction, four chapters, a conclusion and a list of references. The work contains 106 pages of text. The list of references includes 93 titles. In the first chapter, some existing methods for tracking the trajectories of non-maneuvering and weakly maneuvering ATs in the ATC task are considered and analyzed. The second chapter analyzes the known adaptive algorithms for tracking maneuvering targets, which are based on the use of maneuver detectors and correction of either parameters or filter structure. The third chapter analyzes the state of MMA in the ATC AS. In the fourth chapter, a general approach to the construction of multi-model algorithms for the ATC problem is proposed for describing possible models of the motion of an EC by a simply connected Markov chain.
Similar theses in the specialty "Radio engineering, including television systems and devices", 05.12.04 VAK code
Methods and algorithms for information processing in autonomous radio vision systems during low-altitude flights of aircraft 2006, doctor of technical sciences Klochko, Vladimir Konstantinovich
Methods for Improving the Accuracy of Angle Measurements in Radio Engineering Systems with Combined Antenna Beam Control 2011, candidate of technical sciences Razin, Anatoly Anatolyevich
Synthesis of an aircraft control system for monitoring and application of fire extinguishing means 2012, candidate of technical sciences Antipova, Anna Andreevna
Algorithms for Estimating Coordinates and Navigation Parameters of an Air Target in a Multi-Position Radar Based on the Kalman Filter 2015, candidate of technical sciences Masharov, Konstantin Viktorovich
Invariant Methods for the Synthesis of Radio Engineering Systems in Finite-Dimensional Bases and Their Application in the Development of Radar Tracking Systems 1999, Doctor of Technical Sciences Volchkov, Valery Pavlovich
Dissertation conclusion on the topic "Radio engineering, including television systems and devices", Nguyen Chong Luu
§4.4. findings
In this chapter, a general approach was proposed for constructing multi-model algorithms for describing possible models of VC motion by states of a simply connected Markov chain, and the following results were obtained.
Based on the general theory of filtering conditional Markov processes, an algorithm was created in which the filtered parameter vector includes not only the parameters of the target's movement, but also an unknown parameter that determines possible models of the target's movement. As a result, the resulting algorithm is suboptimal due to the Gaussian approximation for the posterior probability density.
With regard to tracking the trajectory of maneuvering ATs, the resulting algorithm is modeled for the case M=2. The results showed that in the sections of the maneuver trajectory, the studied two-dimensional algorithm improves the accuracy of the place estimation by (30 - 60)% compared to the known algorithms. However, an increase in the quality of filtering is achieved by increasing the cost of computing.
CONCLUSION
In the dissertation work, the algorithms for tracking the trajectories of the CC according to the surveillance radar data were studied. The results obtained allow us to evaluate the advantages and disadvantages of each tracking algorithm. In the dissertation, algorithms have been researched and developed to avoid dangerous encounters and improve the accuracy of estimating both the coordinates and the speed of the CC. It is known that the secondary processing of radar information (VORI) is usually performed using a digital computer or digital equipment. In recent years, there has been a rapid development of computer technology, microprocessors, the element base of digital technology, especially VLSI, FPGA, and languages for describing equipment and systems, such as USYL, ASHEL, etc. There has been a tendency to introduce VLSI to create open systems based on international standards , including VORI systems. This allows one to explore more complex algorithms for tracking trajectories of the CC in real time. In the presented work, various algorithms for tracking non-maneuvering and maneuvering ATs are studied based on statistical modeling. The following results were obtained in the dissertation:
1. "Alpha - beta" and "alpha - beta - gamma" filters have been studied, a variant of choosing their gain coefficients while tracking the CC trajectory has been proposed. "Alpha - beta" and "alpha - beta - gamma" filters can reduce the cost of calculations and simplify the procedure for tracking the trajectories of the CC, however, they simultaneously worsen the quality of tracking by (30 - 40)% depending on the range, speed and number of observations compared to with conventional filters.
2. The problem of non-linear filtering is studied, when the surveillance radar measures the polar coordinates of the CC, and the filtered vector includes motion parameters in the Cartesian coordinate system. A simplified Kalman filter is proposed, which converts the measurement coordinates from the polar system to the Cartesian one, and an extended Kalman filter, which linearly approximates the measurement equation by reducing the high-order terms of the Taylor series. The analysis showed that the second simplified and extended Kalman filters give the same result in terms of estimation accuracy, both position and velocity, but the second simplified Kalman filter is more economical in terms of computational costs.
3. Adaptive algorithms based on the joint detection and estimation of the CC maneuver are proposed. The task of detecting a maneuver belongs to the class of tasks of detecting useful signals against the background of white Gaussian noise. In this case, the useful signal to be detected is the expectation of the updating process, which differs from zero in the presence of a maneuver. When solving the maneuver detection problem, the likelihood ratio method was used, and to estimate its intensity, we will consider acceleration as a non-random process, as a result, to synthesize the estimator, it is necessary to use the maximum likelihood criterion. To accompany the maneuvering AT, after the maneuver is detected, either the parameters or the filter structures are changed.
4. An adaptive multi-model algorithm has been researched and developed, which takes into account all possible models corresponding to the trajectory of the CC. Thus, in addition to estimating the vector of motion parameters, it is necessary to estimate the posterior probabilities of all models. The current estimate of the CC coordinates is formed as a weighted sum of estimates relative to all models by a posteriori probabilities. This allows the tracking algorithm to react to the maneuver as soon as it starts. To create adaptive multi-model algorithms, an unknown parameter that determines one of the M possible models of CC motion at each moment of time is described by a simply connected Markov chain. As a result, the resulting algorithm was created from a set of M2 parallel Kalman filters. The simulation results for the case M = 2 showed that in the sections of the maneuver trajectory, the studied two-dimensional algorithm improves the accuracy of estimating the location of the CC by (30 - 60)% compared to the known algorithms. However, an increase in the quality of filtering is achieved by increasing the cost of computing.
5. The developed programs of the experiment on a digital computer make it possible to evaluate the advantages and disadvantages of algorithms, on the basis of which the possibility of their implementation in specific conditions is determined.
List of references for dissertation research Ph.D. Nguyen Chong Luu, 2004
1. Farina A., Studer F. Digital processing of radar information. Per. from English. -M.: Radio and communication, 1993, 319 p.
2. Sage E., Mele J. Theory of evaluation and its application in communication and management. Per. from English. -M.: Communication, 1976,496 p.
3. Bakulev P. A., Stepin V. M. Methods and devices for selection of moving targets. Moscow: Radio and communication, 1986, 288 p.
4. Kuzmin S. 3. Digital radar. Publishing house KV1Ts, Kyiv 2000, 426 p.
5. Sosulin Yu.G. Theoretical foundations of radar and radio navigation. -M.: Radio and communication, 1992.303 p.
6. Bakut P. A., Zhulina Yu. V., Ivanchuk N. A. Detection of moving objects. M.: Soviet radio, 1980, 287 p.
7. Kuzmin S. 3. Digital processing of radar information. M.: Sov. radio, 1967,399 p.
8. Kuzmin S. 3. Fundamentals of the theory of digital processing of radar information. M.: Sov. radio, 1974, 431 p.
9. Kuzmin S. 3. Fundamentals of designing systems for digital processing of radar information. Moscow: Radio and communication, 1986, 352 p.
10. Yu.Sosulin Yu.G. Theory of detection and estimation of stochastic signals. M.: Sov. Radio, 1978, 320 p.
11. P. Shirman Ya. D., Manzhos V. N. Theory and technique of processing radar information against the background of interference. Moscow: Radio and communication, 1981, 416 p.
12. Tikhonov V. I. Statistical radio engineering. Moscow: Radio and communication, 1982, 624 p.
13. Z. Tikhonov V. I., Kharisov V. N. Statistical analysis and synthesis of radio engineering devices and systems. Moscow: Radio and communication, 1991, 608 p.
14. M. Bochkarev A. M., Yuryev A. N., Dolgov M. N., Shcherbinin A. V. Digital processing of radar information // Foreign radio electronics. No. 3, 1991, p. 3 22.
15. Puzyrev V.A., Gostyukhina M.A. Algorithms for estimating the parameters of the movement of aircraft / / Foreign radio electronics, No. 4, 1981, p. 3-25.
16. Gritsenko N.S., Kirichenko A.A., Kolomeytseva T.A., Loginov V.P., Tikhomirova I.G. 3 30.
17. Detkov A. N. Optimization of algorithms for digital filtering of trajectory information when tracking a maneuvering target // Radio engineering, 1997, No. 12, p. 29-33.
18. Zhukov M. N., Lavrov A. A. Improving the accuracy of measuring target parameters using information about the maneuver of the radar carrier // Radio engineering, 1995, No. 11, p. 67 - 71.
19. Bulychev Yu. G., Burlai I. V. Quasi-optimal estimation of the parameters of the trajectories of controlled objects // Radio engineering and electronics, 1996, V. 41, No. 3, p. 298-302.
20. Bibika V. I., Utemov S. V. Tracking filter for maneuvering stealth targets // Radio engineering, 1994, No. 3, p. 11-13.
21. Merkulov V. I., Drogapin V. V., Vikulov O. V. Synthesis of a radar protractor for tracking intensively maneuvering targets // Radio engineering, 1995, No. 11, p. 85 91.
22. Merkulov V. I., Dobykin V. D. Synthesis of the optimal measurement identification algorithm for automatic tracking of air objects in the review mode// Radio engineering and electronics, 1996, V. 41, No. 8, p. 954-958.
23. Merkulov V. I., Khalimov N. R. Detection of target maneuvers with correction of algorithms for the functioning of auto-tracking systems // Radio engineering, 1997, No. 11, p. 15-20.
24. Bar-Shalom Ya., Berver G., Johnson S. Filtering and stochastic control in dynamic systems. Ed. Leondes K. T .: Per. from English. M.: Mir. 1980, 407 pp.
25. Rao S.R. Linear statistical methods and their applications: Per. from English. -M.: Nauka, 1968.
26. Maksimov M.V., Merkulov V.I. Radioelectronic tracking systems. Synthesis by methods of the theory of optimal control. -M.: Radio and communication, 1990.255 p.
27. Kameda N., Matsuzaki T., Kosuge Y. Target Tracking for Maneuvering targets Using Multiple Model Filter// IEEE Trans. Fundamentals, vol. E85-A, No. 3, 2002, p. 573-581.
28. Bar-Shalom Y., Birmiwal K. Variable Dimension Filter for Maneuvering Target Tracking// IEEE Trans, on AES 18, no. 5, 1982, p. 621 - 629.
29. Schooler C. C. Optimal a p Filters For Systems with Modeling Inaccuracies / / IEEE Trans, on AES - 11, No. 6, 1975, p. 1300-1306.
30. Kerim Demirbas. Maneuvering Target Tracking with Hypothesis Testing// IEEE Trans, on AES 23, no. 6, 1987, p. 757 - 765.
31. Michael Greene, John Stensby. Radar Target Pointing Error Reduction Using Extended Kalman Filtering// IEEE Trans, on AES 23, no. 2, 1987, p. 273-278.
32. McAulay R. J., Denlinger E. A. Decision-Directed Adaptive Tracker// IEEE Trans, on AES 9, no. 2, 1973, p. 229 - 236.
33. Bar-Shalom Y., Fortmann T. E. Tracking data association. Boston: Academic Press, 1988, 353 p.
34. Kalata P. R. The Tracking index: a generalized parameter for a P and a - p -y target trackers / / IEEE Trans, on AES - 20, No. 2,1984, p. 174 - 182.
35. Bhagavan B. K., Polge R. J. Performance of g-h Filter For Tracking Maneuvering Targets/IEEE Trans, on AES-10, no. 6, 1974, p. 864 866.
36. Ackerson Guy A., Fu K. S. On State Estimation in Switching Environments// IEEE Trans, on AC-15, no. 1, February 1970, p. 10 17.
37. Bar-shalom Y., Chang K.C., Blom H. A. Tracking a Maneuvering Target Using Input Estimation Versus the Interacting Multiple Model Algorithm// IEEE Trans, on AES-25, No. 2, March 1989, p. 296 300.
38. Wen-Rong Wu, Peen-Pau Cheng, A Nolinear IMM Algorithm for Maneuvering Target Tracking// IEEE Trans, on AES-30, No. 3, July 1994, p. 875-885.
39. Jiin-an Guu, Che-ho Wei. Maneuvering Target Tracking Using IMM Method at High Measurement Frequency// IEEE Trans, on AES-27, No. 3, May 1991, p. 514-519.
40. Blom H. A., Bar-shalom Y. The Interacting Multiple Model Algorithm for Systems with Markovian Switching Coefficients// IEEE Trans, on AC-33, No. 8, August 1988, p. 780-783.
41. Mazor E., Averbuch A., Bar-shalom Y., Dayan J. The Interacting Multiple Model Methods in Target Tracking: A Survey// IEEE Trans, on AES-34, no. 1, 1998, p. 103-123.
42. Benedict T. R., Bordner G. R. Synthesis of an optimal set of radar track-while-scan smoothing equations// IRE Trans, on AC-7, July 1962, p. 27 32.
43. Chan Y. T., Hu A. G. C., Plant J. B. A Kalman Filter Based Tracking Scheme with Input Estimation// IEEE Trans, on AES 15, no. 2, July 1979, p. 237 - 244.
44. Chan Y. T., Plant J. B., Bottomley J. R. T. A Kalman Tracker With a Scheme with Input Estimator// IEEE Trans, on AES 18, no. 2, 1982, p. 235 - 240.
45. Bogler P. L. Tracking a Maneuvering Target Using Input Estimation// IEEE Trans, on AES 23, no. 3, 1987, p. 298 - 310.
46. Steven R. Rogers. Alpha Beta Filter With Correlated Measurement Noise// IEEE Trans, on AES - 23, No. 4, 1987, p. 592 - 594.
47. Baheti R. S. Efficient Approximation of Kalman Filter for Target Tracking// IEEE Trans, on AES 22, No. 1, 1986, p. 8 - 14.
48. Miller K. S., Leskiw D. M. Nonlinear Estimation With Radar Observations// IEEE Trans, on AES 18, no. 2, 1982, p. 192 - 200.
49. Murat E. F., Atherton A. P. Maneuvering target tracking using Adaptive turn rate models in he IMM algorithm// Proceedings of the 35th Conference on Decision & Control. 1996, p. 3151 -3156.
50. Alouani A. T., Xia P., Rice T. R., Blair W. D. On the Optimality of Two-Stage State Estimation In the Presence of Random Bias// IEEE Trans, on AC 38, no. 8, 1993, p. 1279-1282.
51. Julier S., Uhlmann J., Durrant-Whyte H. F. A New Method for the Nonlinear Transformation of Means and Covariances in Filters and Estimators// IEEE Trans, on AC 45, no. 3, 2000, p. 477 - 482.
52. Farina A., Ristic B., Benvenuti D. Tracking a Ballistic Target: Comparison of Several Nonlinear Filters// IEEE Trans, on AES 38, no. 3, 2002, p. 854 - 867.
53. Xuezhi wang, Subhash Challa, Rob Evans. Gating Techniques for Maneuvering Target Tracking in Clutter// IEEE Trans, on AES 38, no. 3, 2002, p. 1087 -1097.
54. Doucet A., Ristic B. Recursive State Estimation for Multiple Switching Models with Unknown Transition Probabilities// IEEE Trans, on AES 38, no. 3, 2002, p. 1098-1104.
55. Willett B., Ruan Y., Streit R. PMHT: Problems and Some Solutions// IEEE Trans, on AES 38, no. 3, 2002, p. 738 - 754.
56. Watson G. A., Blair W. D. Interacting Acceleration Compensation Algorithm For Tracking Maneuvering Targets// IEEE Trans, on AES -31, no. 3, 1995, p. 1152-1159.
57. Watson G. A., Blair W. D. Interacting Multiple Bias Model Algorithm with Application To Tracking Maneuvering Targets// Proceedings of the 31st Conference on Decision and Control. December 1992, p. 3790 3795.
58. Kameda H., Tsujimichi S., Kosuge Y. A Comparison of Multiple Model Filters For Maneuvering Target Tracking// SICE 2000, p. 55 60.
59. Kameda H., Tsujimichi S., Kosuge Y. Target Tracking Under Dense Environments using Range Rate Measurements// SICE 1998, p. 927 - 932.
60. Rong Li X., Bar-Shalom Y. Performance Prediction of the Interacting Multiple Model Algorithm// IEEE Trans, on AES 29, no. 3, 1993, p. 755 - 771.
61. Ito M., Tsujimichi S., Kosuge Y. Tracking a three-dimensional Moving Target with two-dimensional Angular Measurements from Multiple Passive Sensors// SICE 1999, p. 1117-1122.
62. De Feo M., Graziano A., Miglioli R., Farina A. IMMJPDA versus MHT and Kalman Filter with NN correlation: performance comparison// IEE Proc. Radar, Sonar Navigation, Vol. 144, No. 2, April 1997, p. 49 56.
63. Lerro D., Bar-Shalom Y. Interacting Multiple Model Tracking with Target Amplitude Feature// IEEE Trans, on AES 29, no. 2, 1993, p. 494 - 509.
64. Jilkov V. P., Angelova D. S., Semerdjiev T.Z. A. Design and Comparison of Mode-Set Adaptive IMM Algorithm for Maneuvering Target Tracking// IEEE Trans, on AES 35, no. 1, 1999, p. 343 - 350.
65. He Yan, Zhi-jiang G., Jing-ping J. Design of the Adaptive Interacting Multiple Model Algorithm// Proceedings of the American Control Conference, May 2002, p. 1538-1542.
66. Buckley K., Vaddiraju A., Perry R. A New Pruning/Merging Algorithm For MHT Multitarget Tracking// IEEE International Radar Conference 2000, p. 71-75.
67. Bar-Shalom Y. Update with Out-of-Sequence Measurements in Tracking Exact Solution// IEEE Trans, on AES 38, no. 3,2002, p. 769 - 778.
68. Munir A., Atherton A. P. Maneuvering target tracking using different turn rate models in he IMM algornthm// Proceedings of the 34th Conference on Decision & Control, 1995, p. 2747 2751.
69. Bar-Shalom (Ed.) Y. Multitarget-multisensor Tracking: Advanced applications. Vol. I. Norwood, MA: Artech House, 1990.
70. Bar-Shalom (Ed.) Y. Multitarget-multisensor Tracking: Advanced applications. Vol. II. Norwood, MA: Artech House, 1992.
71. Blackman S. S. Multiple Target Tracking with Radar Applications. Norwood, MA: Artech House, 1986.
72. Campo L., Mookerjee P., Bar-Shalom Y. State Estimation for Systems with Sojourn-Time-Dependent Markov Model Switching// IEEE Trans, on AC-36, no. 2, 1991, p. 238-243.
73. Sengupta D., litis R. A. Neural Solution to the Multitarget Tracking Data Association Problem// IEEE Trans, on AES 25, no. 1, 1989, p. 96 - 108.
74. Merkulov V. I., Lepin V. N. Aviation radio control systems. 1996, p. 391.
75. Perov A. I. Adaptive algorithms for tracking maneuvering targets//Radio engineering, No. 7,2002, p. 73 81.
76. Kanashchenkov A. I., Merkulov V. I. Protection of radar systems from interference. - M .: "Radio engineering", 2003.
77. Qiang Gan, Chris J. Harris. Comparison of Two Measurement Fusion Methods for Kalman-Filter-Based Multisensor Data Fusion// IEEE Trans, on AES 37, No. 1,2001, p. 273-280.
78. Blackman S., Popoli R. Design and Analysis of Modern Tracking Systems. Artech House, 1999, 1230 p.
79. Neal S. R. Discussion on "Parametric relations for the a-^-y filter predictor"// IEEE Trans, on AC-12, June 1967, p. 315 316.
80. Repin V. G., Tartakovskii G. P. Statistical synthesis with a priori uncertainty and adaptation of information systems. M.: "Soviet radio", 1977, 432 p.
81. Stratonovich R. L. Principles of adaptive reception. M.: Sov. radio, 1973, 143 p.
82. Tikhonov V.I., Teplinskiy I.S. Quasi-optimal tracking of maneuvering objects // Radio engineering and electronics, 1989, V.34, No. 4, p. 792-797.
83. Perov A.I. Statistical theory of radio engineering systems. Tutorial. -M.: Radio engineering, 2003.
84. Darymov Yu. P., Kryzhanovsky G. A., Solodukhin V. A., Kivko V. G., Kirov B. A. Automation of air traffic control processes. Moscow: Transport, 1981,400 p.
85. Anodina T. G., Kuznetsov A. A., Markovich E. D. Automation of air traffic control. M.: Transport, 1992, 280 p.
86. Bakulev P.A., Sychev M.I., Nguyen Chong Luu. Tracking a Maneuvering Target Using an Interactive Multi-Model Algorithm // Electronic Journal, No. 9, 2002 Proceedings of the Moscow Aviation Institute.
87. Bakulev P.A., Sychev M.I., Nguyen Chong Luu. Study of the algorithm for filtering the trajectories of maneuvering radar targets// Digital signal processing and its application, Report of the 5th International Conference. M.: 2003, T. 1. - p. 201 - 203.
88. Bakulev P.A., Sychev M.I., Nguyen Chong Luu. Multi-model algorithm for tracking the trajectory of a maneuvering target according to surveillance radar data // Radio engineering, No. 1, 2004.
89. Nguyen Chong Luu. Synthesis of a multi-model algorithm for tracking the trajectory of a maneuvering target // Aerospace Instrumentation, No. 1, 2004.
90. Nguyen Chong Luu. Study of multi-model algorithms for filtering the trajectories of maneuvering radar targets// Thesis of the report, international conference and exhibition "Aviation and Cosmonautics 2003", MAI 2003.
Please note that the scientific texts presented above are posted for review and obtained through original dissertation text recognition (OCR). In this connection, they may contain errors related to the imperfection of recognition algorithms. There are no such errors in the PDF files of dissertations and abstracts that we deliver.
All-round detection radar (SRS) is designed to solve the problems of searching, detecting and tracking air targets, determining their nationality. The SRS implements various survey procedures that significantly increase noise immunity, the probability of detecting low-observable and high-speed targets, and the quality of tracking of maneuvering targets. The developer of the RLO is the Research Institute of Instrument Engineering.
The combat control post (PBU) of the air defense system as part of the grouping carries out, according to the coordinate information of the SRS, the linkage and tracking of the routes of detected targets, the opening of the air enemy strike plan, the distribution of targets between the air defense systems in the group, the issuance of target designations of the air defense system, the interaction between the air defense systems conducting combat operations, as well as interaction with other forces and means of air defense. A high degree of automation of processes allows the combat crew to focus on solving operational and operational-tactical tasks, using the advantages of man-machine systems to the fullest extent. The PBU provides combat work from higher command posts and, in cooperation with the PBU, controls of neighboring groups.
The main components of the S-ZOOPMU, S-ZOOPMU1 air defense systems:
Multifunctional radar for target illumination and missile guidance(RPN) receives and develops target designations from 83M6E controls and attached autonomous sources of information, detection, incl. in autonomous mode, capturing and auto-tracking targets, determining their nationality, capturing, tracking and guiding missiles, highlighting fired targets to ensure the operation of semi-active homing heads of guided missiles.
The on-load tap-changer also performs the functions of an ADMS command post: - according to information from PBU 83M6E, it controls the ADMS assets; - selects targets for priority firing; - solves the launch problem and determines the results of firing; - provides information interaction with the PBU of 83M6E controls.
The all-round view increases the search capabilities of air defense systems in the independent conduct of hostilities, and also ensures the detection and tracking of targets in sectors that, for some reason, are inaccessible to the SART and RPN. The 36D6 radar and the 5N66M low-altitude detector can be used as an autonomous attached tool.
Attached autonomous means of detection and target designation
Launchers Launchers (up to 12) are designed for storage, transportation, pre-launch preparation and missile launch. Launchers are placed on a self-propelled chassis or road train. Each launcher has up to 4 missiles in transport and launch containers. Provides long-term (up to 10 years) storage of missiles without any maintenance measures with the opening of containers. The developers of the launcher are the design bureau of special engineering, the design bureau of the Nizhny Novgorod Ministry of Health.
Launchers
rockets- single-stage, solid-propellant, with a vertical start, equipped with an onboard semi-active radio direction finder. The lead developer of the rocket is MKB Fakel.
83M6E controls provide: - detection of aircraft, cruise missiles in the entire range of their practical application and ballistic missiles with a launch range of up to 1000 km; - route tracking up to 100 targets; - management of up to 6 air defense systems; - maximum detection range - 300 km.
The S-ZOOPMU1 air defense system is a deep modernization of the S-ZOOPMU and is actually a transitional link to third-generation systems.
S-ZOOPMU1 provides: - hitting targets at ranges from 5 to 150 km, in the range of altitudes from 0.01 to 27 km, speed of hit targets up to 2800 m/s; - defeat of non-strategic ballistic missiles with a launch range of up to 1000 km at ranges of up to 40 km when receiving target designation from 83M6E controls; - simultaneous firing of up to 6 targets with guidance of up to 2 missiles for each target; in the basic type of missiles - 48N6E; - rate of fire 3-5 sec.
If necessary, the S-ZOOPMU1 air defense system can be modified to use the 5V55 missiles of the S-ZOOPMU system.
The ancestor of the S-ZOOP family - the S-ZOOPMU air defense system provides:-> defeat targets at ranges from 5 to 90 km, in the altitude range from 0.025 to 27 km, the speed of hit targets up to 1150 m / s; - defeat of ballistic targets with a launch range of up to 300 km at ranges of up to 35 km with target designation from controls; - simultaneous firing of up to 6 targets with guidance of up to 2 missiles for each target; - basic type of missiles 5V55; - rate of fire 3-5 sec.
ALTEC-300
Educational and training complex
|
|
|
Usage: in automated digital systems for detecting and processing radar information. The essence of the invention: in a discrete radar measurement of the coordinates of an air target, smoothing the current parameters of the target trajectory with a change in the filter gains depending on the accumulated maneuver probability. What is new is the setting of the filter gains at the moment the target enters the zone of possible maneuver, depending on the accumulated maneuver probability. An increase in tracking accuracy is achieved by compensating for the dynamic component of the tracking error due to the target maneuver. 3 ill.
The invention relates to radar and can be used in automated digital systems for detecting and processing radar information. Methods and devices for tracking a maneuvering air target are known, based on discrete radar measurements of coordinates and the current assessment (smoothing and extrapolation) of its trajectory parameters (coordinates and their rates of change). when a maneuver is detected, the memory of the recurrent smoothing filter is minimized. In this case, although the dynamic smoothing error due to the discrepancy between the hypothesis about the degree of the polynomial describing the true trajectory of the maneuvering target and the linear hypothesis of its movement is compensated, the random component of the smoothing error acquires the maximum value for the given coordinate measurement accuracy, and the total error increases. Of the known methods of tracking a maneuvering air target, the closest to the proposed one in terms of technical essence and the achieved effect is the method in which the maneuver is detected based on the analysis of the magnitude of the deviation of the current values of the parameters of the tracked trajectory from their measured values and comparison of this deviation with the threshold value, when the maneuver is detected, it is smoothed trajectory parameters with filter gains equal to unity Due to the fact that when smoothing the trajectory parameters, only the fact of the presence of a maneuver is taken into account, the smoothing errors with this method remain quite large. The aim of the invention is to improve the accuracy of tracking a low-flying maneuvering air target. This is achieved by the fact that with the method of tracking a low-flying maneuvering air target, based on discrete radar measurement of coordinates and smoothing the parameters of the target trajectory using a - filter, in sections of rectilinear movement with filter gains due to the noise of the target state, which are determined from the bearing ratios , according to the rate of change of the bearing , and the change in the filter gains in the sections of the target maneuver, at the moment of entering the trajectory section, on which, according to a priori information about the trajectory features, a maneuver is possible, the target bearing signal is smoothed with the filter gains set in accordance with the accumulated probability of maneuver followed targets: Р n = 1/(N-n+1), where N is the number of measurements in the area of possible maneuver and n is the number of the smoothing cycle in the area of possible maneuver, from the ratios for bearing (p n) + -1 (1) for the rate of change of bearing (P n) - , where a + 2 (2) r 
(3) where is the variance of bearing measurement errors; a is the maximum acceleration of the target along the bearing during the maneuver; P ohm is the probability of correct detection of the maneuver; T o the period of the radar survey, and at the moment the target maneuver is detected, the bearing signal is smoothed once with the filter gains and , from relations (1) and (2) with the value r from the relation r (4) subsequent smoothing cycles, the target trajectory parameters are smoothed with the filter gains, which are determined from the relations
where
(n) (n)
n= int 
m and m are the filter gains at the time the target maneuver is detected. Known methods of tracking a low-flying maneuvering air target do not have features similar to those that distinguish the proposed method from the prototype. The presence of a newly introduced sequence of actions makes it possible to increase the accuracy of tracking due to a priori information about the tracking trajectory of an air target and, in connection with this, to minimize the tracking errors that occur when a target maneuver is missed. Therefore, the claimed method satisfies the criteria of "Novelty" and "Inventive step". The possibility of achieving a positive effect from the proposed method with newly introduced features is due to the compensation of the influence of the dynamic bearing extrapolation error, determined by the target maneuver missed by the maneuver detector, by changing the filter gains in accordance with the accumulated maneuver probability. In FIG. 1 shows a diagram of target maneuvering; in fig. 2 graphs illustrating the effectiveness of the proposed method; in fig. 3 shows the electrical block diagram of the device for implementing the proposed method. Since any low-flying high-speed aerial target suddenly appeared and detected, for example, on a radar carrier ship, will be classified as an attacker, it is reasonable to assume that this target will turn towards the ship with a high probability, performing a homing maneuver. In other words, in order to hit a ship, a low-flying high-speed air target must perform a maneuver at a certain point in time, as a result of which the course parameter of the target relative to the ship must become equal to zero. In this regard, the assumption of a mandatory target maneuver is fundamentally justified. In the future, we will consider an anti-ship cruise missile (ASC) performing a homing maneuver as an air target. The method is based on the use of the trajectory features of the PCR in the final section of the trajectory. The trajectory of the RCC (see Fig. 1) at a distance from the object of destruction of less than 30 km includes three characteristic sections of the trajectory: a straight section before the start of the homing maneuver of the RCC; site of a possible homing maneuver; straight section of the trajectory after the completion of the homing maneuver. It is known that the homing maneuver of the RCC, for example, of the "Harpoon" type, is performed at distances from the target ship of 5, 3.20.2 km. It can be assumed that at distances greater than 20.2 km, the maneuver probability is close to zero, and the need to limit the filter gains is due only to the presence of target state noise. In the absence of a priori data on the method of firing anti-ship missiles used by the enemy in this particular tactical situation, there is reason to assume that the start of a homing maneuver is equally probable at any time when the anti-ship missile is in the interval of distances from the ship D min 5.3 km and D max 20.2 km . The missile overcomes the specified range interval in
t 1 \u003d 50 s where V 290 m / s flight speed pkr. Therefore, it can be assumed that during the time the RCC is at a distance from the ship, allowing it to start a homing maneuver, N N +1 + 1 measurements of its coordinates will be made. Since the maneuver can start with equal probability at any intersurvey interval, the probability of an event consisting in the beginning of the maneuver at the n-th (n 1, 2,) interval is a priori equal to
P
If the beginning of the maneuver is not detected on the (n-1)-th dimension of coordinates, then the accumulated probability of the maneuver on the n-th dimension is determined by the relation
P=
The dependence of the variance of the acceleration pcr on the maneuver on the accumulated probability can be expressed as follows:
2 a = (1+4P n)(1-P ohm) (5) where a is the maximum acceleration of the PKR along the bearing during the maneuver (3.5g);
P ohm is the probability of correct detection of the maneuver. Knowing the acceleration variance pcr ( a ), and also assuming that the values of the bearing measurement errors are known, it is possible to calculate the optimal values of the filter gain coefficients for the current ratios of the variance of errors in measuring the coordinates, disturbing the bearing acceleration and the survey period of the radar: by bearing
(P n) (6) by the rate of change of bearing (P n) where o 2 variance of bearing estimation errors;
dispersion of bearing measurement errors;
R is the correlation coefficient of bearing estimation errors and the rate of its change. The values of o and Rо are defined by the following relations
2o = + -1
R o = (7)
Substituting relations (2) and (3) into relation (7), we obtain the dispersion of bearing estimation errors and the correlation coefficient of bearing estimation errors and the rate of its change, and, substituting into expression (6), we obtain the filter gains determined by relation (1). Obviously, as pcr approaches with each survey, the accumulated maneuver probability increases, which causes an increase in the acceleration dispersion n cr and, accordingly, leads to an increase in the filter gains and . With the detection of a maneuver, the cumulative maneuver probability is assigned the value "one", and the acceleration variance pcr is calculated as follows:
= a 2 (1-P crowbar) (8) where P crowbar is the probability of false detection of the maneuver. In this case, r is calculated from relation (4), the filter gains acquire the maximum value. Taking into account the short duration of the PKR maneuver (1.3 s), one smoothing with increased gain factors is sufficient (this is confirmed by the simulation results). The procedure for estimating the maneuver probability is performed in the range interval from 20.2 to 5.3 km. After the maneuver is detected, the bearing filter gains are set to values determined only by the target state noise, the range gains remain constant throughout the tracking time, and their values are chosen in accordance with the target state noise. In FIG. 3 shows a device for automatic tracking of a maneuvering air target that implements the proposed method. It contains a measured coordinates sensor 1, a smoothing unit 2, an extrapolation unit 3, a first delay unit 4, a memory unit 5, a maneuver detection unit 6, a comparison unit 7, a second delay unit 8, a unit 9 for calculating filter gains. The device for automatic tracking of a maneuvering air target consists of a series-connected sensor 1 of the measured coordinates, the input of which is the input of the device, the output of the sensor 1 of the measured coordinates is connected to the 1st input of the smoothing block 2 and to the 1st input of the maneuver detection block 6, the output of the smoothing block 2 connected to the input of the extrapolation block 3, the 1st output of the extrapolation block 3 is connected to the input of the comparison block 7 and through the delay block 4 with the 4th input of the smoothing block 2 and with the 2nd input of the maneuver detection block 6, the 2nd output of the block 3 extrapolation is the output of the device, the output of the block 6 detection of the maneuver is connected to the 2nd input of the block 9 for calculating the filter gains and through the delay block 8 with the 2nd input of the memory block 5 and with the 3rd input of the block 9 for calculating the filter gains, the output of the block 7 comparison is connected to the 1st input of the memory block 5 and the 1st input of the block 9 for calculating the filter gains, the output of the memory block 5 is connected to the 2nd input of the block and 2 smoothing, the output of block 9 for calculating the filter gains is connected to the 3rd input of block 2 smoothing. The device works as follows. The video signal of the current n-th cycle of measuring the coordinates of the tracked target from the output of the receiving device is fed to the input of the tracking device and, accordingly, to the sensor 1 of the measured coordinates. The measured coordinates sensor 1 converts the video signal from analog to digital form, extracts the useful signal and measures the values of the coordinates: bearing (P n) and range (D n). The sensor 1 of the measured coordinates can be implemented according to one of the known schemes of an automatic air target detector. The values of the measured target coordinates (P n and D n) in the form of signal codes are fed to the 1st input of the smoothing block 2, which implements the coordinate processing operation as follows: when n 1, the current estimate of the target coordinates is
= M n , where M n = P n , D for n 2 the current estimate of the parameters of the target trajectory is
= M n , V= (M n-1 -M n)/T o where T about the review period of the radar; for n>2, the current estimate of the parameters of the target trajectory is
= +(M)
= +(M)/T where and are weight coefficients (filter gains);
and estimates of coordinates and their rate of change extrapolated to one survey. From block 2, the smoothed values of the coordinates and their rate of change are fed to the input of extrapolation block 3. Extrapolation block 3 generates estimates of trajectory parameters extrapolated for a given time:
= +VT e; = where T e is the specified value of extrapolation time intervals. In this device, T e T o, T e T zu. In this case, the coordinate values extrapolated for the time from the 1st output are fed through the delay block 4 to the 4th input of the smoothing block 2, where they are used to calculate the trajectory parameters in the next cycle, and to the 2nd input of the maneuver detection block 6, where they are is subtracted from the measured bearing values supplied to the 1st input of the maneuver detection unit 6 from the measured coordinates sensor 1, and the resulting difference is compared with the threshold as follows:
П n ->
Threshold values are chosen based on the required false detection probability of the maneuver. From the same output, the extrapolated coordinates are fed to the input of the comparison block 7, where the values of the extrapolated range are compared with the range of a possible maneuver from 5.3 to 20.2 km. Extrapolated for time T e coordinate values are fed to the 2nd output of the extrapolation block 3 (device output) and are used to generate and issue target designation data for consumers. In the comparison unit 7, a logical unit signal is generated if the values of the extrapolated range lie in the interval of the possible manner, which from the output of the comparison unit 7 is fed to the 1st input of the memory unit 5, while prohibiting the issuance of the filter gains to the smoothing unit 2, at the same time the same signal is fed to the 1st input of the block 9 for calculating the filter gains and initiates the issuance of the gains to the block 2 smoothing. If the values of the extrapolated range do not lie within the interval of the range of a possible maneuver, then a logical zero signal is generated, which prohibits the output of gain factors from block 9 for calculating filter gain factors and initiates the output of gain factors from memory block 5. The memory block 5 stores the filter gains, the values of which are due to the target state noise. In block 9 for calculating the filter gain coefficients, the gain coefficients are calculated in the case of the arrival of a logical unit signal and the absence of a maneuver detection signal according to relations (1), (2) and (3), and in the case of the arrival of the "maneuver detected" signal according to relations (1) , (2) and (4). In block 6, a “maneuver detected” signal is generated and fed to block 9 for calculating filter gains, the same signal is sent to delay block 8 and delayed by one review period is fed to memory blocks 5 and 9 and calculating filter gains. The effectiveness of the proposed method was evaluated by simulation with the following initial data:
The launch range of the "harpoon" anti-ship missile system is 100 km;
PKR overload on a 4 g maneuver;
The duration of the maneuver is 4 s;
Radar survey period 2s;
The maneuver begins between the 13th and 14th surveys. In FIG. Figure 2 shows the dependence of the normalized error of extrapolation of the coordinate to one survey on the measurement number where:
1 proposed method;
2 known way. When implementing the proposed method, the accuracy of the extrapolation of the coordinate is doubled.
Claim
METHOD FOR TRACKING AN AIR TARGET MANEUVERING, based on discrete radar measurement of coordinates, smoothing target trajectory parameters using a - -filter in sections of rectilinear movement with filter amplifier coefficients determined by target state noise, which are determined from the ratios: by bearing 
where j is the current smoothing cycle;
by bearing change rate
and changing the gain of the filter in the sections of the target maneuver, characterized in that at the moment of entering the section of the trajectory, on which, according to a priori information about the trajectory features of the target, a maneuver is possible, the target bearing signal is smoothed with the filter gain coefficients set in accordance with the accumulated probability of the maneuver of the tracked target ,
P n (N n + 1),
where N is the number of measurements in the area of possible maneuver;
n is the number of the smoothing cycle in the smoothing section in the area of possible maneuver from bearing relations (1)
by bearing change rate (2) 
where 2 is the dispersion of bearing measurement errors;
a maximum acceleration of the target in bearing during the manoeuvre;
P about. m is the probability of correctly detecting the maneuver;
T o radar survey period,
and at the moment of detection of the target maneuver, the bearing signal is smoothed once with the filter gains a and b from relations (1) and (2), with the value r from the relation 
where P l. about. m is the probability of false detection of the maneuver, and on subsequent smoothing cycles, the trajectory parameters are smoothed with filter gains, the values of which correspond to subsequent numbers of the current smoothing cycle, which are determined from the relation 
where i 0, 1, 2, the number of the cycle after the detection of the maneuver;
set filter memory due to target state noise;
m and m are the filter gains at the time of the target maneuver.
Two heads and six legs; four walk, and two lie still
Self-esteem - what is it: concept, structure, types and levels
Cassandra's Path, or Pasta Adventures War on Earth and Underground