EntranceA method of tracking a maneuvering air target. Method of tracking a maneuvering air target Recommended list of dissertations
As a result of the initial processing of radar information, two streams of target marks are received at the input of the auto-tracking algorithm:
“true targets”, grouped near the actual position of the targets;
“false targets,” one part of which is tied to areas of interference and reflections from local objects, and the other is evenly distributed throughout the station’s viewing area.
If it is decided that a certain set of marks, each received in its own radar survey, belongs to the same trajectory, then the next task is to estimate the parameters of this trajectory, which consists of calculating the parameters discussed in paragraph 2.2 X 0 ,U 0 ,N 0 ,V x ,V y ,V H ,a x ,a y And a H. If there are two target marks as initial coordinates X 0 ,U 0 And N 0 the coordinates of the last mark and the velocity components are accepted V x , V y And V H are calculated in the same way as for automatic trajectory capture.
When distinguishing a larger number of marks, it is possible to switch to a more complex model of target movement and smooth out the trajectory parameters. Smoothing is performed in order to reduce the influence of errors in measuring the radar target coordinates on the tracking accuracy. Most often in ACS there is a linear model of target movement and sequential smoothing of trajectory parameters.
The essence of the sequential smoothing method is that the smoothed values of the trajectory parameters in the next k th o6zor are determined from the smoothed values obtained in ( k-1) 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 the new observation are used in the next calculation cycle. At the same time, the requirements for storage capacity and hardware speed are significantly reduced.
The final expressions for smoothing the position and velocity in the k-th radar survey are as follows:
And in these formulas it is clear that the smoothed coordinate value is equal to the sum extrapolated at the moment k- observations of smoothed coordinates U* FE and taken with 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 coefficient k speed increment that is proportional to the deviation.
U=U K- U CE.
N
Rice. 2.5. Smoothing target trajectory parameters.
The dotted line in Fig. 2.5 means the smoothed trajectory of the target, calculated in the ACS computer in k-th review. Due to the fact that the coefficients of smoothed coordinates k and k lie within 0...1, the smoothed initial coordinate is in the interval U* CE... U K, and the smoothed speed is V * U K-1… V * U K.
It has been proven that with rectilinear uniform motion of the target, tracking errors will be minimal if the coefficients k and k are calculated using the formulas:
(2.9)
Figure 2.6 shows the dependence k and k from review number k. The graphs in the figure show that the coefficients asymptotically approach zero. In the limit at kThis ensures 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.
The effect of smoothing on the accuracy of target tracking can be qualitatively assessed using Fig. 2.7. In the section of straight-line motion, the error of the smoothed target coordinates is less than the unsmoothed ones: the dotted line segments are located closer to the true target trajectory than the solid line segments. In the maneuver area, due to the discrepancy between the true nature of the target’s movement and the hypothetical one, dynamic tracking errors arise. Now segments of solid lines more accurately determine the actual position of the target compared to segments of dotted lines.
In the air defense automated control system, when accompanying 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 throughout the entire maintenance period. In the latter case, optimal sequential smoothing turns into so-called exponential smoothing. Detection of target maneuver can be done visually by the operator or automatically. In both cases, the target is considered to be maneuvering if the measured target coordinate differs from the extrapolated one by an amount exceeding the permissible coordinate measurement errors.
Z
Rice. 2.6. Dependence of smoothing coefficients on K.
Rice. 2.7. The influence of smoothing trajectory parameters on the accuracy of target tracking
Typically, the calculation of current (extrapolated at a given time) target coordinates is timed to coincide with the moments of information output to indicators, communication channels, memory zones of other algorithms, etc. The predicted values of target coordinates are calculated using 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 solving the problem of correlating newly appearing marks with existing trajectories. This problem is solved by the method of 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 strobes are most often used. Their parameters are shown in Fig. 2.8.
Let X Uh, U E - extrapolated target coordinates at some point in time t. To find out which of the marks received in the next review relates to a given trajectory, you need to check the conditions:
n
Rice. 2.8. Gate 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 pp, (2.12)
Where X page, Y str - dimensions of the rectangular strobe;
R pp - size of the circular strobe.
As a result of enumerating all possible “trajectory-mark” pairs, in each review it is established which marks continue the existing ones and which initiate new routes.
From the description of algorithms for tracking target trajectories, it is clear that processing information about the air situation is a very labor-intensive process that requires a lot of RAM and the speed of the ACS computer.
A maneuver of a tracked target, which exceeds in duration the period of updating information at the input of the VDU, manifests itself in the appearance of a systematic component in dynamic filtering errors.
Let us consider, as an example, the process of constructing a target trajectory that reaches a point B(Fig. 12.15) moved evenly and rectilinearly, and then began a maneuver with large (1), medium (2) or small (3) overload (dashed-dotted lines). Based on the assessment of the parameters of the straight section of the trajectory based on the results of filtering n measurements (marked with a circle in the figure), the current coordinates of the target (dashed line) and extrapolated coordinates to ( n+1)th review (triangle).
| A |
| B |
As can be seen from the figure, after the start of the maneuver, the current coordinates of the target, issued to consumers, will contain a dynamic error, the magnitude of which is greater, the greater the overload of the target during the maneuver and the period of viewing the space.
To automatically track a target under these conditions, it is necessary, firstly, to detect (identify) a maneuver and, secondly, by abandoning the hypothesis of rectilinear and uniform target movement, determine the parameters of the maneuver and, on this basis, use a new hypothesis of target movement.
There are a number of known methods for detecting a maneuver based on the results of discrete measurements of target coordinates:
1. The basis for stopping filtering according to the straight-line hypothesis uniform motion the residual modulus may exceed a certain constant value. In this case necessary condition continue filtering after receiving n th mark can be presented in the following form:
; 
(1)
where: Δ P, Δ D- constants that determine the permissible value of the discrepancy and depend on the radar review period and the accepted value of target overload during the maneuver;
P n, D n- bearing and range values measured in the nth survey;
, - bearing and range values extrapolated at the time of the nth measurement.
2. With higher requirements for the quality of maneuver detection in the horizontal plane in conditions of tracking trajectories in a rectangular coordinate system, the permissible value of the discrepancy is determined at each review and the problem is solved as follows:
a) based on the results of each coordinate measurement, the residual modules of the extrapolated and measured coordinate values are calculated
; 
;
b) the variance of discrete measurement errors is calculated
where σ D, σ P- root mean square errors of discrete measurement of range and bearing;
c) the variance of extrapolation errors is calculated
,
d) the variance of the total error of coordinate measurement and extrapolation is calculated
| (5) |
e) values are compared d And 
, where is the coefficient selected for reasons of ensuring an acceptable probability of false detection of a maneuver.
If upon comparison it turns out that d> 
, then the decision “waiting for maneuver” is made. If the inequality is satisfied a second time, then the “maneuver” decision is made and the filtering of the trajectory parameters according to the hypothesis used is stopped.
3. Another approach to choosing a maneuver detection criterion is also used. In each survey, the autocorrelation function of the residuals is calculated polar coordinates in previous and current reviews
,
If there is no maneuver, then Δ D n and Δ P n independent from review to review and the autocorrelation functions of the residuals are small or even zero. The presence of maneuver significantly increases mathematical expectation products of residuals. The decision to start a maneuver is made when the autocorrelation functions exceed a certain threshold level.
SECOND STUDY QUESTION: Target tracking during maneuver.
In the simplest case, when the start of a maneuver is detected after the (n+1)-th irradiation of the target at two points - the estimated coordinates in the n-th survey (open circle) and the measured coordinates in ( n The +1)th survey (solid circle) calculates the target's velocity vector, which can be used to calculate the current coordinates and extrapolated coordinates on ( n+2)th review. Subsequently, the target coordinates measured in the current and previous surveys are used to construct the target trajectory and calculate extrapolated coordinates. A filter operating using this algorithm is called a two-point extrapolator.
When using such an extrapolator, the deviation of the extrapolated coordinates from the true position of the target ( L 1, L 2, L 3) with a long viewing period and large target overloads during a maneuver can be quite significant; in this case, the current coordinates of the target will be given to consumers with large errors. Large extrapolation errors can lead to the fact that the next target mark will be outside the boundaries of the auto-tracking strobe. Since there are usually false marks within the strobe, one of them will be selected and used to continue the trajectory in the wrong direction, and auto tracking true goal will be torn down.
During a prolonged maneuver with constant overload, the accuracy of target tracking can be increased by determining the rectangular components of the target's acceleration from the first three marks obtained on the curved section of the trajectory, and further filtering the acceleration. This problem is solved using "α-β-γ"- filter, the recurrent algorithm of which for estimating coordinates and the rate of their change remains the same as in "α-β"- filter, and the estimation of target acceleration, for example, by coordinate X upon receipt of the mark in n-th review is calculated by the formula
The all-round detection radar (SAR) is designed to solve the problems of searching, detecting and tracking air targets, and determining their nationality. The radar system implements various review procedures that significantly increase noise immunity, the likelihood of detecting low-profile and high-speed targets, and the quality of tracking maneuvering targets. The developer of the radar is the Research Institute of Instrument Engineering.
The combat control point (CCP) of an air defense system as part of a grouping carries out, using SAR coordinate information, the initiation and tracking of routes of detected targets, the discovery of enemy air strike plans, the distribution of targets between air defense systems in the group, the issuance of target designations for air defense systems, the interaction between air defense systems conducting combat operations, as well as interaction with other air defense forces and means. A high degree of automation of processes allows combat crews to focus on solving operational and operational-tactical tasks, making full use of the advantages of human-machine systems. The PBU ensures combat operations from higher command posts and, in interaction with the PBU, control facilities of neighboring groups.
The main components of the S-ZOPMU, S-ZOPMU1 air defense systems:
Multifunctional target illumination and missile guidance radar(RPN) receives and processes target designations from 83M6E controls and attached autonomous information sources, detection, incl. in autonomous mode, capture and automatic tracking of targets, determination of their nationality, capture, tracking and guidance of missiles, illumination of targets being fired to ensure the operation of semi-active homing heads of guided missiles.
The on-load tap-changer also performs the functions of an air defense missile system command post: - according to information from PBU 83M6E, it controls air defense systems; - selects targets for priority firing; - solves the launch problem and determines the results of firing; - provides information interaction with the control unit of the 83M6E controls.
all-round visibility increases the search capabilities of air defense systems during independent combat operations, and also ensures detection and tracking of targets in sectors that are for some reason inaccessible to radar and on-load tap-changers. The 36D6 radar and the 5N66M low-altitude detector can be used as an autonomous attached means.
Attached autonomous means of detection and target designation
Launchers Launchers (up to 12) are designed for storage, transportation, pre-launch preparation and launch of missiles. The launchers are placed on a self-propelled chassis or road train. Each launcher carries up to 4 missiles in transport and launch containers. Long-term (up to 10 years) storage of missiles is provided without any measures maintenance with opening of containers. The developers of the PU are the Special Engineering Design Bureau, the Design Bureau of the Nizhny Novgorod Ministry of Health.
Launchers
Rockets- single-stage, solid fuel, with vertical launch, equipped with an on-board semi-active radio direction finder. The lead developer of the rocket is the Fakel design bureau.
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 of up to 100 targets; - control of up to 6 air defense systems; - maximum detection range - 300 km.
The S-ZOPMU1 air defense system is a deep modernization of the S-ZOPMU and, in fact, a transitional link to third-generation systems.
S-ZOPMU1 provides: - hitting targets at ranges from 5 to 150 km, in the altitude range from 0.01 to 27 km, speed of targets hit up to 2800 m/sec; - 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 at each target; in the basic type of missiles - 48N6E; - rate of fire 3-5 sec.
If necessary, the S-ZOPMU1 air defense system can be modified to use 5V55 missiles of the S-ZOPMU system.
The founder of the S-ZOOP family, the S-ZOPMU air defense system, provides:-> hitting targets at ranges from 5 to 90 km, in the altitude range from 0.025 to 27 km, speed of targets hit up to 1150 m/sec; - destruction of ballistic targets with a launch range of up to 300 km at ranges of up to 35 km with target designation from control equipment; - simultaneous firing of up to 6 targets with guidance of up to 2 missiles at each target; - basic type of missiles 5V55; - rate of fire 3-5 sec.
ALTEK-300
Educational and training complex
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Maneuvering a target in the horizontal plane comes down to changing course and flight speed. The influence of an air target maneuver in the first and second stages of fighter guidance using the “Maneuver” method manifests itself in different ways.
Let us assume that guidance is carried out at the first stage, when the air target and the fighter were respectively at points IN And A (Fig. 7.9.), and their meeting was possible at the point S o .
Rice. 7.9. Effect of target maneuver in the horizontal plane
on the flight path of a fighter
If the air target is at the point IN maneuvered course and time t turned to the corner w t , then for the fighter to follow tangent to the turn arc of the second stage of guidance, its course must change by an angle at the same time w and t . After the air target completes the maneuver, a meeting with it will become possible at the point WITH , and the length of the air target’s path to the point will change to DSc.
If we imagine that the starting point of the turn is moving together with the TC, located relative to it at the same interval and distance as the fighter at the moment the turn begins, then the fighter is guided towards this point using the “Parallel Approach” method. If the CC is at a long distance To from a fighter, compared with which the interval I and preemptive turning distance Dupr can be neglected, then in general the properties of the “Maneuver” method are close to the properties of the “Parallel Approach” method.
To a later fighter encounter with a target (DSc > 0) leads her to turn away from the fighter (DΘ and > 0) , and turning towards the fighter leads to an earlier meeting. Therefore, a measure to counteract the target’s course maneuver, as with guidance using the “Parallel Approach” method, can be the simultaneous targeting of groups of fighters at it from different directions.
As the distance to the TC decreases, the difference between the properties of the “Maneuver” method and the properties of the “Parallel Approach” method becomes more and more apparent. During the time of turning the VT, the fighter needs to turn at ever larger angles, that is, its angular velocity w increases.
Change in value w and when a fighter is flying on a collision course with an air target (UR = 180°) characterizes the graph of the relationship between 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 differs slightly from the angular velocity of the maneuvering target. With a decrease in range, to about three Super , the value of wi grows intensively, and when the fighter approaches the starting point of the turn (D/Dupr = 1)w and increases to infinity.
Thus, when aiming using the “Maneuver” method at a maneuvering CC, it is almost impossible to bring the fighter to the point at which the turn begins with the calculated radius.
Rice. 7.10. Dependence of the ratio of angular velocities w and / w c when maneuvering the target
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 B1 can turn on the fighter, resulting in a point A1 it must be turned away from its previous course and the direction of the previously planned 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 segments between them. All this complicates the execution of a flight to an air battle.
We will consider the influence of an air target maneuver at the second stage of fighter guidance using the “Maneuver” method using Figure 7.11:
Rice. 7.11. Effect of maneuver of an air target in the horizontal plane
at the second stage of guidance using the “Maneuver” method onto the fighter’s flight path
Let us assume that at some moment of the second stage of guidance the fighter and the air target are respectively at the points A And IN and to meet the target at the point Co fighter makes a turn with a radius Ro and angular velocity w and = Vi/ Ro .
If for some period of time Dt the air target will change its flight direction by an angle w × Dt , then meeting with her will become possible at the point WITH . To reach this point from a point A the fighter would need to make a turn with a different radius R . But in advance Dt he would have to additionally turn the corner w and D × Dt .
Thus, the maneuver of an air target at the second stage of guidance leads to the emergence of an additional angular speed of 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 the fighter into 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 the fighter using the “Pursuit” method.