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 about .
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 of starting the turn, then the fighter is guided towards this point using the “Parallel Approach” method. If the CC is at a long distance Before 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 IN 1 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 c × 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 in time 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 practically 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.
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:
P
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.
Use: in automated digital systems for detecting and processing radar information. The essence of the invention: 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 probability of the maneuver. What is new is the installation of filter gain coefficients at the moment the target enters the possible maneuver zone, depending on the accumulated probability of the maneuver. Increasing tracking accuracy is achieved by compensating for the dynamic component of the tracking error caused by the target maneuver. 3 ill.
The invention relates to radar and can be used in automated digital systems for detecting and processing radar information. There are known methods and devices for tracking a maneuvering air target, based on discrete radar measurements of coordinates and current assessment (smoothing and extrapolation) of its trajectory parameters (coordinates and rates of change) Under the assumption that during the observation period the target will make only one deliberate maneuver of high intensity, with When a maneuver is detected, the memory of the recurrent smoothing filter is minimized. In this case, although the dynamic smoothing error, caused by 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 a maximum value for a given accuracy of coordinate measurement, 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 achieved effect is the method in which the maneuver is identified based on an analysis of the magnitude of the deviation of the current values of the parameters of the tracked trajectory from their measured values and comparing this deviation with a threshold value; when the maneuver is identified, it is smoothed out trajectory parameters with filter gain coefficients equal to unity Due to the fact that when smoothing trajectory parameters only the fact of the presence of a maneuver is taken into account, smoothing errors with this method remain quite large. The purpose of the invention is to improve the accuracy of tracking a low-flying maneuvering air target. This is achieved by the fact that in the method of tracking a low-flying maneuvering air target, based on discrete radar measurement of coordinates and smoothing the parameters of the target's trajectory using a filter, in sections of straight-line movement with filter gains determined by the noise of the target state, which are determined from the bearing relations, according to the rate of change of bearing, and the change in the filter gain coefficients in the target maneuver sections, at the moment of entering the trajectory section in which, according to a priori information about the trajectory features, the maneuver is possible, the target bearing signal is smoothed with filter gain factors set in accordance with the accumulated probability of the maneuver accompanied targets: Р n = 1/(N-n+1), where N is the number of measurements in the area of a possible maneuver and n is the number of the smoothing cycle in the area of a 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 om probability of correct detection of the maneuver; T is the radar review period, and at the moment the target maneuver is detected, the bearing signal is smoothed once with filter gain coefficients and , from relations (1) and (2) with the value r from relation r (4) where R is the probability of false detection of a maneuver, and on In subsequent smoothing cycles, the parameters of the target trajectory are smoothed with filter gain coefficients, which are determined from the relations
Where
(n) (n)
n= int 
m and m are the filter gains at the moment the target maneuver is detected. Known methods for tracking a low-flying maneuvering air target do not have features similar to the features 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 trajectory of tracking an air target and, therefore, to minimize tracking errors that arise when the target maneuver is missed. Consequently, 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 probability of the maneuver. In fig. 1 shows a diagram of target maneuvering; in fig. 2 graphs illustrating the effectiveness of the proposed method; in fig. Figure 3 shows an electrical block diagram of the device for implementing the proposed method. Since any low-flying high-speed air target that suddenly appears and is detected, for example, on a radar carrier ship, will be classified as attacking, it is reasonable to assume that this target will most likely turn toward the ship, performing a homing maneuver. In other words, in order to hit a ship at a certain point in time, a low-flying high-speed air target must perform a maneuver, as a result of which the target’s heading parameter relative to the ship must become equal to zero. In this regard, the assumption of mandatory target maneuver is fundamentally justified. In the future, we will consider an anti-ship cruise missile (ASCM) performing a homing maneuver as an air target. The method is based on the use of trajectory features of the anti-ship missile system at the final section of the trajectory. The anti-ship missile trajectory (see Fig. 1) at a distance from the target of destruction less than 30 km includes three characteristic sections of the trajectory: a straight section before the start of the anti-ship missile homing maneuver; area of possible homing maneuver; straight section of the trajectory after completion of the homing maneuver. It is known that the homing maneuver of anti-ship missiles, 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 probability of maneuver 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 specific tactical situation, there is reason to assume that the start of a homing maneuver is equally likely at any time when the anti-ship missile is within the range of distances from the ship D min 5.3 km and D max 20.2 km . The missile covers the specified range interval in
t 1 = 50 s where V 290 m/s PCR flight speed. Consequently, it can be assumed that during the time the anti-ship missile is at a distance from the ship, allowing it to begin the homing maneuver, N N +1 + 1 measurements of its coordinates will be made. Since a maneuver can begin with equal probability at any inter-view interval, the probability of an event consisting of the beginning of a maneuver at the nth (n 1, 2,) interval is a priori equal to
P
If the beginning of the maneuver is not detected at the (n-1)th coordinate dimension, then the accumulated probability of the maneuver at the nth dimension is determined by the relation
P=
The dependence of the acceleration dispersion of the anti-ship missile during a 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 anti-ship missile system along the bearing during the maneuver (3.5g);
P om the probability of correct detection of the maneuver. Knowing the dispersion of the acceleration of the PCR (a), and also assuming that the values of the bearing measurement errors are known, it is possible to calculate the values of the filter gain coefficients that are optimal for the current ratios of the dispersion of coordinate measurement errors, the acceleration disturbing the bearing and the radar viewing period: by bearing
(P n) (6) by the rate of change of bearing (P n) where o 2 is the variance of bearing estimation errors;
bearing measurement error variance;
R is the correlation coefficient between bearing estimation errors and the rate of its change. The values of o and R o are determined by the following relations
2 o = + -1
R o = (7)
Substituting into relation (7) relations (2) and (3), 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). It is obvious that as the pcr approaches with each review, the accumulated probability of the maneuver increases, which causes an increase in the acceleration dispersion p cr and, accordingly, entails an increase in the filter gains and . When a maneuver is detected, the accumulated probability of the maneuver is assigned the value “one”, and the acceleration dispersion of the PCR is calculated as follows:
= a 2 (1-P scrap) (8) where P scrap is the probability of false detection of a maneuver. In this case, r is calculated from relation (4), the filter gains acquire their maximum value. Considering the short duration of the PCR maneuver (1.3 s), one smoothing with increased gain factors is sufficient (this is confirmed by the results of simulation modeling). The procedure for assessing the probability of maneuver is performed in the range from 20.2 to 5.3 km. After detecting a maneuver, the bearing filter gains are assigned values determined only by the target state noise; the range gains remain constant throughout the tracking time, and their values are selected in accordance with the target state noise. In fig. Figure 3 shows a device for automatic tracking of a maneuvering air target that implements the proposed method. It contains a measured coordinate sensor 1, a smoothing block 2, an extrapolation block 3, a first delay block 4, a memory block 5, a maneuver detection block 6, a comparison block 7, a second delay block 8, a block 9 for calculating filter gains. The device for automatic tracking of a maneuvering air target consists of a serially connected sensor 1 measured coordinates, the input of which is the input of the device, the output of the sensor 1 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 to the 4th input of the smoothing block 2 and to the 2nd input of the maneuver detection block 6, the 2nd output of block 3 extrapolation is the output of the device, the output of the maneuver detection block 6 is connected to the 2nd input of the filter gain calculation block 9 and through the delay block 8 to the 2nd input of the memory block 5 and to the 3rd input of the filter gain calculation block 9, the output of the block Comparison 7 is connected to the 1st input of memory block 5 and the 1st input of block 9 for calculating filter gains, the output of memory block 5 is connected to the 2nd input of smoothing block 2, the output of block 9 for calculating filter gains is connected to the 3rd input block 2 smoothing. The device works as follows. The video signal of the current nth cycle of measuring the coordinates of the tracked target from the output of the receiving device is supplied to the input of the tracking device and, accordingly, to sensor 1 of the measured coordinates. The measured coordinate sensor 1 converts the video signal from analog to digital form, selects the useful signal and measures the coordinate values: bearing (П n) and range (D n). Sensor 1 of 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 supplied 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 = П n, D for n 2, the current estimate of the target trajectory parameters is equal to
= M n , V= (M n-1 -M n)/T o where T is the radar review period; for n>2, the current estimate of the target trajectory parameters is equal to
= +(M)
= +(M)/T where and are weighting coefficients (filter gains);
and estimates of coordinates and the rate of their change extrapolated to one survey. From block 2, the smoothed values of the coordinates and the rate of their change are supplied to the input of extrapolation block 3. Extrapolation block 3 generates estimates of trajectory parameters extrapolated to 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 tsu. In this case, the time-extrapolated coordinate values from the 1st output are supplied 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 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:
P n ->
Threshold values are selected based on the required probability of false detection of a maneuver. From the same output, the extrapolated coordinates are sent to the input of 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. The coordinate values extrapolated to time T e are supplied to the 2nd output of the extrapolation block 3 (device output) and are used to generate and issue target designation data to consumers. In the comparison block 7, a logical one signal is generated if the value of the extrapolated range lies in the range of possible values, which from the output of the comparison block 7 is supplied to the 1st input of the memory block 5, while prohibiting the issuance of filter gains to the smoothing block 2, at the same time the same signal arrives at the 1st input of block 9 for calculating filter gains and initiates the output of gains to block 2 for smoothing. If the values of the extrapolated range do not lie within the range interval of a possible maneuver, then a logical zero signal is generated, prohibiting the issuance of gain factors from block 9 for calculating filter gains and initiating the issuance of gain factors from memory block 5. Memory block 5 stores filter gains, the values of which are determined by the noise of the target state. In block 9 for calculating the filter gains, the gains are calculated in the case of the arrival of a logical one signal and the absence of a maneuver detection signal according to relations (1), (2) and (3), and in the case of the arrival of a “maneuver detected” signal according to relations (1) , (2) and (4). In block 6, a “maneuver detected” signal is generated and sent to block 9 for calculating filter gains, the same signal is sent to delay block 8 and, delayed by one review period, is sent to memory blocks 5 and 9 and calculating filter gains. The effectiveness of the proposed method was assessed using simulation modeling with the following initial data:
The launch range of the harpoon-type anti-ship missile system is 100 km;
RCC overload during maneuver 4 g;
Maneuver duration 4 s;
Radar review period 2s;
The maneuver begins between 13 and 14 reviews. In fig. Figure 2 shows the dependence of the normalized coordinate extrapolation error per survey on the measurement number where:
1 proposed method;
2 known method. When implementing the proposed method, the accuracy of coordinate extrapolation doubles.
Claim
METHOD OF TRACKING A MANEUVERING AIR TARGET, based on discrete radar measurement of coordinates, smoothing the parameters of the target trajectory using a - - filter in sections of straight-line movement with filter amplifier coefficients determined by the noise of the target state, which are determined from the relations: by bearing 
where j is the current smoothing cycle;
by speed of bearing change
and changing the filter gain coefficient in the target maneuver sections, characterized in that at the moment of entering the trajectory section, in which a maneuver is possible based on a priori information about the target trajectory features, the target bearing signal is smoothed with filter gain coefficients set in accordance with the accumulated probability of maneuver of the tracked target ,
Pn(Nn+1),
where N is the number of measurements in the area of possible maneuver;
n number of the smoothing cycle in the smoothing section in the section of possible maneuver from the bearing relations (1)
by speed of bearing change (2) 
where 2 is the variance of bearing measurement errors;
a the maximum acceleration of the target according to the bearing during the maneuver;
P o. m probability of correct detection of the maneuver;
T about radar review 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. O. m probability of false detection of a maneuver, and in subsequent smoothing cycles the trajectory parameters are smoothed with filter gain coefficients, the values of which correspond to subsequent numbers of the current smoothing cycle, which are determined from the relation 
where i 0, 1, 2, cycle number after detecting the maneuver;
installed filter memory due to target state noise;
m and m of the filter gain at the moment of target maneuver.
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 process automation 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 cooperation 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 maintenance measures and opening the 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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Introduction.
Chapter 1. Analysis of air target trajectories tracking filters.
§1.1. Kalman filter.
§1.2. Application of the Kalman filter to track TC trajectories using surveillance radar data.
§ 1.3. "Alpha - beta" and "Alpha - beta - gamma" filters.
§ 1.4. Statistical modeling.
§1.5. Conclusions.
Chapter 2. Analysis of adaptive methods for tracking the trajectories of maneuvering air targets based on maneuver detectors.
§ 2.1. Introduction.
§ 2.2. Collaborative target maneuver detection and estimation based on updating process.
§ 2.3. Adaptive algorithms for tracking maneuvering vehicles
CC using maneuver detectors.
§ 2.4. Conclusions.
Chapter 3. Study of well-known multi-model algorithms.
§3.1. Introduction.
§3.2. Adaptive Bayes approach.
§3.3. Study of the well-known MMA trajectory tracking of the CC for surveillance radar.
§3.4. Conclusions.
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 computer.
§4.2.1. Formulation of the problem.
54.2.2. General approach to solving the problem.
04.2.3. Linear algorithm.
§4.3. Comparison of MMA with other algorithms.
§4.4. Conclusions.
Recommended list of dissertations
Secondary information processing 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 assessing the dynamic situation in multi-sensor systems during automatic tracking of surface objects 2001, Doctor of Technical Sciences Beskyd, Pavel Pavlovich
Development of methods for monitoring the location of state aviation aircraft during air traffic control in the off-piste sector of airspace 2009, candidate of technical sciences Shanin, Alexey Vyacheslavovich
Development and research of a method for targeting a maneuvering object based on a stochastic forecast of its movement 2004, Candidate of Technical Sciences Truong Dang Khoa
Introduction of the dissertation (part of the abstract) on the topic “Research of algorithms for tracking trajectories of air targets”
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 approach control. When controlling the movement of a computer, it is necessary to calculate the current coordinates of each computer to avoid dangerous approaches of the computer. Otherwise, the pilots are given commands to correct trajectories. In the collision avoidance mode, an estimate of extrapolated coordinates is generated, on the basis of which dangerous proximity zones are determined. Moreover, air traffic density has also increased in recent years. An increase in air traffic density leads to an increase in the number of dangerous encounters. Preventing dangerous approaches between aircraft centers is part of the most important task of civil aviation - ensuring flight safety. When controlling the movement of the aircraft during the landing approach, the radar checks the correct movement of the aircraft along the specified trajectories.
Therefore, 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 (SRIP) is usually performed by programmed digital processing algorithms on a digital 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 maneuvering of the aircraft during the take-off and landing stages is taken into account, associated with changing flight levels, changing course and performing standard approach procedures, etc.
Let's consider the location of the airspace elements of the ATC area and a typical landing approach. In civil aviation, the airspace is divided into an airway - an established airspace above the surface of the earth in the form of a corridor with a width of (10 - 20) km, along which regular flights are carried out, an airfield area - the airspace above the airfield and the surrounding area and a restricted area - airspace in which aviation flights of all departments are prohibited.
In the area of the airfield, air corridors, take-off and landing zones and waiting areas are organized. An air corridor is a part of the airspace in which aircraft descend and gain altitude. Take-off and landing zone is the airspace from the airfield level to the altitude of the second safe flight level. The dimensions of this zone are determined by the flight performance characteristics of the computers operated at a given aerodrome, the capabilities of radio-technical aids for air traffic control navigation and landing, approach schemes and specific features of the aerodrome area. As a rule, the boundaries of the takeoff and landing zone are 25.30 km away from the airfield. If for some reason the pilot does not land the aircraft on the first approach, then the aircraft goes into the second circle, i.e. it moves along a special route in the circle area (see Fig. B.1). If the CC is not allowed to move along the approach route due to the temporary occupancy or unavailability of the runway (runway), then the CC is sent to a holding area intended to await clearance for the approach to the airfield. These zones are located above the airfield or 50 - 100 km from it (Fig. B.1). Thus, in the area of the airfield, the frequency of maneuvering of the computer is high. This is explained by the fact that there is a high density of computers in this area, and in order to maintain given routes and distances, they are always maneuvering from one zone to another.
1 - routes; 2 - corridors of the airfield area; 3 - circle area; 4-takeoff and landing zone;
5 - waiting areas.
In addition, to improve the safety of the aircraft and passengers during landing, the “box” approach scheme is currently widely used, in which the aircraft must plan (1-2) circles over the airfield before landing (Fig. B.2). This pattern consists of some straight sections and four 90 degree turns.
Rice. AT 2. "Box" approach scheme.
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 increase the accuracy of estimating the coordinates and speed of the computer.
Thus, the study of algorithms for tracking TC trajectories that improve the quality of radar information is an urgent problem.
When processing radar information, a particularly urgent task is to study processing algorithms in areas of the CC maneuver, which lead to a discrepancy between the real movement of the CC and the motion model used in the algorithm. As a result, the accuracy of the estimation results deteriorates and the obtained radar information becomes unreliable. Known approaches to increasing the accuracy of tracking the trajectory of a computer in maneuver sections are mainly based on solving the problem of detecting the beginning and end of a maneuver and correspondingly changing the parameters of the tracking filter. These approaches lead to a scheme of "alpha - beta" and "alpha - beta - gamma" filters, or a Kalman filter (KF) in combination with a maneuver detector.
It is known that in detection and estimation theory, an adaptive Bayesian approach can also be used to solve a priori uncertainty. When filtering in the state space, this approach consists in taking into account all possible variants of state models, and with each variant its posterior probability is calculated. Its application to solving the problem of tracking the trajectories of maneuvering computers has been developed in recent years. In this case, the trajectory of the TC is described simultaneously by several models and it is assumed that the transition process 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 possible model hypotheses, and the resulting algorithm is called a “multi-model algorithm” (MMA).
The dissertation analyzes the above mentioned approaches, shows their advantages and disadvantages, and develops a new MMA. In contrast to the well-known MMA, the proposed algorithm is created on the basis of a Gaussian approximation for the posterior probability density of the VC state vector; according to this, the resulting algorithm has advantages over known adaptive algorithms. The result of statistical modeling showed that the algorithm under study makes it possible to increase the accuracy of estimating the location of the computer compared to the adaptive FC and the known MMA when tracking the trajectory of a maneuvering computer. The results of the study showed that the cost of calculating the first simplified FC is reduced compared to the second simplified and extended FC, while at the same time its accuracy of estimating both coordinates and speed of the computer increases by (30-50)% compared to “alpha - beta” and “ alpha - beta - gamma filters. Therefore, the use of the first simplified FC to accompany the trajectory of non-maneuvering CCs is more preferable.
Purpose and objectives of the work
The purpose of the dissertation work is to study and analyze algorithms for tracking TC trajectories, develop a new MMA and compare the resulting MMA with known adaptive algorithms. In accordance with the stated goal, the following tasks were solved in the dissertation work:
Study of the general theory of estimation in state space, and its application to filtering the trajectories of the movement of a computer.
Analysis of “alpha - beta” and “alpha - beta - gamma” filters and a method for selecting their gain factors in the maneuver and non-maneuver sections.
Study of adaptive FCs for tracking the trajectories of maneuvering computers with a detector of the moment of the start of the maneuver.
Optimal estimation in state space with an extended state vector, which includes, in addition to the vector of state parameters, an unknown parameter that determines all possible variants of the state model.
Study of known MMA and development of a new MMA for tracking maneuvering computers based on the description of the trajectory of the computer simultaneously by several models, which are states of a simply connected Markov chain.
Research methods
Theoretical research and creation of algorithms for tracking VC trajectories were carried out on the basis of the theory of filtering conditional Markov processes in discrete time. The resulting algorithms are analyzed based on statistical modeling. The scientific novelty of the work lies in the following: MMA has been developed to describe the trajectory of the VC simultaneously using several models for a simply connected Markov chain.
The reliability of the obtained work results is confirmed by the results of statistical modeling.
Practical significance of the work results
An algorithm for tracking the trajectory of a maneuvering computer has been developed and studied, improving the accuracy of tracking in the maneuver sections.
Approbation of work results and publications
The main scientific results of the work were published in articles in the journals “Radio Engineering”, “Electronic Journal Proceedings of the MAI” and “Aerospace Instrumentation”, and were presented at the 5th international conference “Digital Processing and Its Application” (Moscow, 2003), at an international conference and exhibition “Aviation and Cosmonautics 2003” (MAI 2003). Scope and structure of work
The dissertation 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 computers in the air traffic control problem are reviewed and analyzed. The second chapter analyzes well-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 air traffic control systems. In the fourth chapter, a general approach to the construction of multi-model algorithms for the air traffic control problem is proposed when describing possible models of the movement of an air traffic center by a simply connected Markov chain.
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§4.4. conclusions
In this chapter, a general approach to constructing multi-model algorithms was proposed to describe possible models of the motion of a computer center 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 vector of parameters includes not only the parameters of the target’s movement, but also an unknown parameter that determines the possible models of the target’s movement. As a result, the resulting algorithm is suboptimal, which is determined by the Gaussian approximation for the posterior probability density.
In relation to tracking the trajectory of maneuvering computers, the resulting algorithm was simulated for the case of M=2. The results showed that in sections of the maneuver trajectory, the two-dimensional algorithm under study increases the accuracy of location estimation by (30 - 60)% compared to known algorithms. However, increasing the quality of filtering is achieved by increasing computational costs.
CONCLUSION
In the dissertation work, algorithms for tracking TC trajectories based on surveillance radar data were studied. The results obtained allow us to evaluate the advantages and disadvantages of each maintenance algorithm. In the dissertation, algorithms were studied and developed to avoid dangerous approaches and increase the accuracy of estimating both the coordinates and speed of the computer. It is known that secondary processing of radar information (SRIP) is usually performed using a digital computer or digital equipment. In recent years, there has been a rapid development of computer technology, microprocessors, the elemental base of digital technology, especially VLSI, FPGA, and hardware and system description languages, such as URUL, ASHEL, etc. There has been a tendency to introduce VLSI to create open systems based on international standards , including VORI systems. This makes it possible to study more complex algorithms for tracking trajectories of computers in real time. In the presented work, different algorithms for tracking non-maneuvering and maneuvering computers based on statistical modeling are studied. The following results were obtained in the dissertation:
1. “Alpha - beta” and “alpha - beta - gamma” filters have been studied, and a variant of choosing their gain factors when accompanying the CC trajectory has been proposed. “Alpha - beta” and “alpha - beta - gamma” filters make it possible to reduce computational costs and simplify the procedure for tracking TC trajectories, however, they simultaneously degrade the quality of tracking by (30 - 40)% depending on the range, speed and number of observations compared with conventional filters.
2. The problem of nonlinear filtering has been 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, which converts measurement coordinates from a polar system to a Cartesian system, and an extended Kalman filter, which linearly approximates the measurement equation by canceling high-order terms of the Taylor series, are proposed. The analysis showed that the second simplified and extended Kalman filters give the same result in terms of estimation accuracy of both position and speed, but in terms of computational costs, the second simplified Kalman filter is more economical.
3. Adaptive algorithms are proposed based on joint detection and evaluation of the CC maneuver. The maneuver detection problem belongs to the class of problems of detecting useful signals against a background of white Gaussian noise. In this case, the detected useful signal is the mathematical expectation of the updating process, which differs from zero in the presence of a maneuver. When solving the problem of detecting a maneuver, we used the likelihood ratio method, and to estimate its intensity, we will consider acceleration to be a non-random process; as a result, to synthesize an estimator, it is necessary to use the maximum likelihood criterion. To accompany a maneuvering computer, after detecting a maneuver, either the parameters or 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 VC movement. 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 coordinates of the VC is formed as a weighted sum of estimates relative to all models based on posterior probabilities. This allows the tracking algorithm to react to the maneuver immediately after it begins. To create adaptive multi-model algorithms, the unknown parameter that determines one of the M possible models of the movement of the computer at each moment of time is described by a simply connected Markov chain. As a result, the resulting algorithm is created from a set of M2 parallel Kalman filters. The simulation results for the case M = 2 showed that in sections of the maneuver trajectory, the two-dimensional algorithm under study increases the accuracy of estimating the location of the TC by (30 - 60)% compared to known algorithms. However, increasing the quality of filtering is achieved by increasing computational costs.
5. The developed experimental programs 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.
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