RU2048684C1 - Method for tracking maneuvering aerial target - Google Patents

Abstract

FIELD: computer-aided digital systems for detecting and processing radar information. SUBSTANCE: method involves digital radar measurement of aerial target coordinate rates, smoothing down of current parameters of target path accompanied by variation of filter gain depending on stored maneuver probability. Novelty is setting of filter gain at the moment of target entrance into probable maneuver region depending on stored maneuver probability. EFFECT: improved tracking accuracy due to compensation for dynamic component of tracking error caused by target maneuver. 3 dwg

Description

 The invention relates to radar and can be used in automated digital systems for the detection and processing of radar information.

 Known methods and devices for tracking a maneuvering air target based on discrete radar measurements of coordinates and current estimation (smoothing and extrapolation) of its trajectory parameters (coordinates and rates of change) [1] [2] Under the assumption that during the observation time only one deliberate maneuver of high intensity; when a maneuver is detected, the memory of the recurrent smoothing filter is minimized. In this case, although the dynamic error of smoothing due to the inconsistency of the hypothesis about the degree of the polynomial that describes 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 technical essence and the achieved effect is a method in which a maneuver is detected based on the analysis of the deviation of the current values of the parameters of the trajectory from their measured values and comparing this deviation with a threshold value, smoothing the maneuver trajectory parameters with filter gains equal to unity [2]
Due to the fact that when smoothing the parameters of the trajectory, only the fact of the presence of a maneuver is taken into account, the errors of smoothing with this method are kept quite large.

 The aim of the invention is to improve the accuracy of tracking low-flying maneuvering air targets.

, по скорости изменения пеленга β

, и изменении коэффициентов усиления фильтра на участках маневра цели, в момент вхождения на участок траектории, на котором по априорной информации о траекторных особенностях возможен маневр, сглаживают сигнал пеленга цели с коэффициентами усиления фильтра, установленными в соответствии с накопленной вероятностью маневра сопровождаемой цели: Р_n= 1/(N-n+1), где N количество измерений на участке возможного маневра и n номер цикла сглаживания на участке возможного маневра, из соотношений по пеленгу
α(p_n)

+

-1

(1) по скорости изменения пеленга β(P_n)

-

, где
a

+ 2

(2)
r

(3) где

дисперсия ошибок измерения пеленга;
a

- максимальное ускорение цели по пеленгу на маневре;
Р_ом вероятность правильного обнаружения маневра;
Т_о период обзора РЛС, а в момент обнаружения маневра цели сигнал пеленга однократно сглаживают с коэффициентами усиления фильтра α и β, из соотношения (1) и (2) со значением r из соотношения
r

(4) где Р_лом вероятность ложного обнаружения маневра, а на последующих циклах сглаживания параметры траектории цели сглаживают с коэффициентами усиления фильтра, которые определяют из соотношений
α

β

где
α(n

)

β(n

)

n

= int

где i 0, 1, 2, номер цикла после обнаружения маневра;
α_m и β_m коэффициенты усиления фильтра в момент обнаружения маневра цели.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’s trajectory using an α-β filter, in sections of rectilinear motion with filter gains due to the noise of the target’s state, which are determined from the relations bearing α

, by the rate of change of bearing β

, and changing the filter gains in the areas of the target’s maneuver, at the moment of entering the section of the trajectory where maneuver is possible according to a priori information about the trajectory features, smooth the target bearing signal with filter gains established in accordance with the accumulated probability of the target’s maneuver: P _n = 1 / (N-n + 1), where N is the number of measurements in the area of the possible maneuver and n is the number of the smoothing cycle in the area of the possible maneuver, from bearing ratios
α (p _n )

+

-1

(1) the rate of change of bearing β (P _n )

-

where
a

+ 2

(2)
r

(3) where

variance of bearing measurement errors;
a

- maximum acceleration of the target in the bearing on the maneuver;
R _{om the} probability of the correct detection of the maneuver;
T _about the radar survey period, and at the moment of detecting the maneuver of the target, the bearing signal is smoothed out once with filter gains α and β, from relation (1) and (2) with the value r from relation
r

(4) where Р _{scrap is the} probability of false detection of the maneuver, and in subsequent smoothing cycles, the parameters of the target path are smoothed with the filter gains, which are determined from the relations
α

β

Where
α (n

)

β (n

)

n

= int

where i 0, 1, 2, cycle number after detecting the maneuver;
α _m and β _m filter gains at the time the target maneuver is detected.

 Known methods of tracking low-flying maneuvering air targets 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 tracking accuracy due to a priori information about the trajectory of tracking an air target and to minimize tracking errors resulting from missing a target’s maneuver. Therefore, the claimed method meets 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 compensation for the influence of the dynamic error of bearing extrapolation, determined by the target maneuver missed by the maneuver detector, by changing the filter gain in accordance with the accumulated probability of maneuver.

 In FIG. 1 shows a diagram of maneuvering a target; in FIG. 2 graphs illustrating the effectiveness of the proposed method; in FIG. 3 shows the electrical structural diagram of a device for implementing the proposed method.

 Since any suddenly appearing and detected, for example, on a radar carrier ship, a low-flying high-speed air target will be classified as an attacking one, it is legitimate to assume that this target will most likely turn onto the ship, performing a homing maneuver. In other words, a low-flying high-speed air target for hitting a ship at a certain point in time must perform a maneuver, as a result of which the target parameter of the target relative to the ship should become zero. In this regard, the assumption of mandatory target maneuver is fundamentally justified. In the future, we will consider an anti-ship cruise missile (PCR) as an air target, performing a homing maneuver.

 The method is based on the use of trajectory features of the PCR in the final section of the trajectory.

 The PCR trajectory (see Fig. 1) at a distance from the target of less than 30 km includes three characteristic sections of the trajectory: a straight section before the PCR homing; site of a possible homing maneuver; straight section of the trajectory after the completion of the homing maneuver.

 It is known that the self-homing maneuvers of the PKR, for example, of the Harpoon type, are carried out 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 gain is due only to the presence of noise in the target state.

≃ 50 c где V 290 м/с скорость полета пкр.In the absence of a priori data on the enemy’s method of firing PKR in this particular tactical situation, there is reason to believe that the beginning of a homing maneuver is equally probable at any time when the PKR is in the range of distances from the ship of D _min 5.3 km and D _max 20.2 km . The missile overcomes the specified range interval for
t ₁ =

≃ 50 s where V 290 m / s flight speed pcr.

+1 + 1 измерений ее координат. Поскольку маневр с равной вероятностью может начаться на любом межобзорном интервале, вероятность события, состоящего в начале маневра на n-м (n 1, 2,) интервале априорно равна
P

Если на (n-1)-м измерении координат начало маневра не обнаружено, то накопленная вероятность маневра на n-м измерении определяется соотношением
P

=

Зависимость дисперсии ускорения пкр на маневре от накопленной вероятности может быть выражена следующим образом:
σ $\genfrac{}{}{0ex}{}{\text{2}}{\text{a}}$ _β=

(1+4P_n)(1-P_ом) (5) где a

максимальное ускорение пкр по пеленгу на маневре (3.5g);
Р_ом вероятность правильного обнаружения маневра.Therefore, it can be assumed that during the time the PCR is located at a distance from the ship, allowing it to begin homing maneuvers, NN

+1 + 1 measurements of its coordinates. Since a maneuver with equal probability can begin on any inter-review interval, the probability of an event consisting at the beginning of a maneuver on the nth (n 1, 2,) interval is a priori
P

If the beginning of the maneuver is not detected in the (n-1) -th dimension of coordinates, then the accumulated probability of maneuver in the nth dimension is determined by the relation
P

=

The dependence of the dispersion of the acceleration of PCR on the maneuver on the accumulated probability can be expressed as follows:
σ $\genfrac{}{}{0ex}{}{\text{2}}{\text{a}}$ _β =

(1 + 4P _n ) (1-P _ohm ) (5) where a

maximum PCR acceleration by bearing on the maneuver (3.5g);
_{Rm is the} probability of the correct detection of the maneuver.

), а также полагая известными значения ошибок измерения пеленга

, можно рассчитать оптимальные для текущих соотношений дисперсии ошибок измерений координат, возмущающего пеленг ускорения и период обзора РЛС значения коэффициентов усиления фильтра: по пеленгу
α(P_n)

(6) по скорости изменения пеленга β(P_n)

где σ_o ² дисперсия ошибок оценивания пеленга;

дисперсия ошибок измерения пеленга;
R_о коэффициент корреляции ошибок оценивания пеленга и скорости его изменения.Knowing the variance of the acceleration of the PCR (σ a

), as well as considering the known values of the errors of bearing measurement

, it is possible to calculate the optimal for the current dispersion ratios of measurement errors of coordinates perturbing the acceleration bearing and the radar scan period of the filter gain values: from the bearing
α (P _n )

(6) the rate of change of bearing β (P _n )

where σ _o ^{2 the} variance of the estimation errors of the bearing;

variance of bearing measurement errors;
R _about the correlation coefficient of the estimation errors of the bearing and its rate of change.

+

-1

R_o=

(7)
Подставляя в соотношение (7) соотношения (2) и (3) получаем дисперсию ошибок оценивания пеленга и коэффициента корреляции ошибок оценивания пеленга и скорости его изменения, и, подставляя в выражение (6), получаем коэффициенты усиления фильтра, определяемые соотношением (1).The values of σ _o and R _{about are} defined by the following relations
σ $\genfrac{}{}{0ex}{}{\text{2}}{\text{o}}$ =

+

-1

R _o =

(7)
Substituting relations (2) and (3) into relation (7), we obtain the variance of the bearing estimation errors and the correlation coefficient of the bearing estimation errors and its rate of change, and substituting into expression (6), we obtain the filter gains determined by relation (1).

Obviously, as the PCR approaches with each review, the accumulated probability of maneuver increases, which causes an increase in the dispersion of acceleration p _cr and, accordingly, entails an increase in the gain of the filters α and β.

=

a $\genfrac{}{}{0ex}{}{\text{2}}{\text{β}}$ (1-P_лом) (8) где Р_лом вероятность ложного обнаружения маневра.With the detection of the maneuver of the accumulated probability, the maneuver is assigned the value "one", and the variance of the acceleration of the PCR is calculated as follows:

=

a $\genfrac{}{}{0ex}{}{\text{2}}{\text{β}}$ (1-P _scrap ) (8) where P _{scrap is the} probability of a false detection of a maneuver.

 In this case, r is calculated from relation (4), the filter gains gain a maximum value.

 Given the short duration of the PCR maneuver (1. 3 s), one smoothing with increased amplification factors is sufficient (this is confirmed by the results of simulation modeling).

 The procedure for assessing the probability of maneuver is carried out in the range from 20.2 to 5.3 km.

 After the maneuver is detected, the gain of the filter along the bearing is assigned values determined solely by the noise of the target state, the gain coefficients in range throughout the entire tracking time remain constant, and their values are selected in accordance with the noise of the target state.

 In FIG. 3 shows a device for automatically tracking a maneuvering air target that implements the proposed method.

 It contains a sensor of measured coordinates 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, and a filter gain calculation unit 9.

 The device for automatically tracking a maneuvering air target consists of a series-connected sensor 1 of 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 unit 2 and to the 1st input of the maneuver detection unit 6, the output of smoothing unit 2 connected to the input of the extrapolation unit 3, the 1st output of the extrapolation unit 3 is connected to the input of the comparison unit 7 and through the delay unit 4 with the 4th input of the smoothing unit 2 and with the 2nd input of the maneuver detection unit 6, the 2nd output of the extrapolation 3 is the output of the device, the output of the maneuver detection unit 6 is connected to the 2nd input of the filter gain coefficient calculation unit 9 and through the delay unit 8 with the 2nd input of the memory unit 5 and the 3rd input of the filter gain calculation unit 9, the output of the comparison unit 7 is connected to the 1st input of the memory unit 5 and the 1st input of the filter gain calculation unit 9, the output of the memory unit 5 is connected to the 2nd input of the smoothing unit 2, the output of the filter gain calculation unit 9 is connected to 3- m smoothing unit 2 input I am.

 The device operates as follows.

The video signal of the current n-th cycle of measuring the coordinates of the tracking 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 sensor 1 of the measured coordinates converts the video signal from analog to digital, selects a useful signal and measures 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 detector of air targets.

= M_n, где M_n=

П_n, D

при n 2 текущая оценка параметров траектории цели равна

= M_n, V

= (M_n-1-M_n)/T_o где Т_о период обзора РЛС; при n>2 текущая оценка параметров траектории цели равна

=

+α(M

)

=

+β(M

)/T где α и β весовые коэффициенты (коэффициенты усиления фильтра);

и

экстраполированные на один обзор оценки координат и скорости их изменения.The values of the measured coordinates of the target (P _n and D _n ) in the form of signal codes are fed to the 1st input of smoothing unit 2, which implements the coordinate processing operation as follows: for n 1, the current estimate of the target coordinates is

= M _n , where M _n =

P _n , D

when 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 is _the radar survey period; for n> 2, the current estimate of the parameters of the target trajectory is

=

+ α (M

)

=

+ β (M

) / T where α and β are weight coefficients (filter gains);

and

estimates of coordinates and their rate of change extrapolated to one review.

 From block 2, the smoothed coordinate values and the rate of change are fed to the input of extrapolation block 3.

=

+V

T_э;

=

где Т_э заданное значение временных интервалов экстраполяции.Block 3 extrapolation carries out the formation of extrapolated for a given time estimates of the parameters of the trajectory:

=

+ V

T _e ;

=

where T _{e the} specified value of the time intervals of extrapolation.

П_n-

> ρ
Значения порога ρ выбирают по соображениям требуемой вероятности ложного обнаружения маневра.In this device, T _e T _o , T _e T _tsu . In this case, the coordinate values extrapolated for a while from the 1st output arrive through delay unit 4 to the 4th input of smoothing unit 2, where they are used to calculate the trajectory parameters in the next cycle, and to the 2nd input of the maneuver detection unit 6, where subtract from the measured values of the bearing supplied to the 1st input of the maneuver detection unit 6 from the sensor 1 of the measured coordinates, and the resulting difference is compared with a threshold as follows:

P _n -

> ρ
The threshold ρ is chosen for reasons of the required probability of false detection of the maneuver.

 From the same output, the extrapolated coordinates go to the input of the comparison unit 7, where the values of the extrapolated range are compared with the range of the range of a possible maneuver from 5.3 to 20.2 km.

The values of coordinates extrapolated to the time T _e are supplied to the 2nd output of extrapolation unit 3 (device output) and used to generate and issue target designation data to consumers.

 In the block 7 comparison produces a signal of a logical unit, if the values of the extrapolated range lies in the range of a possible manner, which from the output of the block 7 comparison goes to the 1st input of the block 5 memory, while prohibiting the issuance of the gain of the filter in block 2 smoothing, at the same time the same signal is fed to the 1st input of the filter gain coefficient calculation unit 9 and initiates the output of the gain factors to the smoothing unit 2. If the values of the extrapolated range do not lie within the range of the range of a possible maneuver, then a logical zero signal is generated that prohibits the output of the gain from the filter gain calculation unit 9 and initiates the output of the gain from the memory unit 5.

 In memory block 5, filter gains are stored, 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 unit signal and the absence of a signal to detect maneuver by the relations (1), (2) and (3), and in the case of the arrival of the signal “maneuver was detected” by the relations (1) , (2) and (4).

 In block 6, a “maneuver detected” signal is generated and is sent to block 9 for calculating the filter gain, the same signal is sent to block 8, and delayed by one review period, it is sent to blocks 5 and 9 of the memory and for calculating filter gains.

The effectiveness of the proposed method was evaluated by simulation using the following initial data:
The launch range of the harpoon type PKR is 100 km;
PCR overload on 4 g maneuver;
Maneuver duration 4 s;
Radar 2c review period;
The maneuver begins between 13 and 14 reviews.

In FIG. 2 shows the dependence of the normalized error of the extrapolation of the coordinate for one review from the measurement number where:
1 proposed method;
2 known method.

 When implementing the proposed method, the accuracy of the extrapolation of the coordinate is doubled.

Claims (1)

METHOD FOR SUPPORTING A MANEUVING AIR TARGET based on discrete radar coordinate measurement, smoothing target path parameters using an α-β filter in sections of rectilinear motion with filter amplifier coefficients due to target state noise, which are determined from the relations:

where j is the current smoothing cycle;
by bearing change rate

and a change in the filter gain in the areas of the target’s maneuver, characterized in that at the moment of entering the section of the trajectory, which can be maneuvered according to a priori information about the path features of the target, the target bearing signal is smoothed out with filter gain coefficients set in accordance with the accumulated probability of the target’s maneuver ,
P _n (N n + 1),
where N is the number of measurements on the site of a possible maneuver;
n number of the smoothing cycle in the smoothing area in the area of possible maneuver from bearing ratios (1)

by bearing change rate (2)

where σ $\genfrac{}{}{0ex}{}{\text{2}}{\text{β}}$ variance of bearing measurement errors;
a _β maximum acceleration of the target by bearing on the maneuver;
P _{about . m} probability of correct detection of maneuver;
T _about the radar review period,
and at the time of detection of the target’s maneuver, the bearing signal is smoothed out 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 a false detection of a maneuver, and in subsequent smoothing cycles, the trajectory parameters are smoothed out with filter gains, the values of which correspond to the subsequent numbers of the current smoothing cycle, which are determined from the relation

where i 0, 1, 2, cycle number after detecting the maneuver;

the installed filter memory due to the noise of the target state;
α _m and β _m filter gain at the time of maneuver of the target.

Images