RU2724115C1 - Method for automatic tracking of a mobile target when smoothing in cartesian coordinates taking into account radial velocity component measurements - Google Patents

Abstract

FIELD: radio electronics.SUBSTANCE: invention relates to radio electronics and concerns principles of constructing a system for processing hydroacoustic or radar information in part of automatic tracking of a mobile target. In modern information processing systems, the coordinates of the tracked target are smoothed as a rule in a Cartesian coordinate system. Accounting when smoothing results of independent measurements of the rate of change of coordinates, for example radial component of velocity, theoretically enables to reduce tracking errors, especially when a limited number of contacts with a target. However, in practice, this method is not widely used due to its low reliability. According to the proposed method, when calculating the Kalman filter coefficients, variance from cycle to cycle of processing dispersions of both Cartesian coordinates and Cartesian components of radial velocity is taken into account. At that, dispersions of Cartesian components of radial velocity are determined by dispersions of radial velocity and course of tracked target. Since the course estimation accuracy is low, it is proposed to smooth out the calculated course. As follows from the results of statistical modeling, the proposed smoothing method enables reducing smoothing errors by 20–30 % and extrapolation errors in the sustained tracking area (i>10) by 30–40 %. But, what is especially important, the gain in accuracy of tracking with a limited number of contacts with the target (i<10) can reach 1.5–2 times.EFFECT: disclosed method can be used in receiving paths of active locators of hydroacoustic and radar systems and other information systems, in which automatic tracking of mobile targets is used.4 cl, 7 dwg

Description

The invention relates to electronics and relates to the principles of constructing a system for processing sonar or radar information in terms of automatic tracking of a moving target.

Only automatic multi-purpose tracking under the influence of intense unsteady noise can cope with the increased flow of information, however, the reliability of automatic tracking is still low, which limits the possibility of its use in real conditions.

The known method of automatic tracking [1, 2] involves the emission and reception of sounding signals from reflecting objects, after which they decide to detect the target mark (true or false), which corresponds to some measured values of the polar coordinates: range D _i and bearing P _i . Each mark found in the current i-th cycle of processing (location) is checked for its belonging to already followed trajectories for deviation of the coordinates of the mark from the assumed (extrapolated) values. According to [1, 2], the mark falling into the tracking strobe closest in position to the extrapolated value is selected as the tracked one. The disadvantage of this method of selection is its low noise immunity. A more noiseless is the strobeless tracking method [3

The coordinates of the mark selected for each tracked target are further evaluated (smoothed) using a smoothing filter. For this purpose, a linear Kalman filter is often used as the most accurate and simple to implement [1, 2].

In modern information processing systems, the smoothing of the coordinates of the target being followed, as a rule, is performed in the Cartesian coordinate system. The main advantage of such processing is the linear nature of the change in time of the smoothed coordinates of the target with constant courses, as well as the speeds of the target and the carrier of the processing system, which theoretically improves the accuracy of tracking when using a linear Kalman filter [2, p. 207-217].

The Cartesian coordinates of the detected elevation (X _i , Y _i ) are obtained by recalculating the measured values of the polar coordinates - range and bearing (D _i , P _i ):

In this case, the law on the normality and independence of the estimated Cartesian coordinates is violated, which does not correspond to the assumptions made when choosing the weight coefficients of the Kalman linear filter. The influence of such distortions leads to an increase in tracking errors.

A significant drawback of the Kalman linear filter is its inertia, which leads to low tracking accuracy in the initial section of the trajectory, i.e. with a small number of contacts with a target (n <10). In this case, smoothing errors can exceed measurement errors by 20% or more, and extrapolation errors by 2 or more times.

It is known [1, 2] that taking into account when smoothing the coordinates of the tracking target the results of independent measurements of the rate of change of this coordinate, for example, the radial component of the velocity, theoretically allows to reduce tracking errors especially with a limited number of contacts with the target [2, p. 248, prototype]. However, in practice, this method does not find wide application due to its low reliability.

So the value of the radial velocity component Vp _i (hereinafter referred to as the radial velocity) can be obtained using the Doppler frequency shift of the received hydroacoustic echo signal dхо _i , according to the expression [3]:

where Sv = 1500 m / s - the speed of sound in water;

ƒо - operating frequency (kHz).

The presence of radial velocity measurements when detecting the first mark can be used to reduce coordinate estimation errors with a small number of contacts with a target. The absence of such data necessitates the detection of at least two marks of the target to calculate the speed of the target in its rough approximation [1].

The Cartesian components of the obtained measurements of the radial velocity Vx _i and Vy _i are equal to:

where Kc _i is the target angle of the target.

The main disadvantage of this method of automatic tracking is its low reliability, which is due to the nonlinear dependence of the Cartesian components of the radial velocity on the target angle of the target.

The aim of the present invention is to reduce errors and increase the reliability of automatic tracking of high-speed targets with a limited number of contacts with the target.

According to the proposed method, when calculating the Kalman filter coefficients, the variability from a cycle to a processing cycle of dispersions of both Cartesian coordinates (σX _i ² , σY _i ² ) and Cartesian components of the radial velocity (σVx _i ² , σVy _i ² ) calculated according to the expressions:

where σD is the standard deviation (measuring error) in range;

σР - standard deviation (measuring error) along the bearing;

σVp - standard deviation (measuring error) in the radial component of the target velocity;

σKc _i - standard deviation (measuring error) in the course angle.

From the expressions (4) it follows that, when passing to smoothing in Cartesian coordinates, the variances of the latter depend both on the range and on the bearing of the detected target marks and their dispersions. In this case, the variances of the Cartesian components of the radial velocity (σVx _i ² , σVy _i ² ) are determined by the radial velocity and the course of the target being tracked, as well as their variances. As a result, the nature of the change in time of the Cartesian coordinates and their velocities even with the above limitations becomes nonlinear, which can explain the increase in errors and the decrease in the reliability of automatic tracking in a known manner.

The target course can be obtained by measuring the Cartesian coordinates of the detected target marks according to the expression:

Since the accuracy of the course estimation is not high, we suggest smoothing the calculated course. The easiest way to smooth the course is to use it with inter-cycle weight processing (smoothing):

where α is a given coefficient.

As shown by the results of studies, σKc _i can reach a significant value and varies over the entire observation interval. It is permissible to set σKc _i ≈ 0.2 Kc _i and α = 0.3.

As the initial (i = 1) smoothed course value, its measured value is taken.

Algorithms for calculating the smoothed values of the Cartesian coordinates Xs _i and Ys _i and their change rates Vxs _i and Vys _i have the form [1]:

In this case, the extrapolated Cartesian coordinates (Xe _i , Ye _i ) and the rate of change (Vxe _i , Vye _i ) are determined according to the selected linear model of the target’s movement:

The smoothing filter coefficients are proposed to be calculated recursively according to the following expressions [6]:

Where

The initial values of the smoothing filter coefficients for the second processing cycle in the case of detecting the second mark of the target (i = 2) are set equal to [1]:

Where

Thus, the novelty of the proposed method for automatically tracking a moving target is as follows:

- Smoothing the coordinates of the moving target is performed in a Cartesian coordinate system, determined through the measured polar coordinates, taking into account the Cartesian components of the radial velocity of the target. Moreover, on each processing cycle, starting from the moment of detecting the second target mark, the smoothed Cartesian coordinates of the moving target (Xs _i , Ys _i ) are obtained as a linear combination of Cartesian coordinates extrapolated to the current review cycle - (Xe _i , Ye _i ), weighted mismatch values extrapolated Cartesian coordinates with their measured values (X _i , Y _i ) and weighted values of the mismatch of the extrapolated Cartesian components of the radial velocity of the target (Vxe _i , Vye _i ) with their measured values (Vx _i , Vy _i ) according to expressions (8, 9), wherein the weighting coefficients of the smoothing filter are calculated recursively according to expressions (12-15), and the initial values are calculated according to expressions (16, 17).

- At each processing cycle, the target course Kc _{i is} determined according to expression (6) and its smoothed value Kcs _i , as a weighted linear combination of the measured current course Kc _i and its value Kcs _i-1 smoothed at the previous processing cycle according to expression (7).

- At each processing cycle is calculated MSE (measurement error) of Cartesian coordinates (σX _i, σY _i), as a weighted linear combination of the measured polar coordinates (D _i, P _i) and the error measure them (σD and σR) according to expressions (4).

- At each processing cycle, the standard deviations (measurement errors) of the Cartesian components of the radial velocity (σVx _i , σVy _i ) are calculated as a weighted linear combination of the measured radial velocity Vp, the target course Kc _i and their measurement errors (σVp and σKc _i ) according to the expressions (5 )

The effectiveness of the proposed method was evaluated by the results of statistical simulation for M = 100 implementations after i processing cycles (contacts with the goal) using a simulation model of an automatic tracking system [7]. As performance indicators, the standard deviations of the polar coordinates (σD, σР) of the standard deviation (errors) of smoothing σDs _i , σPs _i and extrapolation of σDe _i , σPe _i in range and bearing calculated according to the expressions [8] are considered:

where j = 1, ..., M is the number of the test, M = 100 is the total number of tests;

i is the processing cycle;

Ds _ji , Ps _ji are smoothed, De _ji , Pe _ji are extrapolated and Dist _i , Rist _i are the true range and bearing values during the j test for the i treatment cycle.

In the calculations, the probabilities of detecting the target path of 0.9 and the false path of 10 ^{-6 were} assumed. The GAS carrier remained motionless, the bearing of the target was 45 °, the range of primary detection of the target was 20 km. The target moved in a straight line with a speed of 12 knots and a course of Kc = 225 ° (“towards us”), σD = 1% Dm and σР = 1 °.

In FIG. Figures 1 and 2 show the dependences of smoothing errors σDs _i , σPs _i and extrapolation σDe _i , σPe _i on the number of location i cycles obtained for the prototype when accompanied in Cartesian coordinates, but without taking into account the radial velocity (Fig. 1) and the proposed method (Fig. 2) taking into account the radial velocity. The solid line shows the dependencies corresponding to the smoothing errors, and the dot-and-dot curve shows the extrapolation errors.

As follows from the presented dependencies, the proposed method allows to reduce smoothing errors by 20-30% and extrapolation errors by 30–30% in the stable tracking section (i> 10). But, what is especially important, the gain in tracking accuracy with a limited number of contacts with the target (i <10) can reach 1.5-2 times.

With an increase in the target’s speed of movement, for example, up to 30 knots, tracking errors for the prototype grow up to 30-50%. Moreover, as follows from the simulation results presented in FIG. 3 and 4, the errors of smoothing and extrapolation for the proposed method are 2-3 times lower than for the prototype.

A change in the course of the target, as follows from the simulation results presented in FIG. 5 also leads to a significant increase in maintenance errors for the prototype. The proposed method (Fig. 6) can significantly reduce the influence of the target's course on the accuracy of its tracking.

The proposed method can be applied in the receiving paths of active locators of sonar and radar systems and other information systems that use automatic tracking of moving targets.

The invention is implemented by software and hardware of a digital computer system of an information processing system. As an example of the implementation of the proposed method, a block diagram of the device (Fig. 7), corresponding to the GAS processing system operating in the active mode, is considered.

The device consists of a series-connected receiving path 1, a detector of target marks / false marks 2, a coordinate meter of the detected marks 3 and a computing device 4, as well as a series-connected block of a comb of Doppler filters 5 and a calculator of radial velocity 6. The receiving path 1 is connected to an additional output with an additional output the input of the coordinate meter 3, and the third output through a series of connected Doppler filters 5 and the radial velocity calculator 6 with an additional input of the computing device 4.

Computing device 4 consists of a series-connected identification block of detected marks 4-1, a start / stop block of tracking 4-2, a block for estimating (smoothing) the parameters of the path 4-3, an extrapolation unit for the parameters of the path 4-4, and a block for storing the parameters of the path 4-5 , its first output connected to the second input of the identification unit 4-1, the second output - with an additional input of the start / stop unit of tracking 4-2, the third output - with the corresponding input of the extrapolation unit 4-4 and the fourth output - with the corresponding input of the evaluation unit 4 -3. In this case, the start / stop block of tracking 4-2 with an additional output is connected to the corresponding input of the memory block 6-5.

The signal received by the antenna (input) is fed to the input of the receiving path 1 and then to the detector 2, where it is compared with the detection threshold. In case the signal exceeds the threshold, a command is sent to the coordinate meter 3, from the output of which the measured coordinate values of the detected mark are sent to the computing device 4.

In the identification unit 4-1 of the computing device 4, the detected mark is attached to one of the trajectories followed or identified as “primary”. These data are received in the storage unit 4-5 and at the first input of the coordinate estimation unit 4-3. In block 4-2, a decision is made on the beginning or termination of tracking of the trajectories of targets whose marks were not found in the current processing cycle.

In block 4-3, an estimate (smoothing) of the coordinates of the detected mark is performed according to the proposed method, taking into account the (extrapolated) data stored in the previous processing cycle. In block 4-4, in accordance with the selected algorithm, the coordinate values extrapolated to the next processing cycle are determined, which are stored in block 4-5.

In blocks 5 and 6, the radial velocity of the target is determined by the number of the Doppler channel in which the maximum signal is detected.

Sources of information

1. Kuzmin S.Z. Fundamentals of the theory of digital processing of radar information. - M .: Sov. Radio, 1974.

2. Kuzmin S.Z. Digital radar. Introduction to Theory - Kiev .: 2000 .: Computer-Publishing Information Center (KBIС), 2000. 428 p.

3. Svetlichnaya A. A., Yakovleva Z. V. Method of strobeless automatic tracking of a moving target. Patent No. 2551356 C1 (RU), G01S 7/41, op. 05/25/2015.

4. Svetlichnaya A.A. Evaluation of the effectiveness of multi-purpose automatic tracking using a sequential analysis algorithm. Proceedings of the XXX All-Russian Symposium "Radar research of natural environments." Vol. 12. St. Petersburg, 2017.

5. Urik R. J. Fundamentals of hydroacoustics. L .: Shipbuilding, 1978.

6. Svetlichnaya A.A. and others. "A method for automatically tracking a maneuvering target in the active location of a sonar or radar system." Patent RU No. 2260197 G0S 13/66, op. 01/15/2003.

7. Svetlichnaya A.A. "A simulation model for evaluating the effectiveness of an automatic tracking system for two closely located sonar targets, taking into account possible omissions of target marks and the presence of false marks." Certificate of state registration of a computer program No. RU 2017662146 of 10.30.2017.

Claims (13)

1. A method for automatically tracking a moving target when smoothing in Cartesian coordinates, taking into account measurements of the radial component of the velocity, based on the emission and reception of sounding signals reflected by the target, deciding whether to detect the mark of the target (true or false), measuring its coordinates, checking for ownership of the detected marks the paths already followed, smoothing the coordinates of the target and extrapolating its position to subsequent processing cycles, characterized in that the smoothing is performed in Cartesian coordinates using a linear Kalman filter taking into account the results of independent measurements of radial velocity, and the variances of Cartesian coordinates are determined on each processing cycle ( σX _i ² , σY _i ² ) and Cartesian components of the radial velocity (σVx _i ² , σVy _i ² ), which are taken into account when calculating the filter weight coefficients. 2. The method of claim. 1, characterized in that in each processing cycle is calculated MSE (measurement error) of Cartesian coordinates (σX _i, σY _i) as a weighted linear combination of the measured polar coordinates (D _i, P _i) and the error of measurement ( σD and σР) according to the expressions:

where σD is the standard deviation (measuring error) in range; σР - standard deviation (measuring error) along the bearing. 3. The method according to p. 1, characterized in that at each processing cycle, the smoothed course value of the followed target Kcs _{i is} determined as a weighted linear combination of the measured current rate Kc _i and its value Kcs _i-1 smoothed at the previous processing cycle according to the expression: Kcs _i = Kc _i α + (1-α) Kcs _i-1 , where α is a given coefficient, Kcs ₁ = Kc ₁ . 4. The method according to claim 1, characterized in that on each processing cycle, the standard deviations (measurement errors) of the Cartesian components of the radial velocity (σVx _i , σVy _i ) are calculated as a weighted linear combination of the measured radial velocity Vp _i , the smoothed course value of the tracking target Kcs _i and measurement errors of the radial component of the target’s speed (σVp) and its course (σKc _i ) according to the expressions:

where σVp is the standard deviation (measuring error) in the radial velocity of the target; σKc _i - standard deviation (measuring error) in the course angle.

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