A Method for Tracking Maneuvering Targets under Pure Angle Measurement

Abstract

The present invention discloses a method for tracking a maneuvering target under pure angle measurement. According to the prior information of the optical detection system, the initial distance range of the target is estimated, sub-intervals are divided, and the filter weights, state and covariance initial values of the sub-intervals are calculated under the assumption of uniform distribution; a constant velocity model of the target and a pure azimuth tracking model are established, and the deviation compensation pseudo-linear filtering method is used to update the sub-interval weights, state and covariance, a weight threshold is set, and the sub-interval filters with weights less than the threshold are deleted to reduce the number of sub-interval filters for parallel calculation; a maneuver detection factor is defined, a maneuver identification threshold is set, and when the maneuver detection factor is greater than the identification threshold, a re-initialization strategy is used to track the maneuvering target. The present invention improves the pure azimuth positioning accuracy of the maneuvering target while greatly improving the generality and real-time performance of the existing pure azimuth tracking method, making the algorithm applicable to the passive positioning of future ground targets.

Description

Technical Field

[0001] The present invention belongs to the field of target tracking, and specifically relates to a pure azimuth tracking algorithm for maneuvering targets that designs multiple sub-interval filters based on a distance parameterization method and applies a deviation compensation pseudo-linear algorithm for parallel operation and weighted fusion output of the target state when a single-station passive detection system is used for ground target positioning. At the same time, it re-initializes the strategy based on maneuver detection. The method realizes that the single-station passive detection system only uses the azimuth measurement data to make the target positioning error converge quickly, and at the same time re-initializes the sub-filter after detecting the target maneuver to avoid the problem of a sharp increase in the positioning error. Background Art

[0002] In the environment of electronic warfare and information warfare, traditional active detection systems expose their own targets by actively radiating electromagnetic wave signals. It is not only difficult to complete the predetermined tasks, but also their own survival faces serious threats. The single-station passive tracking system only relies on passive reception of the radiation information of the target radiation source to achieve detection, identification, positioning and tracking. It has the characteristics of strong concealment, small equipment volume, long operating distance, large coverage area, good maneuverability, etc. More importantly, it avoids complex time synchronization and data fusion between multiple observation stations and has attracted much attention, and has extremely important military significance for modern information warfare.

[0003] As the detection link of ground combat, the target positioning accuracy obtained by the passive tracking system directly affects the judgment of the weapon system on the strike timing. Therefore, quickly reducing the target positioning error is the core task of the passive tracking system. Generally speaking, there are two difficulties in single-station positioning: one is that the relationship between the angle measurement value and the target state is non-linear, which is a typical non-linear tracking problem, and simple Kalman filtering methods are not applicable under such conditions; the other is that in a bistatic positioning system, the target initial position information can be directly obtained by cross-positioning and other means based on the angle information of two observation stations in the same period, while the single-station cannot use this method to obtain the target initial position information. If the initial value is not selected properly, it will directly lead to the divergence or even collapse of the filter operation result.

[0004] In the current passive tracking system, single-station positioning mostly realizes the initial information estimation through the angle data of several consecutive sampling periods and based on the target motion characteristics, thus effectively obtaining the basis for selecting the initial value of passive tracking and positioning, and greatly improving the stability of tracking filtering. However, in the context of current information-based warfare, this method has disadvantages such as limited accuracy, poor generality, and long initial information estimation time. In particular, it can only perform initial information estimation for a single known target motion model, which greatly restricts the application development of single-station positioning. In response, a single-station positioning method based on the combination of distance parameterization and nonlinear filtering algorithm has emerged in this context, that is, the target initial information is divided into several intervals, and it is considered that the target follows a uniform distribution in the interval. From this information, the mean and covariance information of the target in the interval can be obtained, weights are assigned to each interval, and the target state information can be obtained by updating the weights through a nonlinear filter and based on the weighted fusion method. It has the characteristics of good generality and high accuracy, but the calculation and processing are complex and time-consuming. Especially when the initial distance range of the target is large, more sub-intervals need to be divided to generate more sub-filters, so the calculation amount is larger, affecting the real-time performance.

[0005] For pure azimuth target tracking, a linearized recursive Bayesian estimator can be formulated by replacing the nonlinear azimuth measurement with a pseudo-linear equation that constitutes a well-known pseudo-linear estimator (PLE). This method is usually called the pseudo-linear Kalman filter (PLKF). Compared with other nonlinear Kalman filtering algorithms (such as UKF), PLKF requires lower computational complexity and provides good tracking performance at the same time. However, the main disadvantage of PLKF is the serious bias problem. The bias-compensated pseudo-linear Kalman filtering algorithm (BC-PLKF) compensates for the state estimation bias term caused by the correlation between the pseudo-linear measurement and the measurement vector, and obtains better estimation performance while retaining the high stability and low complexity of PLKF. Therefore, it is considered to use bias-compensated pseudo-linear filtering to replace the nonlinear filtering algorithm, and at the same time set a weight threshold. When the weight after the update of the sub-interval filter is less than the weight threshold, the filter is deleted, and the remaining sub-interval weights are renormalized, which can quickly reduce the number of filters, thus greatly improving the real-time performance of the algorithm while ensuring the filtering accuracy.

[0006] Single-station positioning mostly adopts a constant velocity motion model to model the target motion. However, when the target maneuvers, the filtering result will inevitably diverge in positioning error. In response, some scholars consider starting from the target motion model and adopting methods such as interacting multiple models and current statistical models to re-model the target. However, the lack of distance information in pure angle measurement makes it difficult for these methods to produce good tracking effects.

[0007] In view of this, the present invention introduces distance parameterization and deviation compensation pseudo-linear filtering algorithm into the single-station positioning algorithm. By dividing sub-intervals to construct sub-filters and weighted-fusing to output the target state, the generality and accuracy of the passive tracking system are greatly improved. At the same time, to avoid the problem of divergence of positioning errors caused by model mismatch when the target maneuvers, based on the detection of the weight threshold to the unique filter, the present invention sets a maneuver recognition threshold, calculates the maneuver detection factor according to historical filtering data, re-initializes the sub-filters in four directions based on the original speed after detecting the maneuver, updates the sub-filter weights according to the measurement likelihood function and weighted-fuses to output the target state value, reducing the filtering error caused by the mismatch of the target maneuver model. Thus, in the algorithm execution mechanism, the problem of divergence of filtering errors caused by target maneuvers is effectively overcome. Summary of the Invention

[0008] The object of the present invention is to provide a bearing-only tracking method applicable to maneuvering targets, introducing distance parameterization and deviation compensation pseudo-linear filtering algorithm into single-station positioning, greatly improving the overall stability and accuracy of single-station positioning; increasing sub-filters using a re-initialization strategy after detecting target maneuvers, avoiding modification of the target motion model, and improving the tracking accuracy of single-station positioning.

[0009] The technical solution for achieving the object of the present invention is: a method for tracking maneuvering targets under pure angle measurement, comprising the following steps:

[0010] Step 1, selection of initial values of sub-filters: obtain the distance range between the target initial position and the observation platform, divide this range into multiple sub-intervals based on the idea of distance parameterization, determine the mean, standard deviation and weight of the target initial distance within each sub-interval, so as to obtain the initial values of the state, covariance and weight of the sub-filter corresponding to each sub-interval;

[0011] Step 2, bearing-only target tracking: according to the state value and covariance of each sub-filter at the previous moment, combined with the angle measurement value at the current moment, update the state value and state covariance of the sub-filter using the deviation compensation pseudo-linear filtering algorithm, and update the sub-filter weights according to the measurement likelihood function and normalize them;

[0012] Step 3, removal of sub-filters with small weights: set a filter weight threshold, remove the sub-filters with weights less than the weight threshold from the calculation, and normalize the weights of the remaining sub-filters. When the number of sub-filters is one, enter Step 4, otherwise enter Step 5;

[0013] Step 4, Maneuver Detection: Set the maneuver recognition threshold, calculate the maneuver detection factor at the current moment. When the maneuver detection factor is greater than the recognition threshold, keep the target position coordinates unchanged, divide the speed into multiple directions, each speed direction corresponds to a new target state, generate the initial state values of the sub-filters based on these state quantities, and update the states, covariances, and weights of these sub-filters when the angle measurement value is input at the next moment. Otherwise, directly enter Step 5;

[0014] Step 5, Target State Output: According to the state values and weights of each sub-filter, perform weighted fusion to output the target state estimation result at the current moment, and then jump to Step 2 at the next moment.

[0015] Step 1, Selection of Initial Values of Sub-Filters, the specific method is as follows:

[0016] Assume that the distance between the target's initial position and the observation platform is distributed in the interval (r min , r max ). Divide this interval into N small intervals, where the nth small interval is (r min ρ n-1 , r min ρ n ), and the expression of the scale factor ρ is:

[0017]

[0018] The mean value and the standard deviation of the target's initial distance in this interval are respectively:

[0019]

[0020]

[0021] Assign initial weights to each interval. Assume that the target distance follows a uniform distribution within the interval. Then the weight of the nth small interval at the initial moment 0 is:

[0022]

[0023] Realize the initialization of the target's position in each interval through the statistical information of the target distance in each interval and the obtained angle information;

[0024]

[0025]

[0026]

[0027]

[0028] Among them, Mx n and My n are the initial position states of the target in two-axis directions within the nth small interval, Mp x and Mp y are the initial position covariances of the target in two-axis directions respectively, and θ is the angle information measured at the initial moment;

[0029] Select the initial velocity value as 0, and select a prior initial standard deviation σ v of velocity according to the target type to realize the initialization of the velocity of each interval of the target;

[0030]

[0031]

[0032]

[0033]

[0034] Among them, and are the initial velocity states of the target in two-axis directions within the nth small interval, and are the initial velocity covariances of the target in two-axis directions respectively;

[0035] According to the above initialization results of positions and velocities of each interval, obtain the initial state initial covariance and initial weight of the nth sub-filter as:

[0036]

[0037]

[0038]

[0039] Step 2, Sub-filter tracking, the specific method is as follows:

[0040] If the current time is the initial time, the initial values of the sub-filter state and covariance obtained in step 1 are used as the input of the corresponding sub-filter. If the current time is not the initial time, the state and covariance estimation values tracked by the sub-filter at the previous time are used as the input of the corresponding sub-filter. During the filtering process of each sub-filter, the pseudo-linear Kalman filtering algorithm is used to construct a pseudo-linear measurement equation to obtain the pseudo-linear measurement value, pseudo-linear measurement matrix, and pseudo-linear measurement noise. The constant velocity motion model is used as the target motion model, and the target angle measurement value at the current time is input. Under the Kalman filtering framework, the state estimation value and state covariance estimation value are obtained, the pseudo-linear Kalman filtering estimation deviation is calculated, and the sub-filter state estimation value is updated by compensating for the deviation of the estimation error. Specifically:

[0041] Let the position and velocity of the target at time k be represented as p k and v k , and the target state vector is represented as The position of the observation station is represented as s k =[s x,k ,s y,k T , the true angle at time k is represented as β k , and the angle measured by the observation station is represented as The measurement equation is represented as where n k is the measurement noise with a mean of 0 and a variance of ; The pseudo-linear measurement equation is constructed as follows:

[0042] z k =H k x k +η k

[0043] Pseudo-linear measurement value Pseudo-linear measurement matrix Pseudo-linear noise η k =-d k sinn k , where d k represents the relative distance between the target and the observation station, and the covariance of η k is When the measurement noise n k is very small, there is established;

[0044] The nth sub-filter uses the deviation compensation pseudo-linear Kalman filtering algorithm for filtering calculation. The algorithm inputs are: the sub-filter state estimation value at time k-1 State covariance estimation value The algorithm outputs are: the sub-filter state estimation value at time k State covariance estimation value​ The filtering steps are as follows;

[0045] (1) Calculate the state prediction value

[0046]

[0047] (2) Calculate the state covariance prediction value P k|k-1 :

[0048]

[0049] (3) Calculate the filtering gain value

[0050]

[0051] (4) Calculate the state update value

[0052]

[0053] (5) Calculate the state covariance update value

[0054]

[0055] (6) Calculate the state value after bias compensation

[0056]

[0057] where F and Q represent the state transition matrix and state noise matrix of the target constant velocity motion model, represents the bias compensation term, and M = [I 2×2 0 2×2 ;

[0058] In addition to updating the state information of each sub-filter, after the sub-filtering is completed, the weights of each interval at the next moment need to be obtained, and the weight intervals are updated according to the measurement likelihood function and normalized;

[0059]

[0060] where, is the weight of the nth sub-filter at time k - 1, that is, the weight before update, is the weight of the nth sub-filter at time k, that is, the weight after update, is the measurement covariance obtained by the nth sub-filter, is the predicted measurement obtained by the nth sub-filter.

[0061] Step 3, removing sub - filters with small weights. The specific method is as follows:

[0062] Set the filter weight threshold T m1 , and remove the sub - filters whose corresponding weights are less than the weight threshold from the calculation, and normalize the weights of the remaining sub - filters. Assume that the weight of the m - th sub - filter is less than the weight threshold T m1 , then the following normalization is performed on the remaining sub - filters, is the weight after removing sub - filters with small weights and renormalization;

[0063]

[0064] Step 4, maneuver detection. The specific method is as follows:

[0065] Define the maneuver detection factor at time k as:

[0066]

[0067] where represents the difference between the target angle measurement value and the predicted value in the filter, that is, the filter innovation, S t = P zz,k|k-1 represents the innovation covariance. If δ t is a white zero - mean covariance variable with covariance S t , then I k follows a chi - square distribution with W1 degrees of freedom;

[0068] Set the maneuver recognition threshold T m2 . If I k < T m2 , it is considered that the target has not maneuvered, and directly output the target state estimation value of the current filter; if I k > T m2 , it is considered that the target has maneuvered, which means that the estimated target innovation at time k, including distance, heading, and speed, has deviated from the true target information;

[0069] Before initialization, mark the only sub - filter as "only", and represent its state, state covariance, and weight as and When it is detected that the target has maneuvered, at time k, initialize N f sub - filters, each sub - filter having a different target initial heading angle value; the state of the j - th sub - filter at time k is initialized as:

[0070]

[0071] where and represent the position and velocity components of the only filter on the two coordinate axes before initialization, φ j = 2πj / N f , 1 ≤ j ≤ N f represents the rotation angle of the target heading after maneuvering, and the state covariance of the j-th sub-filter at time k and the weight are initialized as follows:

[0072]

[0073]

[0074] If the re-initialization operation is performed after maneuver detection, the weights and states of the sub-filters at time k are as shown above, and the number of sub-filters is adjusted to N = N f , if the re-initialization operation is not performed after maneuver detection, the sub-filter at time k is still the original only filter, and its weight is 1.

[0075] The target state X k|k can be obtained using the new weights and the state information of each sub-filter.

[0076]

[0077] A maneuvering target tracking system under pure angle measurement, based on the above-mentioned maneuvering target tracking method under pure angle measurement, realizes the tracking of maneuvering targets under pure angle measurement.

[0078] A computer device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, based on the above-mentioned maneuvering target tracking method under pure angle measurement, it realizes the tracking of maneuvering targets under pure angle measurement.

[0079] A computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, based on the above-mentioned maneuvering target tracking method under pure angle measurement, it realizes the tracking of maneuvering targets under pure angle measurement.

[0080] Compared with the prior art, the significant advantages of the present invention are as follows: (1) By introducing distance parameterization, the filtering stability is significantly improved compared with calculating the target position through several sampling periods. When the target tracking time is within 8 s, the target positioning error of this method has converged to less than 200 m, which well meets the actual ground combat requirements; (2) By introducing the deviation compensation pseudo-linear filtering algorithm to filter the target state, the algorithm structure is simple, the computational complexity is low, and the tracking effect is good, which well meets the real-time requirements of actual combat; (3) The pure bearing tracking method for maneuvering targets proposed in the present invention has a tracking error far lower than that of general pure bearing tracking methods after the target maneuvers, and has an obvious improvement in the generality of target tracking, making it possible for this algorithm to be applied in the engineering of future ground target pure bearing tracking systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 is the schematic diagram of the overall process of the maneuvering target tracking method under pure angle measurement of the present invention.

[0082] Figure 2 is the schematic diagram of the sensor azimuth measurement coordinate system.

[0083] Figure 3 is the schematic diagram of re-initializing the velocity direction.

[0084] Figure 4 is the schematic diagram of the vehicle body and the target movement scene.

[0085] Figure 5 is the schematic diagram of the mean square error of the positioning errors of RPBCPLKF and MRPBCPLKF when the measurement error is small.

[0086] Figure 6 is the schematic diagram of the mean square error of the positioning errors of the non-linear filtering and pseudo-linear filtering when the measurement error is small.

[0087] Figure 7 is the schematic diagram of the mean square error of the positioning errors of RPBCPLKF and MRPBCPLKF when the measurement error is large.

[0088] Figure 8 is the schematic diagram of the mean square error of the positioning errors of the non-linear filtering and pseudo-linear filtering when the measurement error is large. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0089] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0090] Combined with Figure 1 , the maneuvering target tracking method under pure angle measurement of the present invention is specifically as follows:

[0091] Step 1: Selection of Initial Values of Sub - filters

[0092] When measuring the angle in a two - dimensional plane, the azimuth measurement value received by the moving observation station is as Figure 2 shown.

[0093] Let p k and v k represent the position and velocity of the target at time k respectively. Then the target state vector The position of the observation station is represented by the vector s k = [s x,k , s y,k T which is considered as a known quantity during the tracking process.

[0094] Assume that the target motion follows a CV model, then the state equation is:[[]]

[0095] x k = Fx k-1 + w k-1

[0096] where F is the state transition matrix, and w k-1 is the process noise, and the mean of w k-1 is 0 4×1 and the covariance is Q.

[0097]

[0098] where T is the sampling period, and q x , q y are the power spectral densities of the process noise on the two coordinate axes.

[0099] The target angle measured by the observation station at time K is expressed as The measurement equation is:[[]]

[0100]

[0101]

[0102] where Δx k = p x,k - s x,k , Δy k = p y,k - s y,k , n k is the angle measurement noise, the mean of n k is 0 and the variance is The measurement noise is independent of the process noise. From the state - space and measurement models, it can be seen that the single - vehicle positioning system is essentially a non - linear system. ​

[0103] Assume that the distance between the target's initial position and the observation platform is distributed in the interval (r min , r max ). Divide this interval into N small intervals, where the nth small interval is (r min ρ n-1 , r min ρ n ), and the expression of the scale factor ρ is

[0104]

[0105] The mean value of the target's initial distance and the standard deviation in this interval are respectively

[0106]

[0107]

[0108] When combining distance parameterization with the filtering algorithm of the filtering, it is necessary to assign an initial weight to each interval. Assume that the target distance follows a uniform distribution within the interval. Then, the weight of the nth small interval at the initial moment 0 is

[0109]

[0110] Realize the initialization of the target position in each interval through the statistical information of the target distance in each interval and the obtained angle information;

[0111]

[0112]

[0113]

[0114]

[0115] where Mx n and My n are the initial position states of the target in the two-axis directions within the nth small interval, and Mp x and Mp y are the initial position covariances of the target in the two-axis directions respectively, and θ is the angle information measured at the initial moment;

[0116] Select the initial velocity value as 0, and select a prior initial standard deviation σ v of the velocity according to the target type to realize the initialization of the target velocity in each interval;

[0117]

[0118]

[0119]

[0120]

[0121] Among them, and are the initial velocity states of the target in the two-axis directions within the nth small interval, and are the initial covariance of the velocity of the target in the two-axis directions respectively;

[0122] According to the above position and velocity initialization results of each interval, the initial state initial covariance and initial weight of the nth sub-filter are:

[0123]

[0124]

[0125]

[0126] Step 2: Sub-filter tracking

[0127] Perform the following transformation on the pure azimuth angle measurement noise:

[0128]

[0129] Multiply both sides of the equation by Note that d k × cosβ k = Δx k , d k × sinβ k = Δy k , then we can obtain:

[0130]

[0131] Then we can obtain the pseudo-linear measurement equation:

[0132] z k = H k x k + η k

[0133] Among them, the pseudo-linear noise η k = -d k sin n k . ηk Covariance When the measurement noise n k is very small, this equation holds.

[0134] The steps of the pseudo-linear Kalman filtering algorithm (PLKF) are as follows:

[0135] (1) State prediction

[0136]

[0137] (2) State covariance prediction

[0138] P k|k-1 = FP k-1|k-1 F T + Q

[0139] (3) Calculate the gain

[0140]

[0141] (4) State update

[0142]

[0143] (5) State covariance update

[0144] P k|k = (I 4×4 - K k H k )P k|k-1

[0145] where d k and R k The true values cannot be obtained, and approximate values are used for calculation:

[0146]

[0147]

[0148] The estimation error of PLKF can be written in the following form:

[0149] e k = A k + B k + C k

[0150]

[0151]

[0152]

[0153] Among them, the first item A k comes from the propagation of the error at time k-1, which is not the reason for the biased estimation in PLKF. The second item B k comes from k the bias of the correlation between H k-1 and w k-1 If we assume that the process noise w k is relatively small, then B k can be ignored. When it comes to the third item Ck, it propagates the bias generated by the correlation between H k and η k , which cannot be ignored because they both contain the angular measurement noise n k and η k is the correlation between them that leads to the biased estimation. If we can compensate for the bias of the C k term, the estimation bias of can be reduced.

[0154] Since the pseudo-linear noise η k is unknown and the true value of C k cannot be obtained, we replace it with the conditional expectation based on :

[0155]

[0156] Since the true position of the target is also unknown, further approximated by , we can get:

[0157]

[0158] Among them, M = [I 2×2 0 2×2 .

[0159] The steps of the bias compensation pseudo-linear Kalman filter algorithm (BC-PLKF) are as follows:

[0160] The algorithm input is: the state estimate of the sub-filter at time k-1 the state covariance estimate

[0161] The algorithm output is: the state estimate of the sub-filter at time k the state covariance estimate

[0162] The filtering steps are as follows;

[0163] (1) Calculate the state prediction value

[0164]

[0165] (2) Calculate the predicted value of the state covariance P k|k-1 :

[0166]

[0167] (3) Calculate the filter gain value

[0168]

[0169] (4) Calculate the state update value

[0170]

[0171] (5) Calculate the updated value of the state covariance

[0172]

[0173] (6) Calculate the state value after bias compensation

[0174]

[0175] Among them, F and Q represent the state transition matrix and the state noise matrix of the target constant velocity motion model, represents the bias compensation term, and M = [I 2×2 0 2×2 .

[0176] In addition to updating the state information of each sub-filter, after the sub-filter filtering is completed, the weights of each interval at the next moment need to be obtained, and the weight intervals are updated and normalized according to the measurement likelihood function;

[0177]

[0178] Among them, is the weight of the nth sub-filter at time k - 1, that is, the weight before update, is the weight of the nth sub-filter at time k, that is, the weight after update, is the measurement covariance obtained by the nth sub-filter, is the predicted measurement obtained by the nth sub-filter;

[0179] Set the filter weight threshold T m1 , remove the sub-filter with the corresponding weight less than the weight threshold from the calculation, and normalize the weights of the remaining sub-filters. Assume that the weight of the mth sub-filter is less than the weight threshold T m1, the remaining sub - filters are normalized as follows, is the weight after removing the sub - filter with small weight and then renormalizing;

[0180]

[0181] Step 3: Maneuver detection re - initialization

[0182] When only one filter remains after removing the sub - filters with small weights, the maneuver detection factor at time k is defined as:

[0183]

[0184] where represents the difference between the target angle measurement value and the predicted value in the filter, that is, the filter innovation, S t =P zz,k|k-1 represents the innovation covariance. If δ t is a variable with white zero - mean covariance S t , then I k follows a chi - square distribution with W1 degrees of freedom;

[0185] Set the maneuver recognition threshold T m2 . If I k <T m2 , it is considered that the target has not maneuvered, and the target state estimation value of the current filter is directly output; if I k >T m2 , it is considered that the target has maneuvered, which means that the estimated target innovation (distance, heading, and speed) at time k has deviated from the true target information;

[0186] Before initialization, mark the only sub - filter as "only", then its state, state covariance, and weight can be expressed as and

[0187] When it is detected that the target has maneuvered, at time k, initialize N f sub - filters, each sub - filter having a different target initial heading angle value;

[0188] The state of the j - th sub - filter at time k is initialized as:

[0189]

[0190] where and represent the components of the state of the only filter before initialization. φ j =2πj / N f , 1 ≤ j ≤ N fThe rotation angle representing the target heading after maneuvering, and the state covariance of the j-th sub-filter at time k and the weight value The initialization is expressed as:

[0191]

[0192]

[0193] If the re-initialization operation is performed after maneuver detection, the weights and states of the sub-filters at time k are as shown above, and the number of sub-filters is adjusted to N = N f . If the re-initialization operation is not performed after maneuver detection, the sub-filter at time k remains the original single filter, and its weight is 1;

[0194] Finally, based on the weights and state information of each sub-filter, the target state Xout output by the algorithm at time k is determined k ;

[0195]

[0196] A maneuvering target tracking system under pure angle measurement, which realizes the tracking of a maneuvering target under pure angle measurement based on the above-mentioned maneuvering target tracking method under pure angle measurement.

[0197] A computer device includes a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, it realizes the tracking of a maneuvering target under pure angle measurement based on the above-mentioned maneuvering target tracking method under pure angle measurement.

[0198] A computer-readable storage medium has a computer program stored thereon. When the computer program is executed by a processor, it realizes the tracking of a maneuvering target under pure angle measurement based on the above-mentioned maneuvering target tracking method under pure angle measurement.

[0199] Embodiment

[0200] To verify the effectiveness of the proposed solution of the present invention, the following simulation experiments are carried out.

[0201] 1. Simulation conditions

[0202] In this paper, distance estimation of the target is considered by changing the vehicle body movement mode, and the movement mode of "uniform acceleration-uniform turn-uniform speed" is adopted, with the maximum speed of the vehicle body being 60 km / h. Under this movement condition, the specific movement of the vehicle body is as follows: the initial speed is (0,0), and it performs an acceleration of (0.8 m / s 2 , -0.8 m / s 2) Uniformly accelerated motion; uniformly turning motion with a turning speed of π / 15 from 10 - 25 s; uniform linear motion from 30 - 155 s. The target moves specifically as follows: The initial position is (2000 m, 2000 m), and the initial velocity is (-5.9 m / s, -5.9 m / s). It moves in uniform linear motion from 1 - 40 s; makes a uniformly turning motion with a turning speed of π / 15 from 40 - 55 s; moves in uniform linear motion with a speed of (5.9 m / s, 5.9 m / s) from 55 - 100 s; makes a uniformly turning motion with a turning speed of -π / 15 from 100 - 115 s; moves in uniform linear motion with a speed of (-5.9 m / s, -5.9 m / s) from 115 - 155 s. The motion scenario is as Figure 4 shown.

[0203] Assume the initial distance is between (500 m, 3000 m), the number of sub - intervals N = 4. Divide the sub - intervals according to the distance parameterization method, and give the state quantity, state covariance, and initial weight value of each sub - interval. The sub - filter weight threshold is set to 0.01, the maneuver detection degree of freedom W1 = 30, the maneuver identification threshold is set to 100, and re - initialize the number of sub - filters N f = 4. The number of Monte Carlo simulation experiments is 200 times, the sampling time T = 0.1 s, and the angular measurement error is discussed in two cases. One is when the angular measurement error is small, the azimuth error σ1 = 0.1 mrad; the other is when the angular measurement error is large, the azimuth error σ2 = 1 mrad.

[0204] 2. Simulation content and result analysis

[0205] (1) When the angular measurement error is small

[0206] Simulate and compare the range parameterized bias - compensated pseudo - linear Kalman filter method (RPBCPLKF) and the maneuvering target bearing - only tracking method based on range parameterization and bias - compensated pseudo - linear filtering proposed in this paper (MRPBCPLKF) simultaneously. The simulation results are as Figure 5 shown. Simulate and compare the bias - compensated pseudo - linear Kalman filter (BCPLKF) in the method proposed in this paper with the extended Kalman filter (EKF), cubature Kalman filter (CKF), and pseudo - linear Kalman filter (PLKF) simultaneously. The simulation results are as Figure 6 shown.

[0207] Under the condition that the azimuth measurement error σ1 = 0.1 mrad, there is a serious problem that the RPBCPLKF algorithm without maneuver correction collapses at 45 s and cannot output the filtering result, while the MRPBCPLKF algorithm keeps the error below 200 m after the target maneuvers, achieving a good tracking effect. By comparing the tracking errors of the two pseudo-linear filtering methods with those of two typical non-linear filtering methods through simulation, it can be seen that BCPLKF improves the estimation deviation problem of PLKF and has the best tracking effect when the measurement error is small.

[0208] (2) When the angle measurement error is large

[0209] The range parameterized bias compensation pseudo-linear Kalman filtering method (RPBCPLKF) and the maneuvering target bearing-only tracking method (MRPBCPLKF) proposed in this paper, which combines range parameterization and bias compensation pseudo-linear filtering, are simultaneously simulated and compared. The simulation results are as Figure 7 shown. The bias compensation pseudo-linear Kalman filtering (BCPLKF) in the method proposed in this paper is simultaneously simulated and compared with the extended Kalman filtering (EKF), cubature Kalman filtering (CKF), and pseudo-linear Kalman filtering (PLKF). The simulation results are as Figure 8 shown.

[0210] Under the condition that the azimuth measurement error σ2 = 1 mrad, the filtering error of the RPBCPLKF algorithm without maneuver correction shows a serious divergence phenomenon after the target maneuvers, while the MRPBCPLKF algorithm reduces the filtering error after the target maneuvers. By comparing the tracking errors of the two pseudo-linear filtering methods with those of two typical non-linear filtering methods through simulation, it can be seen that BCPLKF improves the estimation deviation problem of PLKF and also has a tracking effect close to that of the non-linear filtering algorithm when the measurement error is large.

[0211] In summary, in order to improve the accuracy and generality of bearing-only target tracking, the present invention proposes a maneuvering target tracking method under pure angle measurement. The simulation results prove the effectiveness and feasibility of the method, making the algorithm applicable to the passive positioning of ground targets.

[0212] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0213] The above-described embodiments merely represent several implementation manners of the present application. The description thereof is relatively specific and detailed, but it should not be construed as a limitation on the scope of the present application. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present application, several modifications and improvements can still be made, and these all fall within the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the appended claims.

Claims

1. A maneuvering target tracking method under pure angle measurement, characterized in that, It includes the following steps: Step 1, Initial value selection of sub - filters: Obtain the distance range between the target's initial position and the observation platform. Based on the idea of distance parameterization, divide this range into multiple sub - ranges, and determine the mean, standard deviation, and weight of the target's initial distance within each sub - range, so as to obtain the initial values of the state, covariance, and weight of the sub - filters corresponding to each sub - range; Step 2, Tracking of bearings - only targets: According to the state values and covariances of each sub - filter at the previous moment, combined with the angle measurement value at the current moment, use the bias - compensated pseudo - linear filtering algorithm to update the state values and state covariances of the sub - filters, and update and normalize the weights of the sub - filters according to the measurement likelihood function; Step 3, Removal of sub - filters with small weights: Set a filter weight threshold, remove the sub - filters with weights less than the weight threshold, and normalize the weights of the remaining sub - filters. When the number of sub - filters is one, enter Step 4; otherwise, enter Step 5; Step 4, Maneuver detection: Set a maneuver recognition threshold, calculate the maneuver detection factor at the current moment. When the maneuver detection factor is greater than the recognition threshold, keep the target position coordinates unchanged, divide the speed into multiple directions, each speed direction corresponds to a new target state, generate the initial values of the states of the sub - filters according to these state quantities, and update the states, covariances, and weights of these sub - filters after the angle measurement value at the next moment is input; otherwise, directly enter Step 5; Step 5, Output of target state: According to the state values and weights of each sub - filter, perform weighted fusion to output the target state estimation result at the current moment, and then jump to Step 2 at the next moment.

2. The method for tracking a maneuvering target under pure angle measurement according to claim 1, wherein Step 1, Initial value selection of sub - filters, the specific method is as follows: Suppose the distance between the initial position of the target and the observation platform is distributed in the interval (r min , r max ). Divide this interval into N small intervals, where the nth small interval is (r min ρ n-1 , r min ρ n ), and the expression of the scale factor ρ is: The mean of the target initial distance within this interval and the standard deviation are respectively: Assign an initial weight to each interval. Assuming that the target distance follows a uniform distribution within the interval, the weight of the nth small interval at the initial time 0 is: Realize the initialization of the target position in each interval through the statistical information of the target distance in each interval and the obtained angle information; Among them, Mx n and My n are the initial position states of the target in the two-axis directions within the nth small interval, Mp x and Mp y are the initial position covariances of the target in the two-axis directions respectively, and θ is the angle information measured at the initial moment; Set the initial velocity value to 0, and select a prior initial standard deviation of velocity σ according to the target type v , to realize the velocity initialization of each interval of the target; Among them, and are the initial velocity states of the target in the two-axis directions within the nth small interval, and are the initial covariance matrices of the target's velocity in the two-axis directions respectively; Based on the above initial results of the interval positions and velocities, obtain the initial state of the nth sub-filter Initial covariance and the initial weight as follows:

3. The method for tracking a maneuvering target under pure angle measurement according to claim 1, wherein Step 2, Sub - filter tracking, the specific method is as follows: If the current moment is the initial moment, use the initial values of the states and covariances of the sub - filters obtained in Step 1 as the inputs of the corresponding sub - filters. If the current moment is not the initial moment, use the state and covariance estimation values of the sub - filter tracking at the previous moment as the inputs of the corresponding sub - filters; During the filtering process of each sub - filter, use the pseudo - linear Kalman filtering algorithm to construct a pseudo - linear measurement equation, obtain the pseudo - linear measurement value, pseudo - linear measurement matrix, and pseudo - linear measurement noise. Use the constant - velocity motion model as the target motion model, input the target angle measurement value at the current moment, obtain the state estimation value and state covariance estimation value within the Kalman filtering framework, calculate the deviation of the pseudo - linear Kalman filtering estimation, and update the state estimation value of the sub - filter by compensating the estimation error. Specifically: Let the position and velocity of the target at time k be represented as p k and v k , and the target state vector be represented as Let the position of the observation station be represented as s k = [s x,k , s y,k T , and the true angle at time k be represented as β k , and the angle measured by the observation station be represented as The measurement equation is represented as where n k is measurement noise with a mean of 0 and a variance of ; construct the pseudo-linear measurement equation as follows:​ z k = H k x k + η k Pseudo-linear measurement value Pseudo-linear measurement matrix Pseudo-linear noise η k =-d k sinn k where d k represents the relative distance between the target and the observation station, and the covariance of η k When the measurement noise n is very small, we have k established;​ The nth sub-filter performs filtering calculations using the bias compensation pseudo-linear Kalman filtering algorithm. The algorithm inputs are: the state estimate value of the sub-filter at time k-1 The state covariance estimate value The algorithm outputs are: the state estimate value of the sub-filter at time k The state covariance estimate value The filtering steps are as follows; (1) Calculate the predicted value of the status (2) Calculate the predicted value P of the state covariance k|k-1 : (3) Calculate the filtering gain value (4) Calculate the status update value (5) Calculate the updated value of the state covariance (6) Calculate the state value after deviation compensation where F and Q represent the state transition matrix and state noise matrix of the target constant velocity motion model, represents the deviation compensation term, and M = [I 2×2 0 2×2 ; In addition to updating the state information of each sub - filter, after the filtering of the sub - filter, distance parameterization also needs to obtain the weights of each interval at the next moment, update and normalize the weight intervals according to the measurement likelihood function; Among them, is the weight of the nth sub-filter at time k-1, that is, the weight before update, is the weight of the nth sub-filter at time k, that is, the weight after update, is the measurement covariance obtained by the nth sub-filter, is the predicted measurement obtained by the nth sub-filter.

4. The method for tracking a maneuvering target under pure angle measurement according to claim 3, wherein Step 3, Removal of sub - filters with small weights, the specific method is: Set the filter weight threshold T m1 , remove the sub - filters whose corresponding weights are less than the weight threshold from the calculation, and normalize the weights of the remaining sub - filters. Assume that the weight of the m - th sub - filter is less than the weight threshold T m1 , then the remaining sub - filters are normalized as follows, is the weight after removing the sub - filters with small weights and then renormalizing; 5. The method for tracking a maneuvering target under pure angle measurement according to claim 3, characterized in that, Step 4, Maneuver detection, the specific method is as follows: Define the maneuver detection factor at time k as: Among them represents the difference between the target angle measurement value and the predicted value in the filter, that is, the filtering innovation, S t =P zz,k|k-1 represents the innovation covariance. If δ t is a variable with white zero-mean covariance S t then I k follows a chi-square distribution with W1 degrees of freedom; Set the maneuver recognition threshold T m2 , if I k < T m2 , it is considered that the target has not maneuvered, and directly output the target state estimation value of the current filter; if I k > T m2 , it is considered that the target has maneuvered, which means that the target innovation estimated at time k, including range, heading, and speed, has deviated from the true target information; Before initialization, mark the only sub-filter as "only", and represent its state, state covariance, and weight as and When it is detected that the target maneuvers, initialize N f sub-filters at time k, each sub-filter having a different target initial heading angle value; the state of the j-th sub-filter at time k is initialized as: Among them and represent the position and velocity components of each axis of the only filter before initialization. φ j = 2πj / N f , 1 ≤ j ≤ N f represents the rotation angle of the target heading after maneuvering. The state covariance of the j-th sub-filter at time k and the weight are initialized as follows: If a re-initialization operation is performed after maneuver detection, the weights and states of the sub-filters at time k are as shown above, and the number of sub-filters is adjusted to N = N f , if a re-initialization operation is not performed after maneuver detection, the sub-filter at time k remains the original single filter, and its weight is 1.

6. A maneuvering target tracking system under pure angle measurement, characterized in that, Based on the maneuvering target tracking method under pure angle measurement described in any one of claims 1 - 5, realize the tracking of maneuvering targets under pure angle measurement.

7. A computer device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein when the processor executes the computer program, based on the maneuvering target tracking method under pure angle measurement according to any one of claims 1-5, the maneuvering target tracking under pure angle measurement is realized.

8. A computer-readable storage medium, on which a computer program is stored, wherein when the computer program is executed by a processor, based on the maneuvering target tracking method under pure angle measurement according to any one of claims 1-5, the maneuvering target tracking under pure angle measurement is realized.

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