A method for tracking a maneuvering target under pure angle measurement

Abstract

The application discloses a pure angle measurement ground mobile target tracking method. The method comprises the following steps: firstly, the observation range of an optical-electric detection system is divided into several subintervals according to the equal ratio principle, the subinterval filter weight, the state and the covariance initial value are calculated under the uniform distribution assumption, the volume Kalman filter is independently operated in each interval, and the subfilter state and the covariance are updated; then, the subfilter weight is updated and the target maneuver is detected based on the measurement likelihood function, and the system robustness is improved through the subfilter strategy; finally, all the subfilters are pruned and combined, and the state information of each subfilter is weighted and fused. The application improves the pure bearing positioning precision of the ground mobile target, greatly improves the universality and real-time performance of the existing pure bearing tracking method, and makes the algorithm applicable to the passive positioning of the future ground target.

Description

Technical Field

[0001] This invention relates to target tracking technology, specifically to a method for tracking a maneuvering target using pure angle measurement. Background Technology

[0002] In recent years, with the rapid development of electronic information technology, electronic warfare and information warfare have become increasingly important in the military field. However, traditional active target location technologies have some problems, such as poor electromagnetic concealment, counter-surveillance, and counter-jamming capabilities due to the need for self-radiated signals, making it difficult to complete missions and ensure self-safety on the battlefield. In contrast, passive tracking systems, as a technology that passively receives target radiation information, have the advantages of strong concealment, small equipment size, long operating range, large coverage area, and good mobility, making them of significant military importance for modern information warfare.

[0003] In ground combat, the single-station localization stage of a passive tracking system plays a crucial role in determining the timing of weapon strikes. However, single-station localization presents two challenges. First, the relationship between angle measurements and target states is non-linear, representing a typical non-linear tracking problem, making simple Kalman filtering methods unsuitable. Second, unlike bistatic localization systems, which can directly utilize the angle information from two observation stations to obtain the target's initial position information through methods such as cross-localization, single-station systems cannot employ this approach. Furthermore, improper selection of initial values ​​can lead to filter divergence or even system failure.

[0004] In current passive tracking systems, single-station localization typically estimates initial information using angle data from several consecutive sampling periods and target motion characteristics, effectively improving the stability of tracking filtering. However, in the context of modern information warfare, this method suffers from limited accuracy, poor versatility, and long initial information estimation time. In particular, it can only estimate initial information for a single, known target motion model, significantly hindering the application development of single-station localization. Furthermore, single-station localization often uses a constant-velocity motion model to model target motion, but when the target maneuvers, the filtering results often exhibit divergent localization errors. To address this issue, researchers have started with the target motion model, employing methods such as interactive multi-model and current statistical models to remodel the target. However, due to the lack of distance information in pure angle measurements, these methods struggle to produce good tracking results. Other researchers have used strong tracking filters for filtering and localizing maneuvering targets, but this easily leads to algorithm instability. Summary of the Invention

[0005] The purpose of this invention is to provide a method for tracking moving targets under pure angle measurement, so as to improve the overall stability and accuracy of single-station positioning.

[0006] The technical solution to achieve the objective of this invention is: a method for tracking a maneuvering target under pure angle measurement, comprising the following steps:

[0007] Step 1: Sub-filter tracking

[0008] The observation station's detection range is divided into multiple sub-intervals according to the principle of equal proportions. Statistical information (mean and standard deviation of the initial distance between the target and the observation station) is calculated for each sub-interval. A sub-filter operates independently for each sub-interval, and the initial state estimates (position and velocity), state covariance, and weights of each sub-filter are calculated based on the sub-interval statistical information. The target angle measurement is input based on sensor information, and the sub-filter state estimates and state covariance are updated within the capacitive Kalman filter framework. The sub-filter weights are updated based on the measurement likelihood function, and the dynamic detection factor is calculated.

[0009] Step 2, Sub-filter Motion Detection

[0010] Based on prior information, a maneuver detection threshold is set. The maneuver detection factor of each sub-filter is compared with the detection threshold. If the maneuver detection factor of a certain sub-filter is greater than the detection threshold, the operation of that sub-filter is terminated and it is replaced with N new sub-filters. The parameters of the new sub-filters are calculated from the parameters and measurement values ​​of the original filters. Otherwise, proceed directly to step three.

[0011] Step 3: Sub-filter trimming and merging

[0012] All sub-filter weights are sorted in descending order. If a sub-filter weight is less than a set weight threshold, the sub-filter is deleted, and the remaining sub-interval filters are normalized. If the total number of sub-filters is greater than the set maximum number of sub-filters, the sub-filters with smaller weights are merged to keep the number of sub-filters within the set range in the next time step.

[0013] Step 4: Acquiring the Status of Maneuvering Targets

[0014] Based on the state estimates and weights of each sub-filter, the target state value (position and velocity) at the current moment is weighted and fused to achieve real-time tracking of the maneuvering target.

[0015] Further, in step 1, sub-filter tracking, the specific method is as follows:

[0016] The detection range is divided into N intervals according to the principle of equal proportions. The detection range of the observation station is (r min r max If ), then the nth subinterval is (r min ρ n-1 r min ρ n ), where the expression for the scaling factor ρ is:

[0017]

[0018] Assuming the initial relative distance between the target and the observation station follows a uniform distribution within the interval, then the mean of the initial distance between the target and the observation station in the nth sub-interval is... with standard deviation They are respectively:

[0019]

[0020]

[0021] By running a sub-filter independently in each sub-interval and combining the angle information obtained at the initial moment, the initial state estimate (position and velocity) of the nth sub-filter can be calculated. Initial state covariance for:

[0022]

[0023]

[0024] Where β0 is the initial angle measurement value, σ v The initial standard deviation of the prior velocity is set according to the target type.

[0025] Distance parameterization requires assigning initial weights to each sub-filter, specifically the weights of the nth sub-filter at the initial time. for:

[0026]

[0027] The capacitive Kalman filter algorithm is used to update the state estimate and state covariance of the nth sub-filter.

[0028] After filtering at each time step, distance parameterization requires updating the sub-filter weights. The weight interval is updated based on the measurement likelihood function and then normalized. The weights of the nth sub-filter at time k are... for;

[0029]

[0030] in, It indicates new information.

[0031] Calculate the motion detection factor of the sub-filter at time k.

[0032]

[0033]

[0034] in, Let represent the information covariance, and α represent the lag coefficient.

[0035] Further, in step 2, sub-filter motion detection, the specific method is as follows:

[0036] Based on prior information, a motion detection threshold U1 is set. If... At that time, it is assumed that the target has not moved; if It is assumed that the target has maneuvered, meaning that the target state estimate at time k has deviated from the target's true state. Upon detecting a maneuver, the operation of this sub-filter is terminated, replaced by N new sub-filters, and the maneuver detection process is paused for τ cycles, where τ is the lag step. The state estimate, state covariance, and weights of the j-th new sub-filter calculated from the n-th sub-filter are as follows:

[0037]

[0038]

[0039]

[0040] Where, β k The measurement value at time k is... This is the velocity estimate at time k.

[0041] Further, in step 3, sub-filter trimming and merging, the specific method is as follows:

[0042] All sub-filters are sorted in descending order based on their weights, and the state estimates of the sub-filters are denoted as follows. State covariance is denoted as The weight is denoted as N k This represents the number of sub-filters. If the weight of a sub-filter is less than the weight threshold U2, the operation of the corresponding sub-filter is terminated, and the weights of the remaining sub-filters are normalized.

[0043] If the total number of sub-filters is greater than the maximum number of filters N max Then, the sub-filters with smaller weights are merged. The filters with indices t=1, ...N are retained. max The sub-filter with index -1, for index t = N max , ...N k The state estimates, state covariance, and weights of the sub-filters are merged according to the following rules:

[0044]

[0045]

[0046]

[0047] in, These represent the state estimates, state covariance, and weights of the merged sub-filters, respectively. This represents the normalized weights of the merged sub-filters. Let $\mathbf{k}$ represent the state estimate, state covariance, and weight of the $t$-th sub-filter after sorting at time $k$.

[0048] Further, in step 4, the status of the maneuvering target is obtained, and the specific method is as follows:

[0049] Based on the weights and state estimates of each sub-filter, the target state information (position and velocity) at time k is determined.

[0050]

[0051] Where, N′ k The total number of sub-filters after trimming and merging at time k.

[0052] A maneuvering target tracking system based on pure angle measurement, which realizes maneuvering target tracking under pure angle measurement.

[0053] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it performs maneuvering target tracking under pure angle measurement based on the aforementioned method for tracking maneuvering targets under pure angle measurement.

[0054] A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it realizes the tracking of a maneuvering target under pure angle measurement based on any one of the methods described above.

[0055] Compared with existing technologies, the significant advantages of this invention are: (1) It combines the distance parameterized volumetric Kalman filter algorithm with the maneuver detection concept, reducing the impact of unknown initial distance on tracking accuracy and improving system robustness and tracking accuracy. The target positioning error after filtering convergence is less than 30m, which well meets the actual ground combat requirements; (2) By using the pruning and merging algorithm, the computational complexity is reduced, ensuring filtering stability. It well meets the real-time requirements of actual combat; (3) The maneuvering target pure azimuth tracking method proposed in this invention has a tracking error far lower than that of general maneuvering pure azimuth tracking methods after the target maneuvers, which significantly improves the universality of target tracking, making the engineering application of this algorithm in future ground target pure azimuth tracking systems possible. Attached Figure Description

[0056] Figure 1 This is a schematic diagram of the overall process of the method for tracking moving targets under pure angle measurement according to the present invention.

[0057] Figure 2 This is a schematic diagram of the coordinate system for sensor azimuth angle measurement.

[0058] Figure 3 This is a schematic diagram of the movement trajectory of the observation station and the target.

[0059] Figure 4 This is a schematic diagram of the weight update of MD-RPCKF when the measurement error is small.

[0060] Figure 5 This is a schematic diagram of the weight update of MD-RPCKF when the measurement error is large.

[0061] Figure 6 This is a schematic diagram of the root mean square error of the position of each algorithm when the measurement error is small.

[0062] Figure 7 This is a schematic diagram of the position standard deviation of each algorithm when the measurement error is small.

[0063] Figure 8 This is a schematic diagram of the root mean square error of the position of each algorithm when the measurement error is large.

[0064] Figure 9 This is a schematic diagram of the position standard deviation of each algorithm when the measurement error is large. Detailed Implementation

[0065] Combination Figure 1 The present invention provides a method for tracking moving targets under pure angle measurement, the specific steps of which are as follows:

[0066] Step 1: Sub-filter tracking

[0067] The observation station's detection range is divided into multiple sub-intervals according to the principle of equal proportions. Statistical information (mean and standard deviation of the initial distance between the target and the observation station) is calculated for each sub-interval. A sub-filter operates independently for each sub-interval, and the initial state estimates (position and velocity), state covariance, and weights of each sub-filter are calculated based on the sub-interval statistical information. Based on the target angle measurement input from the sensor, the sub-filter state estimates and state covariance are predicted and updated within the capacitive Kalman filter framework. The sub-filter weights are updated based on the measurement likelihood function, and the dynamic detection factor is calculated.

[0068] Step 1.1: Divide the detection range of the observation station into multiple sub-intervals according to the principle of equal ratio, and calculate the statistical information of the sub-intervals (mean and standard deviation of the initial distance between the target and the observation station); run a sub-filter independently in each sub-interval, and calculate the state estimate (position and velocity), state covariance and weight of each sub-filter at the initial time based on the statistical information of the sub-intervals.

[0069] Step 1.1.1: Divide the detection range of the observation station into multiple sub-intervals according to the principle of equal ratio, and calculate the statistical information of the sub-intervals (mean and standard deviation of the initial distance between the target and the observation station);

[0070] Let the detection range of the observation station be (r) min r max If ), then the nth subinterval is (r min ρ n-1 r max ρ n ), where the expression for the scaling factor ρ is:

[0071]

[0072] Assume that the initial relative distance between the target and the observation station follows a uniform distribution within the interval, and thus obtain the sub-interval statistical information (mean and standard deviation of the initial distance between the target and the observation station);

[0073] The mean of the initial distance between the target and the observation station within this interval with standard deviation They are respectively:

[0074]

[0075]

[0076] Step 1.1.2: Run a sub-filter independently in each sub-interval, and calculate the state estimate (position and velocity), state covariance and weights of each sub-filter at the initial time based on the sub-interval statistics;

[0077] Each sub-interval runs an independent sub-filter, and the initial state estimate of the nth sub-filter is calculated based on the sub-interval statistics. Initial state covariance for:

[0078]

[0079]

[0080] Where β0 is the initial angle measurement value, σ v The initial standard deviation of the prior velocity is set according to the target type.

[0081] Distance parameterization requires assigning initial weights to each sub-filter, and the initial weights of the nth sub-filter are... for

[0082]

[0083]

[0084] Step 1.2: Based on the sensor information, input the target angle measurement value, and predict and update the sub-filter state estimate and state covariance under the capacitive Kalman filter framework;

[0085] The state estimate and state covariance of the nth sub-filter are calculated using capacitive Kalman filtering. During the filtering process, the innovation and innovation covariance of each sub-filter are obtained for weight updates. The innovation and innovation covariance of the nth sub-filter at time k are expressed as follows:

[0086] Step 1.3: Update the sub-filter weights based on the measurement likelihood function and calculate the dynamic detection factor;

[0087] Step 1.3.1: Update the sub-filter weights based on the measurement likelihood function. The specific algorithm is as follows:

[0088] After filtering at each time step, distance parameterization requires updating the sub-filter weights. The weight interval is updated based on the measurement likelihood function and then normalized. The weights of the nth sub-filter at time k are... for;

[0089]

[0090] Step 1.3.2: Calculate the sub-filter motion detection factor based on the measurement likelihood function. The specific algorithm is as follows:

[0091] Calculate the motion detection factor of the nth sub-filter at time k. The formula is as follows:

[0092]

[0093]

[0094] in, 'a' is an intermediate variable, and 'a' represents the lag coefficient.

[0095] Step 2: Sub-filter motion detection

[0096] Based on prior information, a maneuver detection threshold is set. The maneuver detection factor of each sub-filter is compared with the detection threshold. If the maneuver detection factor of a certain sub-filter is greater than the detection threshold, the operation of that sub-filter is terminated and it is replaced with N new sub-filters. The parameters of the new sub-filters are calculated from the parameters and measurement values ​​of the original filters. Otherwise, proceed directly to step three.

[0097] Based on prior information, a motion detection threshold U1 is set. If... At that time, it is assumed that the target has not moved; if It is assumed that the target has already maneuvered, which means that the target state estimate at time k has deviated from the target's true state. When the target maneuver is detected, the operation of this sub-filter is terminated, and it is replaced with N new sub-filters. The maneuver detection process is paused for τ cycles, where τ is the lag step.

[0098] The parameters of the new sub-filter are calculated from the parameters of the original filter and the measurements at the current time. The parameters used at time k include the state estimates and weights of the original sub-filter (the nth sub-filter), expressed as follows: Motor detection factor Speed ​​estimate and the measured value β k ;

[0099] The parameters of the j-th new sub-filter, calculated from the n-th sub-filter, are as follows:

[0100]

[0101]

[0102]

[0103] in, Let N represent the state estimate, state covariance, and weight of the j-th new sub-filter calculated from the n-th sub-filter, respectively, where j≤N.

[0104] Step 3: Sub-filter trimming and merging

[0105] All sub-filter weights are sorted in descending order. If a sub-filter weight is less than a set weight threshold, the sub-filter is deleted, and the remaining sub-interval filters are normalized. If the total number of sub-filters is greater than the set maximum number of sub-filters, sub-filters with smaller weights are merged to keep the number of sub-filters within the set range in the next time step.

[0106] All sub-filters are sorted in descending order based on their weights, and the state estimates of the sub-filters are denoted as follows. State covariance is denoted as The weight is denoted as N k The number of sub-filters; if the weight of a sub-filter is less than the weight threshold U2, the operation of the corresponding sub-filter is terminated, and the weights of the remaining sub-filters are normalized.

[0107] If the total number of sub-filters is greater than the maximum number of filters N max Then, the sub-filters with smaller weights are merged. The filters with indices t=1, ...N are retained. max The sub-filter with a value of -1, for the index t = N max , ...N k The state estimates, state covariance, and weights of the sub-filters are merged according to the following rules:

[0108]

[0109]

[0110]

[0111] in, This represents the normalized weights of the merged sub-filters.

[0112] Step 4: Acquiring the Status of Maneuvering Targets

[0113] Based on the state estimates and weights of each sub-filter, the target state value (position and velocity) at time k is weighted and fused to output the target state value at time k. To enable real-time tracking of moving targets.

[0114]

[0115] in, Let N′ represent the state estimate and weight of the nth sub-filter after sorting at time k, respectively. k The total number of sub-filters after trimming and merging at time k.

[0116] This invention also proposes a maneuvering target tracking system under pure angle measurement, which realizes maneuvering target tracking under pure angle measurement based on the aforementioned maneuvering target tracking method.

[0117] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it performs maneuvering target tracking under pure angle measurement based on the aforementioned method for tracking maneuvering targets under pure angle measurement.

[0118] A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it realizes the tracking of a maneuvering target under pure angle measurement based on any one of the methods described above.

[0119] Example

[0120] The effects of the present invention are further illustrated by the following simulation experiments.

[0121] 1. Simulation conditions

[0122] The observation station's detection range is (500m, 4000m). The initial number of sub-intervals is set to N = 4, the sampling time is T = 0.1s, the maneuver detection threshold is set to U1 = 100, and the sub-filter weight pruning threshold is set to U2 = 0.01. The hysteresis coefficient is set to a = 0.1, and the maximum number of filters is set to N. max =8. Design two simulation scenarios with different measurement noise levels, e1 = 1 mrad and e2 = 2.5 mrad, respectively. Perform 100 Monte Carlo simulations.

[0123] The root mean square error of the position and the deviation standard are used to evaluate the simulation performance, defined as follows:

[0124]

[0125]

[0126] in, and Let represent the estimated and actual positions of the target at time k in the i-th Monte Carlo trial, respectively, where M is the total number of Monte Carlo trials. The specific motion states of the observation station are shown in Table 1, the specific movement states of the target are shown in Table 2, and the trajectories of the target and the observation station are shown in... Figure 3 As shown.

[0127] Table 1. Motion Status of Observation Stations

[0128]

[0129] Table 2 Target Motion Status

[0130]

[0131] 2. Simulation Content and Result Analysis

[0132] The proposed range-parameterized ductile Kalman filter (MD-RPCKF) algorithm for maneuver detection is compared with the range-parameterized ductile Kalman filter (RPCKF) algorithm and the strong tracking range-parameterized ductile Kalman filter (ST-RPCKF) algorithm through simulation. First, the stability of the algorithm is evaluated based on the changes in the sub-filter weights; the faster the convergence of the sub-filter weights, the more stable the designed algorithm. The simulation results of weight changes are as follows: Figure 4 and Figure 5 As shown in the figure. Next, the tracking accuracy of the algorithm is evaluated based on position error, including root mean square error and standard deviation. The algorithm's position tracking accuracy for moving targets is verified under conditions of small and large measurement errors, respectively. The simulation results are shown in the figure. Figures 6 to 9 As shown.

[0133] 2.1 Weight Changes

[0134] The changes in the interval weights of each algorithm are as follows Figure 4 and Figure 5 As shown. From Figure 4 and Figure 5 It can be seen that the initial weight of each sub-filter is proportional to the size of the sub-interval. This proportional weighting more reasonably reflects the relationship between the sub-interval and the weight. The filtering process updates the weights of each sub-interval filter using the measurement likelihood function. The weights of sub-filters with larger initial value deviations gradually decrease, while the weights of sub-filters with initial values ​​close to the true initial position of the target gradually increase. When the measurement error is small, the weights of each sub-filter tend to stabilize within 10 seconds. The weights of sub-filters with initial values ​​close to the true initial position of the target are 1, and the operation of the remaining sub-filters is terminated, with weights of 0. The computational cost of the algorithm is only that of a single sub-filter; even with a larger filtering error, the weights of each sub-filter can still tend to stabilize within 10 seconds.

[0135] 2.2 Position Error

[0136] 2.2.1 When the angle measurement error is small

[0137] When the measurement error is 1 mrad, the root mean square error and standard deviation of the position for each algorithm are as follows: Figure 6 and Figure 7 As shown. From Figure 6 and Figure 7It can be seen that before the target maneuvers, MD-RPCKF exhibits similar performance to other filters. After the target maneuvers, the traditional RPCKF algorithm suffers from significant bias due to filter model mismatch, which cannot be corrected in subsequent filtering processes. ST-RPCKF improves the robustness of the system by amplifying the prediction covariance, but it cannot control the amplification factor, resulting in a larger error compared to the other two algorithms. MD-RPCKF corrects the state estimation of the maneuvering target by generating new sub-filters, compensating for the bias caused by model mismatch, and achieving the lowest tracking error. As the observation station maneuvers, the tracking error of MD-RPCKF gradually decreases, and the tracking accuracy converges to the level before the target maneuvers and remains stable. Although the filtering error of RPCKF also decreases, it never converges and even exhibits divergence in the filtering results. Although ST-RPCKF shows a significant reduction in tracking error, its tracking accuracy remains lower than that of MD-RPCKF.

[0138] The root mean square error of the three algorithms at 200s is shown in Table 3.

[0139] Table 3. Root mean square error of position at 200s for different algorithms (e 1＝1mrad )

[0140]

[0141] 2.2.2 When the angle measurement error is large

[0142] The measurement error is 2.5. mrad At that time, the root mean square error and standard deviation of the position of each algorithm are as follows: Figure 8 and Figure 9 As shown. From Figure 8 and Figure 9 It can be seen that the errors of both ST-RPCKF and MD-RPCKF increase with the increase of measurement noise. The maneuver verification time of MD-RPCKF is delayed, but the filtering error decreases rapidly to convergence. Compared with the case where the measurement error is small, the tracking accuracy of ST-RPCKF is greatly affected. The root mean square error of position and standard deviation decrease and then gradually increase, and the final filtering result diverges. The root mean square error of position of the three algorithms at 200s is shown in Table 4.

[0143] Table 4. Root mean square error of position at 200s for different algorithms (e 2＝2.5mrad )

[0144]

[0145] In summary, to improve the accuracy and versatility of pure azimuth ground maneuvering target tracking, this invention proposes a maneuvering target tracking method based on pure angle measurement. Simulation results demonstrate the effectiveness and feasibility of this method, enabling it to be used in passive localization of ground targets.

Claims

1. A method for tracking a maneuvering target using pure angle measurement, characterized in that, Includes the following steps: Step 1: Sub-filter tracking The observation station's detection range is divided into multiple sub-intervals according to the principle of equal proportions. Statistical information for each sub-interval is calculated, namely the mean and standard deviation of the initial distance between the target and the observation station. Each sub-interval operates an independent sub-filter. Based on the sub-interval statistical information, the initial state estimate of each sub-filter is calculated, namely the state estimate (position and velocity), as well as the state covariance and weights. Based on the target angle measurement value input from the sensor, the sub-filter state estimate and state covariance are updated within the capacitive Kalman filter framework. The sub-filter weights are updated based on the measurement likelihood function, and the dynamic detection factor is calculated. Step 2, Sub-filter Motion Detection Based on prior information, a maneuver detection threshold is set. The maneuver detection factor of each sub-filter is compared with the detection threshold. If the maneuver detection factor of a certain sub-filter is greater than the detection threshold, the operation of that sub-filter is terminated and it is replaced with N new sub-filters. The parameters of the new sub-filters are calculated from the parameters and measurement values ​​of the original filters. Otherwise, proceed directly to step 3. Step 3: Sub-filter trimming and merging All sub-filter weights are sorted in descending order. If a sub-filter weight is less than a set weight threshold, the sub-filter is deleted, and the remaining sub-interval filters are normalized. If the total number of sub-filters is greater than the set maximum number of sub-filters, the sub-filters with smaller weights are merged to keep the number of sub-filters in the next time step within the set range. Step 4: Acquiring the Status of Maneuvering Targets Based on the state estimates and weights of each sub-filter, the target state value at the current moment is output by weighted fusion, thereby realizing real-time tracking of maneuvering targets.

2. The method for tracking a maneuvering target under pure angle measurement according to claim 1, characterized in that, Step 1, sub-filter tracking, the specific method is as follows: The detection range is divided according to the principle of proportionality. The detection range of the observation station is [number] intervals. Then the first The number of sub-intervals is Among them, the scaling factor The expression is: ； Assuming the initial relative distance between the target and the observation station follows a uniform distribution within the interval, then in the th... The average initial distance between the target and the observation station within each sub-interval with standard deviation They are respectively: ； ； Run a sub-filter independently in each sub-interval, and combine the angle information obtained at the initial time to calculate the first... Initial state estimates of each sub-filter Initial state covariance for: ； ； in, The angle measurement value at the initial moment. The initial standard deviation of the prior velocity is set according to the target type; Distance parameterization requires assigning initial weights to each sub-filter, starting at the initial time step. The weights of each sub-filter for: ； Update the first digit using the capacitive Kalman filter algorithm. The state estimates and state covariance values ​​of each sub-filter are obtained during the filtering process. The innovation and innovation covariance of each sub-filter are then used for weight updates. Time of the first The innovation and innovation covariance of each sub-filter are respectively expressed as: , ; After filtering at each time step, distance parameterization requires updating the sub-filter weights. The weight intervals are updated and normalized based on the measurement likelihood function. Sub-filters Time weight for; ； calculate Motion detection factor of time-phase filter : ； ； in, This represents the lag coefficient.

3. The method for tracking a moving target under pure angle measurement according to claim 1, characterized in that, Step 2, sub-filter motion detection, the specific method is as follows: Setting the motion detection threshold based on prior information ,like At that time, it is assumed that the target has not moved; if It is believed that the target has already maneuvered, which means The estimated state of the target at any given time has deviated from the true state of the target; Once a target is detected to be maneuvering, the operation of that sub-filter is terminated, it is replaced with N new sub-filters, and the maneuver detection process is paused. One cycle, The step size is the lag step size; The parameters of the new sub-filter are calculated from the parameters of the original filter and the measurements at the current time. The parameters used at each time point include the original first time point. State estimates of each sub-filter Weight , motor detection factor Speed ​​estimates and measured values ; By the The first sub-filter calculated to obtain the first The parameters of the new sub-filter are as follows: ； ； ； in, They represent the first The first sub-filter calculated to obtain the first The state estimates, state covariance, and weights of the new sub-filters .

4. The method for tracking a maneuvering target under pure angle measurement according to claim 1, characterized in that, Step 3, sub-filter trimming and merging, the specific method is as follows: All sub-filters are sorted in descending order based on their weights, and the state estimates of the sub-filters are denoted as follows. The state covariance is denoted as The weight is denoted as , The number of sub-filters; if the weights of the sub-filters are less than the weight threshold. If the operation of the corresponding sub-filter is terminated, the weights of the remaining sub-filters are normalized. If the total number of sub-filters is greater than the maximum number of filters Then, the sub-filters with smaller weights are merged, retaining those with the following sequence numbers. The sub-filters, for the index of The state estimates, state covariance, and weights of the sub-filters are merged according to the following rules: ； ； ； in, These represent the state estimates, state covariance, and weights of the merged sub-filters, respectively. This represents the normalized weights of the merged sub-filters. They represent After sorting by time, the first The state estimates, state covariance, and weights of each sub-filter.

5. The method for tracking a maneuvering target under pure angle measurement according to claim 1, characterized in that, Step 4, Obtain the status of the maneuvering target, the specific method is as follows: Based on the weights and state estimates of each sub-filter, determine Target state information at any given time ; ； in, They represent After sorting by time, the first The state estimates and weights of each sub-filter for The total number of sub-filters after trimming and merging at any given time.

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

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

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

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