A Distributed Multi-Station Track Plotting Method for High-Precision Seamless Sensing in Cellular Networks

Abstract

The present invention provides a distributed multi-station track plotting method for high-precision seamless sensing in a cellular network, including: Step 1, establishing a target motion model, calculating the measurement error bound according to the signal-to-noise ratio of the base stations, and performing extended Kalman filtering on the measurement data of each base station to obtain each local track; Step 2, using the track of the original base station's private coverage area to assist in reference measurement for track initiation, and obtaining a reference track through extended Kalman filtering; Step 3, performing track fusion on the tracks in the overlapping coverage area of each base station to obtain a high-precision track in the overlapping coverage area; updating the track of the original base station's private coverage area; connecting the updated track of each base station's private coverage area and the track in the overlapping coverage area after fusion to obtain the overall situation of the target track. Using this method can achieve the complete tracking of cross-base station targets, solve the problems of intermittent and insufficient accuracy of the tracks of low-altitude targets detected by multiple base stations at different times, and greatly enhance the practicability and reliability of the system.

Description

Technical Field

[0001] The present invention belongs to the field of target tracking, and in particular relates to a distributed multi-station track drawing method for high-precision seamless perception of cellular networks. Background Art

[0002] In modern urban environments, drones and other micro-aircraft play an increasingly important role in logistics distribution, environmental monitoring, emergency response and other fields due to their fast, compact and highly maneuverable nature. They are of great significance to the development of the low-altitude economy. The challenge that follows is how to effectively detect and track these high-speed moving targets. Traditional single-base station tracking systems have many limitations. First, incomplete target tracking is a significant problem. Due to the limited coverage of a single base station, when the target flies out of the coverage area, tracking will be lost, which cannot meet the needs of large-scale monitoring, especially in complex environments such as cities, where buildings and other obstacles will greatly limit the propagation and reception of signals. In addition, different base stations often use different signal frequencies, which leads to different target data rates, making it difficult to effectively integrate and analyze. In the distributed multi-station detection and tracking scenario, the overlapping area is located at the marginal area of the detection power of each base station, the target signal-to-noise ratio decreases, and the base station loses the measurement accuracy of micro-targets. In addition, the design of the communication base station itself takes into account the wide coverage characteristics, which makes its measurement accuracy limited, especially when using wide beam coverage, the angle measurement accuracy error is large. This will lead to difficulties in starting the track in the overlapping coverage area, and the filter convergence will take a long time, or even fail to converge in the entire overlapping area. Summary of the invention

[0003] Purpose of the invention: The technical problem to be solved by the present invention is to provide a distributed multi-station track drawing method for high-precision seamless perception of cellular networks in view of the shortcomings of the prior art. Based on the target observation data and error bounds of each base station, the problem of incomplete target track tracking across base stations in the city is solved.

[0004] The present invention comprises the following steps:

[0005] Step 1: Obtain the total number of base stations, base station measurement data and the initial state of the target, establish a target motion model, calculate the measurement error bound based on the signal-to-noise ratio of the base station, and perform extended Kalman filtering on the measurement data of each base station to obtain each local track;

[0006] Step 2: In a given overlapping coverage area, the tracks of the overlapping coverage areas of each base station are aligned in time and space and then associated. According to the track measurement values and error bounds of the overlapping coverage areas of each base station that have been successfully associated, the reference measurement is obtained through maximum likelihood estimation. The track is started using the auxiliary reference measurement of the private coverage area track of the original base station, and the reference track is obtained through extended Kalman filtering.

[0007] Step 3: Calculate the reference error between the reference track and the tracks in the overlapping coverage areas of the base stations successfully associated in Step 2. Dynamically allocate weights according to the error, perform track fusion on the tracks in the overlapping coverage areas of each base station to obtain a high-precision track for the overlapping coverage area; use the fused track for the overlapping coverage area to assist the next base station in re-filtering and update the private coverage area track of the base station; connect the updated private coverage area tracks of each base station and the fused track for the overlapping coverage area to obtain the overall situation of the target track.

[0008] Step 1 includes: establishing the following linear system:

[0009] (1),

[0010] (2),

[0011] where represents the state vector at time represents the measurement vector at time represents the state transition matrix at time represents the measurement matrix at time represents the process noise distribution matrix at time represents the process noise, represents the measurement noise, and are both zero-mean Gaussian white noises;

[0012] Step 1-2: Establish a target motion model:

[0013] For a uniform linear motion model, the state vector , the symbol represents the transpose; the state transition is as follows:

[0014] (3),

[0015] where represents the position of the target on the axis at time represents the position of the target on the axis at time represents the velocity of the target on the axis at time represents the velocity of the target on the axis at time Indicates that the target is at a random variation in the axis speed, Indicates that the target is at a random variation in the axis speed, Indicates the sampling interval;

[0016] Steps 1 - 3, calculate the measurement error bound according to the signal - to - noise ratio of each base station:

[0017] The standard deviation of the range measurement error is:

[0018] (4),

[0019] where represents the speed - of - light constant, represents the receiver bandwidth, represents the signal - to - noise ratio of the base station;

[0020] The standard deviation of the azimuth measurement error is:

[0021] (5),

[0022] where represents the antenna beamwidth for measuring the azimuth, represents the monopulse slope;

[0023] Step 1 - 4, perform an extended Kalman filter on the measurements obtained by the base station.

[0024] Step 1 - 4 includes: The dynamic equation and measurement equation of the system satisfy Gaussian conditions, expressed as:

[0025] (6),

[0026] (7),

[0027] where the non - linear functions and represent the dynamic model function and the measurement model function respectively, the process noise and the measurement noise both follow Gaussian distributions, the covariance of the process noise is and the covariance of the measurement noise is ;

[0028] The one - step prediction of the state is expressed as:

[0029] (8),

[0030] where is the state prediction at time At the moment, the state prediction for the moment;

[0031] The one-step prediction of the covariance is expressed as:

[0032] (9),

[0033] where is the state estimation covariance at is the state estimation covariance prediction for the moment at is the Jacobian matrix of the vector , is the transpose matrix of ;

[0034] The measurement predicted value , and the covariance of the measurement predicted value is expressed as:

[0035] (10),

[0036] where is the Jacobian matrix at the moment, is the measurement predicted value for the moment at is the transpose matrix of , is the information covariance matrix at the moment;

[0037] The gain is:

[0038] (11),

[0039] where is the filtering gain at is the inverse matrix of ;

[0040] The state update equation is:

[0041] (12),

[0042] where is the state update at is the measurement value at

[0043] The covariance update equation is as follows:

[0044] (13),

[0045] where is an identity matrix of the same dimension as the covariance, is the transpose matrix;

[0046] Repeat steps 1 - 4 until the state update is completed to obtain the local tracks of each base station , where is the total number of base stations, is the base station the number of tracks.

[0047] Step 2 includes:

[0048] Step 2 - 1, transfer the local tracks of each base station filtered in step 1 to the unified rectangular coordinate system through spatial alignment, and then perform time alignment for interpolation and extrapolation of the overlapping coverage tracks of each base station;

[0049] Step 2 - 2, perform weighted track association on the overlapping coverage area tracks of each base station after spatio - temporal alignment in step 2 - 1:

[0050] Set , for two base stations, namely the first base station and the second base station, use the following formula for the test statistic:

[0051] (14),

[0052] where represents the state estimate of the th target of the first base station at time represents the state estimate of the th target of the second base station at time represents the error covariance of the th target of the first base station at time represents the error covariance of the th target of the second base station at time; if is lower than a certain threshold obtained using the chi - square distribution , then it is determined that the th target of the first base station and the th target of the second base station are the same target, that is, the th track of the first base station and the th track of the second base station are associated;

[0053] Step 2-3: For the track measurement information in the overlapping coverage areas of the associated base stations, calculate the reference measurement according to the error bound through maximum likelihood estimation:

[0054] (15),

[0055] where denotes the likelihood function, denotes the probability density function of the measurement value of the first track in the successfully associated track pair, denotes the probability density function of the measurement value of the second track in the successfully associated track pair, where the probability density function of each measurement value is expressed as:

[0056] (16),

[0057] where denotes the track the position of the measurement value on the axis in the rectangular coordinate system, denotes the track the position of the measurement value on the axis in the rectangular coordinate system, denotes the track the distance measurement error of the measurement value in the polar coordinate system, denotes the track the measurement error of the azimuth angle of the measurement value in the polar coordinate system, denotes the track the distance of the measurement value in the polar coordinate system, denotes the track the azimuth angle of the measurement value in the polar coordinate system, denotes the track the position of the reference measurement on the axis in the rectangular coordinate system, denotes the track the position of the reference measurement on the axis in the rectangular coordinate system, denotes the track the distance of the reference measurement in the polar coordinate system, denotes the track the azimuth angle of the reference measurement in the polar coordinate system; exp denotes the natural exponential function;

[0058] Step 2-4: Adopt the method in Step 1-4 to perform extended Kalman filtering on the reference measurement obtained in Step 2-3 to obtain the reference track filtering value of the target (The target i here refers to the target i confirmed after the successful association of track i and track j. That is, two successfully associated tracks determine a target. The reference measurement and reference track are also in reference to this determined target.)

[0059] Step 3 includes:

[0060] Step 3-1, calculate the reference error between the reference track and the tracks in the overlapping coverage area of each base station successfully associated in Step 2-2. For the target determined by the successful track association , the formula is:

[0061] (17),

[0062] Where represents the filtering value of the th target detected by the base station at time represents the filtering value of the reference track of the th represents the reference error between the track in the overlapping coverage area of the th target of the base station at time and the reference track;

[0063] Step 3-2, perform normalization processing on the reference error of the target :

[0064] (18),

[0065] Where represents the weight participated by the base station when performing state fusion on the th

[0066] Step 3-3, perform dynamic weighted fusion on the tracks in the overlapping coverage area of each base station successfully associated in Step 2-2, and perform weighted accumulation on the inverse of the covariance matrix and the state vector of the target :

[0067] (19),

[0068] (20),

[0069] Where, represents the weighted accumulation of the inverse of the covariance matrix of the track in the overlapping coverage area of the target detected by each base station at time, represents Base station at a certain moment Detected target Inverse of the covariance matrix of denotes Weighted accumulation of the track state vectors of the detected targets at each base station at a certain moment in the overlapping coverage area denotes Base station at a certain moment Detected target Track state vector in the overlapping coverage area;

[0070] Step 3-4, calculate the fused error covariance matrix and state estimate;

[0071] Step 3-5, if the target flies from the overlapping coverage area into the private coverage area of a base station, then use the fused error covariance matrix and state estimate in Step 3-4 to assist the base station in re-filtering and updating the track in the private coverage area of the base station; connect the updated tracks in the private coverage area of each base station and the track in the overlapping coverage area after fusion to obtain the overall situation of the target track.

[0072] In Step 3-4, the following formula is used to calculate the fused error covariance matrix and state estimate:

[0073] (21),

[0074] (22),

[0075] wherein, denotes Fused error covariance matrix of the target at a certain moment , denotes Fused state estimate of the target at a certain moment .

[0076] The present invention also provides an electronic device, including a processor and a memory, where the memory stores program codes, and when the program codes are executed by the processor, the processor is caused to execute the steps of the method.

[0077] The present invention also provides a storage medium, storing a computer program or instruction, and when the computer program or instruction runs on a computer, the steps of the method are executed.

[0078] Beneficial effects: The method of the present invention integrates measurement data from multiple base stations, estimates the measurement error bound according to the signal-to-noise ratio of the base stations to obtain the target local track and the reference track, dynamically allocates weight coefficients in the overlapping coverage area to weight and fuse the target track in the overlapping coverage area, realizes the complete track drawing of the cross-base station target, not only expands the spatio-temporal coverage range of the communication base station detection, but also improves the tracking accuracy. Based on the advantages of 5G communication base stations and the technology of communication and sensing integration, the present invention proposes a distributed multi-station track drawing method for high-precision seamless sensing in cellular networks, which makes full use of the existing 5G base station infrastructure, realizes the integration of communication and sensing functions, and provides strong technical support for the construction of the low-altitude economy. Description of the Drawings

[0079] Figure 1 It is a distributed multi-station detection architecture for high-precision seamless sensing in cellular networks.

[0080] Figure 2 It is the target track diagram under the tracking of the base station in the solution of the present invention.

[0081] Figure 3 It is the target reference track diagram obtained based on the error bound and the measurements of two base stations in the solution of the present invention.

[0082] Figure 4 It is the fused track diagram in the solution of the present invention.

[0083] Figure 5 It is the error comparison diagram between the solution of the present invention and the traditional fusion algorithm. Detailed Embodiments

[0084] The following further specifically describes the present invention in conjunction with the drawings and specific embodiments, and the above and / or other advantages of the present invention will become clearer.

[0085] The embodiment of the present invention provides a distributed multi-station track drawing method for high-precision seamless sensing in cellular networks, including the following steps:

[0086] Step 1, obtain the total number of base stations, the base station measurement data and the target initial state, establish a target motion model, calculate the measurement error bound according to the signal-to-noise ratio of the base stations, and perform extended Kalman filtering on the measurement data of each base station to obtain each local track;

[0087] Step 2, in the given overlapping coverage area, align the spatio-temporal of the tracks of each base station in the overlapping coverage area and then perform association. According to the measurement values and error bounds of the tracks of each base station in the overlapping coverage area with successful association, obtain the reference measurement through maximum likelihood estimation, use the private coverage area track of the original base station to assist the reference measurement for track initiation, and obtain the reference track through extended Kalman filtering;

[0088] Step 3: Calculate the reference error between the reference track and the tracks in the overlapping coverage areas of the base stations successfully associated in Step 2. Dynamically allocate weights according to the error, perform track fusion on the tracks in the overlapping coverage areas of each base station to obtain a high-precision track in the overlapping coverage area; use the fused track in the overlapping coverage area to assist the next base station in re-filtering and update the private coverage area track of the base station; connect the updated private coverage area tracks of each base station and the fused track in the overlapping coverage area to obtain the overall situation of the target track.

[0089] Step 1 includes:

[0090] Step 1-1: Establish the following linear system:

[0091] (1),

[0092] (2),

[0093] where represents the state vector at represents the measurement vector at represents the state transition matrix at represents the measurement matrix at represents the process noise distribution matrix at represents the process noise, represents the measurement noise, and are both zero-mean Gaussian white noises;

[0094] Step 1-2: Establish a target motion model:

[0095] For a uniform linear motion model, the state vector describing the system dynamic characteristics, the symbol represents the transpose; the state transition is as follows:

[0096] (3),

[0097] where represents the position of the target on the axis at represents the position of the target on the axis at represents the position of the target on the axis at represents the position of the target on the The speed of the axis, indicating that the target is at a random variation of the axis speed, indicating that the target is at a random variation of the axis speed, indicating the sampling interval;

[0098] Steps 1 - 3: Calculate the measurement error bound according to the signal - to - noise ratio of each base station:

[0099] The standard deviation of the range measurement error is:

[0100] (4),

[0101] where represents the speed of light constant, represents the receiver bandwidth, represents the signal - to - noise ratio of the base station;

[0102] The standard deviation of the azimuth measurement error is:

[0103] (5),

[0104] where represents the antenna beam width for measuring the azimuth, represents the monopulse slope;

[0105] Step 1 - 4: Perform extended Kalman filtering on the measurements obtained by the base stations.

[0106] Step 1 - 4 includes: The dynamic equation and measurement equation of the system satisfy the Gaussian condition, expressed as:

[0107] (6),

[0108] (7),

[0109] where the nonlinear functions and represent the dynamic model function and measurement model function respectively, the process noise and the measurement noise both follow the Gaussian distribution, the covariance of the process noise is and the covariance of the measurement noise is ;

[0110] The one - step prediction of the state is expressed as:

[0111] (8),

[0112] where For state prediction at time For state prediction at time ;

[0113] The one-step prediction of the covariance is expressed as:

[0114] (9),

[0115] where is the state estimation covariance at time is the predicted state estimation covariance at time ; is the Jacobian matrix of the vector , is the transpose matrix of ;

[0116] The predicted measurement value , and the covariance of the predicted measurement value is expressed as:

[0117] (10),

[0118] where is the Jacobian matrix at time , is the predicted measurement value at time ; is the transpose matrix of , is the information covariance matrix at time ;

[0119] The gain is:

[0120] (11),

[0121] where is the filtering gain at time is the inverse matrix of ;

[0122] The state update equation is:

[0123] (12),

[0124] where is the state update at time is the measurement value at time

[0125] The covariance update equation is as follows:

[0126] (13),

[0127] where is an identity matrix of the same dimension as the covariance, is the transpose matrix of;

[0128] Repeat steps 1 - 4 until the state update is completed to obtain the local tracks of each base station , where is the total number of base stations, is the base station the number of tracks of.

[0129] Step 2 includes:

[0130] Step 2 - 1, transfer the local tracks of each base station filtered in step 1 to the unified rectangular coordinate system through spatial alignment, and then perform time alignment for interpolation and extrapolation of the overlapping coverage tracks of each base station;

[0131] Step 2 - 2, perform weighted track association on the overlapping coverage area tracks of each base station after spatio - temporal alignment in step 2 - 1:

[0132] Set , for two base stations, namely the first base station and the second base station, use the following formula for the test statistic:

[0133] (14),

[0134] where represents the state estimate value of the th target of the first base station at time represents the state estimate value of the th target of the second base station at time represents the error covariance of the th target of the first base station at time represents the error covariance of the th target of the second base station at time; if is lower than a certain threshold obtained using the chi - square distribution , then it is determined that the th target of the first base station and the th target of the second base station are the same target, that is, the rd track of the first base station and the Track association;

[0135] Step 2-3: For the track measurement information in the overlapping coverage area of each base station with successful association, calculate the reference measurement according to the error bound through maximum likelihood estimation:

[0136] (15),

[0137] where represents the likelihood function, represents the probability density function of the measurement value of the first track in the successfully associated track pair, represents the probability density function of the measurement value of the second track in the successfully associated track pair, where the probability density function of each measurement value is expressed as:

[0138] (16),

[0139] where represents the track the position of the measurement value on the axis in the rectangular coordinate system, represents the track the position of the measurement value on the axis in the rectangular coordinate system, represents the track the distance measurement error of the measurement value in the polar coordinate system, represents the track the measurement error of the azimuth angle of the measurement value in the polar coordinate system, represents the track the distance of the measurement value in the polar coordinate system, represents the track the azimuth angle of the measurement value in the polar coordinate system, represents the track the position of the reference measurement on the axis in the rectangular coordinate system, represents the track the position of the reference measurement on the axis in the rectangular coordinate system, represents the track the distance of the reference measurement in the polar coordinate system, represents the track the azimuth angle of the reference measurement in the polar coordinate system; exp represents the natural exponential function;

[0140] Step 2-4: Using the method of Step 1-4, perform extended Kalman filtering on the reference measurement obtained in Step 2-3 to obtain the filtered value of the reference track of the target ​(The target i here represents the target i confirmed after the successful association of track i and track j, that is, two successfully associated tracks determine a target, and the reference measurement and reference track are also for this determined target).

[0141] Step 3 includes:

[0142] Step 3-1, calculate the reference error between the reference track and the track in the overlapping coverage area of each base station successfully associated in Step 2-2, for the target determined by the successful track association , the formula is:

[0143] (17),

[0144] Where represents the filtering value of the th target detected by the base station at represents the filtering value of the reference track of the th represents the reference error between the track in the overlapping coverage area of the th target of the base station and the reference track at

[0145] Step 3-2, normalize the reference error of the target :

[0146] (18),

[0147] Where represents the weight participated by the base station when performing state fusion on the th

[0148] Step 3-3, perform dynamic weighted fusion on the tracks in the overlapping coverage area of each base station successfully associated in Step 2-2, and perform weighted accumulation on the inverse of the covariance matrix and the state vector of the target :

[0149] (19),

[0150] (20),

[0151] Where, represents the weighted accumulation of the inverse of the covariance matrix of the track in the overlapping coverage area of the target detected by each base station at represents Base station at a certain moment Detected target Inverse of the covariance matrix of Indicates Weighted accumulation of the track state vectors of the detected targets at each base station at Overlapping coverage area Indicates Base station at Detected target Track state vector of the overlapping coverage area;

[0152] Step 3-4: Calculate the fused error covariance matrix and state estimate;

[0153] Step 3-5: If the target flies from the overlapping coverage area into the private coverage area of a base station, use the fused error covariance matrix and state estimate in Step 3-4 to assist the base station in re-filtering and updating the track of the private coverage area of the base station; connect the updated tracks of the private coverage areas of each base station and the track of the overlapping coverage area after fusion to obtain the overall situation of the target track.

[0154] In Step 3-4, the following formula is used to calculate the fused error covariance matrix and state estimate:

[0155] (21),

[0156] (22),

[0157] Wherein, Indicates Error covariance matrix after fusion of the target at A certain moment, Indicates State estimate after fusion of the target at A certain moment.

[0158] The present invention also provides an electronic device, including a processor and a memory, where the memory stores program codes, and when the program codes are executed by the processor, the processor is caused to execute the steps of the method.

[0159] The present invention also provides a storage medium storing a computer program or instruction, and when the computer program or instruction runs on a computer, the steps of the method are executed.

[0160] In this embodiment, the fusion error between the method of the present invention and the traditional fast CI fusion algorithm is analyzed, and the simulation parameters are set as shown in Table 1 below.

[0161] Table 1

[0162]

[0163] The specific implementation is carried out according to the following steps:

[0164] Step 1: Design a simulation scenario for a distributed multi-station detection architecture for high-precision seamless sensing in a cellular network. As shown, calculate the error bound based on the signal-to-noise ratio of each base station, and perform extended Kalman filtering on the base station measurements accordingly to obtain the local tracks of each base station for target tracking, as shown Figure 1 in. Figure 2 as shown.

[0165] Step 2: In the given overlapping coverage area, perform spatio-temporal alignment on the tracks in the overlapping coverage areas of each base station and then associate them. Obtain the reference measurement through maximum likelihood estimation based on the associated track measurement values and error bounds in the overlapping coverage areas, and perform extended Kalman filtering with the assistance of the track in the private coverage area of the original base station to obtain the reference track. The reference measurement and the reference track are as shown Figure 3 in.

[0166] Step 3: Calculate the error between the reference track and the tracks in the overlapping coverage areas of each base station that are successfully associated in (2), dynamically allocate weights according to this error, perform track fusion on the tracks in the overlapping coverage areas of each base station to obtain a high-precision track in the overlapping coverage area. Use the fused track in the overlapping coverage area to assist the next base station in re-filtering and update the track in the private coverage area of this base station. Connect the updated tracks in the private coverage areas of each base station and the fused track in the overlapping coverage area to obtain the overall situation of the target track. The complete target track after fusion is as shown Figure 4 in.

[0167] Figure 5 For the simulation scenario of cross-base station target tracking, it is the tracking errors of different tracks. Among them, the black curve is the filtering track error of the first base station, the green curve is the filtering track error of the second base station, the blue curve is the fusion track error of the classical fast CI algorithm, and the red curve is the track error of the distributed multi-station track plotting method for high-precision seamless sensing in a cellular network proposed by the present invention. In the overlapping coverage area, the average value of the filtering track error of the first base station is 1.48 m, the average value of the filtering track error of the second base station is 0.99 m, the average value of the fusion track error of the classical fast CI algorithm is 0.51 m, and the average value of the track error of the distributed multi-station track plotting method for high-precision seamless sensing in a cellular network proposed by the present invention is 0.35 m.

[0168] In summary, the method of the present invention solves the problem of incomplete cross-base station target tracking tracks. The verification and analysis results show that compared with the traditional fast CI fusion algorithm, the method of the present invention realizes the complete track tracking of cross-base station targets and improves the track accuracy of target tracking.

[0169] The present invention provides a distributed multi-station track drawing method for high-precision seamless sensing in cellular networks. There are many methods and ways to specifically implement this technical solution. The above description is only the preferred embodiment of the present invention. It should be noted that for those of ordinary skill in the art in this technical field, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention. Each component not clearly defined in this embodiment can be implemented by existing technologies.

Claims

1. A distributed multi-station track plotting method for high-precision seamless perception in cellular networks, characterized in that It includes the following steps: Step 1: Obtain the total number of base stations, base station measurement data, and the target initial state, establish a target motion model, calculate the measurement error bound according to the signal-to-noise ratio of the base stations, and perform extended Kalman filtering on the measurement data of each base station to obtain each local track; Step 2: In the given overlapping coverage area, perform spatio-temporal alignment on the tracks in the overlapping coverage area of each base station and then correlate them. According to the measurement values and error bounds of the tracks in the overlapping coverage area of each base station with successful correlation, obtain the reference measurement through maximum likelihood estimation, use the tracks in the private coverage area of the original base station to assist the reference measurement for track initiation, and obtain the reference track after extended Kalman filtering; Step 3: Calculate the reference error between the reference track and the tracks in the overlapping coverage area of each base station with successful correlation in Step 2, dynamically allocate weights according to the error, perform track fusion on the tracks in the overlapping coverage area of each base station, and obtain a high-precision track in the overlapping coverage area; Use the fused track in the overlapping coverage area to assist the re-filtering of the next base station and update the tracks in the private coverage area of the base stations; Connect the updated tracks in the private coverage area of each base station and the fused track in the overlapping coverage area to obtain the overall situation of the target track.

2. The method according to claim 1, wherein Step 1 includes: Step 1-1: Establish the following linear system: X(k) = F(k - 1)X(k - 1) + Γ(k - 1)v(k - 1) (1), Z(k) = H(k)X(k) + W(k) (2), where X(k) represents the state vector at time k, Z(k) represents the measurement vector at time k, F(k - 1) represents the state transition matrix at time k - 1, H(k) represents the measurement matrix at time k, Γ(k - 1) represents the process noise distribution matrix at time k - 1, v(k - 1) represents the process noise, W(k) represents the measurement noise, and both v(k - 1) and W(k) are zero-mean Gaussian white noises; Step 1-2: Establish a target motion model; For the uniform rectilinear motion model, the state vector that describes the dynamic characteristics of the system 'The symbol represents the transpose; the state transition is as follows: where x k represents the position of the target on the x-axis at time k, and y k represents the position of the target on the y-axis at time k, represents the velocity of the target on the x-axis at time k, represents the velocity of the target on the y-axis at time k, and v x represents the random variation of the target's velocity on the x-axis, and v y represents the random variation of the target's velocity on the y-axis, and T represents the sampling interval; Step 1-3: Calculate the measurement error bound according to the signal-to-noise ratio of each base station: Standard deviation σ of distance measurement error R is as follows: where c represents the speed of light constant, B represents the receiver bandwidth, and SNR represents the signal-to-noise ratio of the base station; Standard deviation σ of azimuth measurement error θ is where θ represents the antenna beam width of the measurement azimuth angle, and η represents the monopulse slope; Step 1-4: Perform extended Kalman filtering on the measurements obtained by the base stations.

3. The method according to claim 2, wherein Step 1-4 includes: The dynamic equation and measurement equation of the system satisfy the Gaussian condition, expressed as: X(k) = f(X(k - 1)) + V(k) (6), Z(k) = h(X(k)) + W(k) (7), where the nonlinear functions f(·) and h(·) represent the dynamic model function and measurement model function respectively, the process noise V(k) and the measurement noise W(k) both follow Gaussian distributions, the covariance of the process noise is Q(k), and the covariance of the measurement noise is R(k).

4. The method according to claim 3, wherein Step 1-4 also includes: The one-step prediction of the state is expressed as: Among them is the state prediction at time k, is the state prediction at time k for time k + 1.

5. The method according to claim 4, wherein Step 1-4 also includes: The one-step prediction of the covariance is expressed as: P(k + 1|k) = f X (k)P(k|k)f X '(k) + Q(k) (9), where P(k|k) is the state estimation covariance at time k, and P(k + 1|k) is the prediction of the state estimation covariance at time k + 1 given the state at time k; f X (k) is the Jacobian matrix of the vector , and f X '(k) is the transpose matrix of f X (k); Measurement prediction value The covariance of the measurement prediction value is expressed as: S(k + 1)=h X (k + 1)P(k + 1|k)h' X (k + 1)+R(k + 1)(10), where h X (k + 1) is the Jacobian matrix at time k + 1 , is the predicted measurement value at time k + 1 for time k, and h' X (k + 1) is the transpose matrix of h X (k + 1), and S(k + 1) is the information covariance matrix at time k + 1; The gain is: K(k + 1) = P(k + 1|k)h' X (k + 1)S -1 (k + 1)(11), where K(k + 1) is the filtering gain at time k + 1, and S -1 (k + 1) is the inverse matrix of S(k + 1); The state update equation is: where is the state update at time k + 1, and Z(k + 1) is the measurement value at time k + 1; The covariance update equation is: P(k + 1|k + 1) = [I - K(k + 1)h X (k + 1)]P(k + 1|k)[I + K(k + 1)h X (k + 1)]' - K(k + 1)R(k + 1)K'(k + 1)(13), where I is the identity matrix of the same dimension as the covariance, and K'(k + 1) is the transpose matrix of K(k + 1); Repeat steps 1 - 4 until the status update ends to obtain the local tracks of each base station where M is the total number of base stations, and N m is the number of tracks of base station m.

6. The method according to claim 5, characterized in that Step 2 includes: Step 2-1: Transfer the local track of each base station obtained by filtering in Step 1 to a unified rectangular coordinate system through spatial alignment, and then perform time alignment of interpolation and extrapolation on the overlapping coverage tracks of each base station; Step 2-2: Perform weighted track association on the tracks in the overlapping coverage areas of each base station after spatio-temporal alignment in Step 2-1: Set M = 2. For two base stations, namely the first base station and the second base station, use the following formula to calculate the test statistic: Among them represents the state estimate of the i-th target of the first base station at time k, represents the state estimate of the j-th target of the second base station at time k, P i 1 (k|k) represents the error covariance of the i-th target of the first base station at time k, represents the error covariance of the j-th target of the second base station at time k; if α ij (k) is lower than a certain threshold obtained using the chi-square distribution χ 2 then it is determined that the i-th target of the first base station and the j-th target of the second base station are the same target, that is, the i-th track of the first base station is associated with the j-th track of the second base station; Step 2-3: For the measurement information of the tracks in the overlapping coverage areas of each base station with successful association, calculate the reference measurement through maximum likelihood estimation according to the error bound: L(x,y) = P(x1,y1|x es ,y es ,σ R1 ,σ θ1 )·P(x2,y2|x es ,y es ,σ R2 ,σ θ2 ) (15), where \(L(x,y)\) represents the likelihood function, and \(P(x_1,y_1|x\) es ,y es ,\(\sigma\) R1 ,\(\sigma\) θ1 ) represents the probability density function of the measurement value of the first track in the successfully associated track pair, and \(P(x_2,y_2|x\) es ,y es ,\(\sigma\) R2 ,\(\sigma\) θ2 ) represents the probability density function of the measurement value of the second track in the successfully associated track pair. Among them, the probability density function \(P(x\) i ,y i |x es ,y es ,\(\sigma\) Ri ,\(\sigma\) θi ) is expressed as: where x i represents the position of the measurement value of track i on the x-axis in the rectangular coordinate system, and y i represents the position of the measurement value of track i on the y-axis in the rectangular coordinate system, and σ Ri represents the range measurement error of the measurement value of track i in the polar coordinate system, and σ θi represents the measurement error of the azimuth angle of the measurement value of track i in the polar coordinate system, represents the range of the measurement value of track i in the polar coordinate system, and θ i = arctan2(y i , x i ) represents the azimuth angle of the measurement value of track i in the polar coordinate system, and x es represents the position of the reference measurement of track i on the x-axis in the rectangular coordinate system, and y es represents the position of the reference measurement of track i on the y-axis in the rectangular coordinate system, represents the range of the reference measurement of track i in the polar coordinate system, and θ es = arctan2(y es , x es ) represents the azimuth angle of the reference measurement of track i in the polar coordinate system; exp represents the natural exponential function; Step 2-4: Using the method of Step 1-4, perform extended Kalman filtering on the reference measurement obtained in Step 2-3 to obtain the filtered value of the reference track of target i Target i refers to the target confirmed after the successful association of track i and track j.

7. The method according to claim 6, wherein Step 3 includes: Step 3-1: Calculate the reference error between the reference track and the tracks in the overlapping coverage areas of each base station with successful association in Step 2-2. For the target i determined with successful track association, the formula is: Among them represents the filtered value of the i-th target detected by base station m at time k, represents the filtered value of the reference track of the i-th target at time k, represents the reference error between the track of the i-th target overlapping coverage area and the reference track of base station m at time k; Step 3-2: Normalize the reference error of target i: Among them represents the weight of base station m participating in the state fusion of the i-th target at time k; Step 3-3: Perform dynamic weighted fusion on the tracks in the overlapping coverage areas of each base station with successful association in Step 2-2, and perform weighted accumulation on the inverse of the covariance matrix and the state vector of target i: Among them, P sum (k|k) represents the weighted sum of the inverses of the track covariance matrices of the overlapping coverage area of target i detected by each base station at time k, represents the inverse of the covariance matrix of target i detected by base station m at time k, X sum (k|k) represents the weighted sum of the track state vectors of the overlapping coverage area of target i detected by each base station at time k, represents the track state vector of the overlapping coverage area of target i detected by base station m at time k; Step 3-4: Calculate the fused error covariance matrix and state estimation; Step 3-5: If the target flies from the overlapping coverage area into the private coverage area of a base station, then use the fused error covariance matrix and state estimation in Step 3-4 to assist the base station in re-filtering and update the track of the private coverage area of the base station; connect the updated track of the private coverage area of each base station and the track of the overlapping coverage area after fusion to obtain the overall situation of the target track.

8. The method according to claim 7, wherein In Step 3-4, use the following formula to calculate the fused error covariance matrix and state estimation: P i (k|k) = (P sum (k|k)) -1 (21), X i (k|k) = P i (k|k)·X sum (k|k)(22), Among them, P i (k|k) represents the error covariance matrix of the fused target i at time k, X i (k|k) represents the state estimate of the fused target i at time k.

9. An electronic device, characterized in that, It includes a processor and a memory. The memory stores program codes. When the program codes are executed by the processor, the processor executes the steps of the method according to any one of claims 1 to 8.

10. A storage medium, characterized in that, Stores a computer program or instruction. When the computer program or instruction runs on a computer, it executes the steps of the method according to any one of claims 1 to 8.

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