A target tracking sensor scheduling method based on pure azimuth measurement

Abstract

The application discloses a target tracking sensor scheduling method based on pure bearing measurement, and the method comprises the following steps: firstly, initializing a pure bearing target tracking system and initializing UKF filtering; secondly, determining a sensor-target optimal geometric configuration under pure bearing measurement; then, performing one-step prediction on the target position; then, performing sensor optimal geometric configuration matching to complete real-time optimization selection of the sensor; then, performing filtering estimation on the target state; finally, judging whether the filtering process is ended or not. The application provides a fast real-time sensor scheduling method for the case that the target observation radius of the pure bearing target tracking target is limited, the target tracking precision can be controlled through adjustment of the observation circle radius, the selection speed of the sensor combination is effectively improved, and the real-time performance of the optimization selection algorithm applied to the large-scale static sensor network is ensured.

Description

Technical Field

[0001] This invention relates to the field of target tracking technology, and in particular to a target tracking sensor scheduling method based on pure orientation measurement. Background Technology

[0002] Target tracking is divided into active and passive target tracking. Active target tracking uses sensors to emit electromagnetic waves and receive the energy scattered back by the target to determine its position. However, this method is easily detected, interfered with, and counter-tracked by the enemy. Pure azimuth target tracking, as a typical passive tracking technology, does not emit signals itself. Instead, it estimates the target's motion state by passively receiving signals radiated by the target. It has many advantages, such as long operating range, strong anti-interference ability, and good concealment, and is widely used in underwater target detection and tracking.

[0003] Depending on the tracking and detection tools used, underwater target tracking can be divided into target tracking based on acoustic imaging sensors, target tracking based on sonar arrays, and target tracking based on Underwater Wireless Sensor Networks (UWSNs). UWSNs, as an extension of terrestrial sensor networks, consist of a large number of sensor nodes with acoustic communication and computing capabilities. They utilize underwater acoustic communication technology to form a multi-hop self-organizing sensor network system, offering advantages such as rapid deployment, low cost, good self-organization and fault tolerance, and fewer time and space constraints. In a pure azimuth target tracking system based on UWSNs, to fully utilize sensor resources and maximize efficiency, task scheduling and allocation for each sensor are necessary. Sensor scheduling, or sensor resource management, mainly involves the targeted allocation of sensor resources and detection time intervals to improve target tracking accuracy, enhance system survivability, expand detection coverage, and optimize signal processing effects, thereby improving sensor system performance. Real-time allocation and selection of sensor resources is an important direction in sensor scheduling research. Real-time selection of some sensor nodes to dynamically track targets and optimization of the selection scheme to obtain the desired tracking accuracy with as few nodes as possible can effectively reduce the waste of sensor resources and is of great significance to solving the energy efficiency balance problem of large-scale underwater static sensor networks.

[0004] As is well known, the relative geometric configuration between the sensor and the target significantly affects the performance of target localization algorithms. A good sensor-target geometric configuration can, mechanistically, guarantee the optimal accuracy of reachable target localization. Most existing research optimizes sensor selection and deployment by repeatedly calculating performance indicators such as FIM (Fixed Indicator Metrics) in hopes of achieving a good sensor layout, which undoubtedly incurs significant computational costs. In recent years, many scholars have focused on deriving analytical solutions for the optimal sensor-target geometric configuration to facilitate subsequent research. Therefore, this invention studies a sensor matching method based on the optimal sensor-target geometric configuration and, based on this, investigates a real-time sensor selection strategy for target tracking, presenting an optimized sensor scheduling method for target tracking based on pure orientation measurement. This invention selects as few sensors as possible for target tracking while ensuring tracking accuracy, effectively saving network energy. Simultaneously, the sensor selection algorithm based on optimal geometric configuration matching exhibits high real-time performance, making it highly suitable for large-scale underwater sensor networks. Summary of the Invention

[0005] The purpose of this invention is to provide a target tracking sensor scheduling method based on pure orientation measurement with high tracking accuracy and good real-time performance.

[0006] The technical solution for achieving the present invention is as follows: In a first aspect, the present invention provides a target tracking sensor scheduling method based on pure azimuth measurement, comprising the following steps:

[0007] Initialize the pure azimuth target tracking system and initialize the UKF filter;

[0008] Determine the optimal sensor-target geometry for pure orientation measurement;

[0009] Predict the target's position coordinates at time k in one step from the target's state value at time k-1;

[0010] Perform optimal geometric configuration matching to complete real-time sensor optimization and selection;

[0011] Filter and estimate the target state;

[0012] Determine whether the filtering process has ended.

[0013] In a second aspect, the present invention provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the method described in the first aspect.

[0014] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in the first aspect.

[0015] Fourthly, the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the method described in the first aspect.

[0016] Compared with the prior art, the significant advantages of this invention are:

[0017] (1) In the pure orientation target tracking process, the present invention selects the sensor combination closest to the optimal geometric configuration in real time to observe the target, and obtains the desired tracking accuracy with as few sensors as possible, which can effectively balance the energy efficiency of the sensor network.

[0018] (2) Since the sensor selection method in this invention is applied to the target tracking process in real time, as the filtering process converges, the predicted position of the target will gradually approach the actual position of the target, and the selection of the optimal observation combination will be more accurate.

[0019] (3) This invention provides an analytical solution for the optimal geometric configuration of the sensor-target under pure orientation measurement, and gives a sensor optimal combination search method based on optimal geometric configuration matching. By minimizing the angle difference between two geometric configurations, the sensor combination with the highest similarity to the optimal configuration is selected. The given matching method can effectively speed up the search speed of sensor combination and improve the real-time performance of sensor scheduling algorithm. It is very suitable for engineering application scenarios such as large-scale underwater sensor networks. Attached Figure Description

[0020] Figure 1 This is a flowchart of the target tracking sensor scheduling method based on pure orientation measurement according to the present invention.

[0021] Figure 2 This is a schematic diagram of the sensor-target geometry in pure orientation measurement according to the present invention.

[0022] Figure 3 This is a schematic diagram of the optimal geometric configuration of the sensor-target under pure orientation measurement in this invention.

[0023] Figure 4 This is a schematic diagram showing the distribution of observation sensors when the target observation radius is limited in a specific embodiment of the present invention.

[0024] Figure 5 This is a schematic diagram illustrating the optimal geometric configuration matching of the sensor in a specific embodiment of the present invention.

[0025] Figure 6 This is a schematic diagram of the optimal sensor distribution mode when the number of observation sensors n=3 in a specific embodiment of the present invention.

[0026] Figure 7 This is a schematic diagram of the sensor optimization selection process when the number of sensors selected in real time is n=2 in an embodiment of the present invention.

[0027] Figure 8 This is a comparison chart of target tracking RMSE between the scheduling method of this invention and the scheduling method based on exhaustive search for minimum GDOP when the number of sensors selected in real time n=2 in an embodiment of this invention.

[0028] Figure 9 This is a schematic diagram of the sensor optimization selection process when the number of sensors selected in real time is n=3 in an embodiment of the present invention.

[0029] Figure 10 This is a comparison chart of target tracking RMSE between the scheduling method of this invention and the scheduling method based on exhaustive search for minimum GDOP when the number of sensors selected in real time n=3 in an embodiment of this invention. Detailed Implementation

[0030] The basic flow of the target tracking sensor scheduling method based on pure azimuth measurement of the present invention is as follows: Figure 1 It includes the following steps:

[0031] Step 1: Initialize the pure azimuth target tracking system and initialize the UKF filter.

[0032] Initialize a two-dimensional pure orientation target tracking scene, define the target position coordinates as p = (x, y), and initialize the target state values.

[0033] Set the total number of sensors N within the target monitoring range, and the position coordinates s of each sensor. i =(x i ,y i ), i = {1, 2, ..., N};

[0034] Set the sensor's scanning period T, scanning time t, and observation noise standard deviation σ for the target;

[0035] Set the number of sensors to be optimally selected, n;

[0036] Set the maximum observation radius R and the minimum observation radius r of the target;

[0037] The initial position of the target is calculated using the least squares method. Set the initial covariance P0 of the UKF filter and the initial state value of the filter.

[0038] Step 2: Determine the optimal sensor-target geometry for pure orientation measurement.

[0039] See the schematic diagram of the sensor-target geometry. Figure 2 Define θ i Let be the line-of-sight (LOS) angle from the i-th sensor to the target, i.e., the azimuth angle, expressed as:

[0040]

[0041] The pure orientation measurement value of the i-th sensor is:

[0042]

[0043] Measurement error

[0044] Under pure orientation measurement, the variance of the target location estimation error satisfies the following formula:

[0045]

[0046] Where J is the Fisher information matrix. When the inverse of the information matrix exists, it is called the Cramero lower bound, or CRLB. CRLB is typically used to represent the theoretically achievable best estimation accuracy; the smaller the CRLB, the higher the possible estimation accuracy of the unbiased estimator. The Fisher information matrix is ​​calculated as follows:

[0047] J = H T R -1 H (4)

[0048] Where H represents the Jacobian matrix, Let the position coordinates of the i-th sensor be s. i =(x i ,y i ), then f i (p)-arctan((y p -y i ) / (x p -x i )).

[0049] The nonlinear quantity measurement is discretized by taking the first-order linear part through Taylor expansion, and its Jacobian matrix is ​​solved. The result is:

[0050]

[0051] Where d i =||ps i ||,θ i Let be the azimuth angle of the i-th sensor relative to the target. Further calculation yields:

[0052]

[0053] but

[0054]

[0055] For ease of study, the concept of Geometrical Dilution of Precision (GDOP), also known as the geometrical factor of precision, is introduced. GDOP characterizes the impact of the geometric relationship between the observation sensor and the target position on the positioning error when sensor measurement errors exist, and is an important criterion for measuring the positioning accuracy of a tracking system. According to the definition of GDOP:

[0056]

[0057] Substituting and simplifying the formula, we obtain the explicit formula for GDOP as follows:

[0058]

[0059] Where c i =1 / (d i σ i ), θ ij =θ j θ i d i =||ps i ||,i,j∈{1,2,...,n},d i This represents the distance from each sensor to the target.

[0060] Assuming that the distance from each sensor to the target is equal, and the variance of the measurement error of each sensor is equal, i.e., d1 = d2 = ... = d n =r, σ1=σ2=…=σ n =σ, where the sensors are all distributed on a circle with the target as the center and r as the radius, forming an ideal circular array. Therefore, the explicit formula for GDOP can be easily simplified to:

[0061]

[0062] Using the A-optimization principle, that is, minimizing the CRLB of the positioning system to maximize the target's positioning accuracy, according to equation (8), similarly, to minimize GDOP, the optimal geometric configuration of the sensor with respect to the target distribution is obtained.

[0063] If and only if At that time, GDOP takes the global minimum value.

[0064]

[0065] in k∈Φ and Φ={k|k≠mn,k∈Z,m∈Z}.

[0066] In practical engineering applications, θ1 is the optimal deployment offset angle, which can be arbitrarily chosen. The azimuth angle of each sensor is θ.i If i∈{1,2,…,n}, and is usually defined in the interval [0,2π], then the set Φ to which k belongs in the above formula can be compressed into the set Φ1={k|0<k<2n,k≠n,k∈Z}.

[0067] Step 3: Predict the target position coordinates at time k from the target state value at time k-1 in one step.

[0068] The discretized representation of the pure azimuth target tracking model is as follows:

[0069]

[0070] Where X k and X k+1 Z represents the motion state values ​​of the target at time k and time k+1, respectively. k w represents the measured value of the target. k This represents the noise during the target's motion process, used to simulate the disturbance effect during real motion. k The measurement noise is represented by f(·), which describes the measurement error of the sensor. f(·) represents the target state transition equation, which is determined by the motion of the target, and h(·) represents the sensor measurement equation.

[0071] Assuming the target is observed by n sensors, the position coordinates (x, y) of the i-th sensor are... k ,y k The target position coordinates at time k are: The measurement value obtained by the multi-sensor pure azimuth target tracking system at time k is shown in the following formula:

[0072]

[0073] Where V k The measurement error vector consists of the independent errors of n sensors, i.e., v in equation (2). i composition.

[0074] On a two-dimensional plane, the motion state X of the target at time k k for When the target is moving at a constant velocity in a straight line (CV) or at a constant velocity in a turning direction (CT), the motion model can be represented as follows:

[0075] X k+1 =FX k +Gw k (14)

[0076] Where G is the noise driving equation, expressed as:

[0077]

[0078] T is the sampling interval, which can be obtained from the physical laws of uniform linear motion and uniform turning motion:

[0079]

[0080]

[0081] F CV F CV Let F represent the state transition matrix F in the target motion model during CT and CV motion, respectively.

[0082] Given the target state value at time k-1 To predict the target state at time k in one step, the predicted value of the target state is calculated as follows:

[0083]

[0084] Step 4: Perform optimal geometric configuration matching to complete real-time sensor optimization selection.

[0085] Based on the one-step predicted value of the position coordinates at time k, the maximum observation radius R, and the minimum observation radius r, the sensors within the observation ring are initially selected. If there are no sensor nodes within the current ring, the minimum radius is increased while Δr = Rr remains unchanged, or Δr is increased while r remains unchanged.

[0086] Based on the optimal geometric configuration matching method, the set of sensors that are closest to the optimal geometric configuration within the observation ring at time k is selected as the target observation station at time k, and the pure azimuth target observation value is obtained.

[0087] In practical sea surface pure azimuth observation systems, considering the anti-reconnaissance requirements of the observation platform, the maximum detection range limitations of the sensors, and the tracking accuracy requirements, the observation platform cannot be too close to the target nor too far away. Therefore, the optimal selection process of sensors usually takes place within a ring centered on the target, where the ring width Δr is the maximum distance R of the sensor from the target minus the minimum distance r. The distribution of the observation sensors in this case is shown in [the diagram]. Figure 4 When Δr << Rr, the sensors can be approximated as being distributed on a circle.

[0088] From step 3, we can obtain the predicted target state value at time k. Further determine the target prediction position P at time k. k|k-1 Based on the target observation radius requirements, the sensors within the observation ring are first selected and approximated as being distributed on a circle. Then, based on the optimal sensor geometry obtained in step 2, the optimal sensor-target geometry is matched at the current moment.

[0089] The specific steps are as follows:

[0090] Step 1: As Figure 5 As shown in (a), first, a rectangular coordinate system is established, and the predicted target position P at time k is determined. k|k-1 The number of sensors M on the circumference and the position s of each sensor i Each sensor is numbered.

[0091] Step 2: Using P k|k-1 Establish a right-handed coordinate system P with the origin as the origin and the straight line passing through sensor 1 as the x' axis. k x'y', rotate and normalize the position vectors of all sensors. A schematic diagram of the rotation normalization process is shown below. Figure 5 (b)

[0092] The equations of rotation for the coordinate system are as follows:

[0093]

[0094] Where α1=tan -1 (y1' / x1'), [x1', y1'] T =s1-p,s i =[x i ,y i ] T ,i∈{1,2,…,M} represents the sensor position coordinates, p=[x p ,y p ] T Indicates the target location coordinates.

[0095] Then the i-th sensor at P k coordinates in the x'y' coordinate system

[0096] Step 3: Based on the analytical expression of the optimal geometric configuration obtained above, give the optimal mode for n sensors. Considering the symmetry of the optimal geometric configuration, there are n-1 optimal modes for n sensors.

[0097] The unit direction vector of the q-th optimal sensor position relative to the target in the optimal mode is represented as: (q∈{1,2,...,n},n≥2), according to equation (11) and its necessary and sufficient condition, the unit direction vector of the q-th sensor position in the k-th optimal mode can be obtained as follows:

[0098]

[0099] Taking n=3 as an example, such as Figure 6 As shown, there are two optimal modes at this point, and their vector representations are as follows:

[0100] Pattern a:

[0101]

[0102] Pattern b:

[0103]

[0104] For the first optimal pattern, the matching diagram is shown below. Figure 5 (c)

[0105] Solve sequentially for the direction vectors of the M sensors relative to the target. The angle between

[0106]

[0107] in, Let represent the cosine value between the direction vector of the i-th sensor among the candidate sensors and the q-th vector in the optimal mode.

[0108] Find the n sensors whose direction vectors have the smallest angles with the sensor direction vectors in the optimal mode. Record the minimum angle differences as follows:

[0109]

[0110] Find the mean square error of the n smallest included angles, denoted as .

[0111]

[0112] The sensor numbers corresponding to the n smallest included angles are denoted as follows:

[0113] Step 4: Traverse the M sensors, i.e., with P k|k-1 Let the origin be the x-axis, and let the lines connecting it to the m-th (m∈{1,2,...,M} sensors be the x'-axis. Construct a right-handed coordinate system P. k x'y', repeat Step 2-3 to find the one that makes The smallest group of sensors is designated C. * .

[0114]

[0115] Step 5: For the next optimal pattern, repeat Steps 2 through 4 to find the optimal set of J. * .

[0116] Step 6: Compare J * Take J *The smallest set of sensors is optimal, and the numbers of the n selected sensors are obtained in the end.

[0117] Step 5: Perform filtering estimation on the target state

[0118] Based on the target state at time k-1 and the sensor's observation of the target at time k, the UKF filtering algorithm is used for centralized filtering to update the state estimate at time k.

[0119] The UKF filter, based on the original Kalman filter, obtains a set of sigma points through the UT transform to convey the mean and covariance characteristics of the nonlinear system. It has high estimation accuracy and stability. The specific calculation steps are as follows:

[0120] (1) Generate sigma point sets

[0121] Sigma point set: Obtained by UT transformation, a set of sampling points with mean and covariance consistent with the original state distribution is selected. The state estimate and estimation error covariance matrix at time k-1 are known. P k-1k-1 The following 2n+1 sigma points and their corresponding weights are obtained through UT transformation.

[0122]

[0123]

[0124] In the formula, The i-th column represents the square root of the matrix, and n is the dimension of the state vector. λ is a scaling parameter used to reduce the total prediction error, λ = a 2 (n+κ)-n, where a controls the scattering of the sampling points, usually a small positive number (e.g., 0.01), κ is a scalar that controls the distance of each point to the state mean, usually 0. β is a non-negative weighting coefficient that can include the influence of higher-order terms and is used to control the peak error of the estimated state, usually 2. The subscript i represents the sampling point, the superscript m represents the mean, and the superscript c represents the covariance.

[0125] (2) Perform one-step state value prediction and covariance prediction.

[0126]

[0127]

[0128]

[0129] (3) Generate the sigma point set again from the state values ​​and covariance predicted in the first step.

[0130]

[0131] (4) Prediction of measured values ​​and system covariance

[0132]

[0133]

[0134]

[0135]

[0136] (5) Calculate the Kalman gain

[0137]

[0138] (6) Filtering update: Correct the predicted state value using the measurement value at the current time.

[0139]

[0140]

[0141] Step 6: Determine if the filtering process is complete.

[0142] Finally, determine whether the maximum number of samples has been reached at the current sampling time. If yes, exit; otherwise, return to step 3.

[0143] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0144] Example

[0145] This embodiment is based on a Matlab simulation platform. It considers a monitoring area of ​​[-500m 1500m] × [-500m 1500m], with 50 sensor nodes regularly distributed across a stationary sea surface. The standard deviation of the azimuth measurement error for each sensor node is 1°, and the fusion center is located at the center of the area. The target moves at a constant velocity (CV) in a straight line within the monitoring area, with an initial state of X0 = [300m 300m 20m / s 20m / s]. T Q = 0.1 2 The initial position of the target is obtained using the least squares localization method and used as the initial state value for filtering. The initial covariance of the filter is set to P0 = 10. 4 ·I(4,4).

[0146] The target is observed and sampled for 20 seconds, with a sampling interval T of 0.2 seconds. The maximum observation radius R is set to 550m, and the minimum radius r is set to 500m. The optimal geometric configuration matching method is used to select n sensors in real time to participate in target tracking. When n=2, the optimal sensor combination selection process at a certain sampling time is as follows: Figure 7 As shown.

[0147] The optimal sensor-target geometry in this invention is obtained by minimizing the GDOP of the target localization. Since constraints are added in the process of solving the optimal solution, the optimal geometry matching method proposed in this invention will have a decrease in localization and tracking accuracy compared with the method of finding the minimum GDOP by directly calculating the sensor's GDOP value with respect to the target. Figure 8 The paper presents a comparison of the target tracking RMSE between the sensor optimization scheduling method of this invention and the sensor scheduling method based on exhaustive search for the minimum GDOP after 100 Monte Carlo simulation experiments. It can be seen that the method of this invention can achieve target tracking accuracy very close to that of exhaustive search for the minimum GDOP, and the tracking accuracy is significantly better than that of randomly selecting n sensors.

[0148] Figure 9 The scenario is given with 500 sensor nodes distributed within the monitored water area. The target is making a uniform turning motion within the monitored water area, with the initial state X0 = [400m 400m 10m / s 10m / s]. T And when the number of sensors selected in real time is n=3, the process of selecting the optimal combination of sensors at a certain sampling time. Figure 10 A comparison is given between the target tracking accuracy using the optimized scheduling algorithm in this invention and the minimum GDOP search based on exhaustive search.

[0149] Finally, to verify the real-time performance of the proposed optimized scheduling method, we considered that 30, 100, 200, and 300 sensors were randomly distributed within the monitored water area. For any target within the monitored water area, we performed 100 sensor selection operations based on optimal geometric configuration matching and exhaustive search for the minimum GDOP, respectively. We calculated the average time consumption and analyzed the time complexity of the algorithm. When n=2, the average time consumption of the algorithm is shown in Table 1. When n=3, the average time consumption of the algorithm is shown in Table 2.

[0150] Table 1. Comparison of average processing time for sensor optimization selection algorithms when n=2

[0151]

[0152]

[0153] Table 2. Comparison of average processing time for sensor optimization selection algorithms when n=3

[0154]

[0155] The simulation results above show that the target tracking sensor scheduling algorithm based on pure orientation measurement proposed in this invention greatly improves the search speed of sensor combinations while ensuring tracking accuracy. It can effectively improve the real-time performance of sensor scheduling algorithms for target tracking and is very suitable for engineering application scenarios such as large-scale underwater sensor networks.

[0156] The above description details the basic principles, main features, and advantages of this invention. Those skilled in the art should understand that this invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to this invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A target tracking sensor scheduling method based on pure azimuth measurement, characterized in that, Includes the following steps: Initialize the pure azimuth target tracking system and initialize the UKF filter. The specific method is as follows: Initialize a 2D pure orientation target tracking scene, defining the target position coordinates as follows: Initialize target state value ; Set the total number of sensors within the target monitoring range The position coordinates of each sensor , ; Set the sensor's scanning period T, scanning time t, and observation noise standard deviation for the target. ; Set the number of sensors to be optimally selected, n; Set the maximum observation radius R and the minimum observation radius r of the target; The initial position of the target is calculated using the least squares method. Set the initial covariance of the UKF filter. Initial state value of filtering ; The optimal sensor-target geometry for pure orientation measurement is determined using the following method: definition Let be the line-of-sight angle from the i-th sensor to the target, expressed as: （1） The pure orientation measurement value of the i-th sensor is: （2） Measurement error ; Under pure orientation measurement, the variance of the target location estimation error satisfies the following formula: （3） in, Let be the Fisher information matrix. When the inverse of the information matrix exists, it is called the Cramero lower bound, or CRLB. The Fisher information matrix is ​​calculated as follows: （4） in, Represents the Jacobian matrix. Let the position coordinates of the i-th sensor be... ,but ; The nonlinear quantity measurement is discretized by taking the first-order linear part through Taylor expansion, and its Jacobian matrix is ​​solved. The result is: （5） in , Let be the azimuth angle of the i-th sensor relative to the target. Further calculation yields: （6） but （7） Introducing Geometric Dilution of Positioning Error (GDOP), GDOP characterizes the impact of the geometric relationship between the observed sensor and the target position on the positioning error when sensor measurement errors exist. Based on the definition of GDOP: （8） Substituting and simplifying the formula, we obtain the explicit formula for GDOP as follows: （9） in , , , d i The distance from each sensor to the target; When the distances from each sensor to the target are equal, the variances of the measurement errors of each sensor are equal, that is... , The sensors are all distributed on a circle with the target as the center and r as the radius, forming a circular array. The explicit formula for GDOP then simplifies to: （10） Using the A-optimization principle, that is, minimizing the CRLB of the positioning system to maximize the target's positioning accuracy, according to equation (8), the analytical solution of the optimal sensor-target geometric configuration is obtained by minimizing GDOP as follows: ； Where θ1∈ , k ∈ Φ and Φ ; At this point, GDOP takes the global minimum value as follows: （11） θ1 is the optimal deployment offset angle, and the azimuth angle of each sensor is θ. i , i ∈{1,2,…,n}, defined in Within the interval, the set Φ to which k belongs in the above formula is compressed to the set... middle; The target's position coordinates at time k are predicted in one step from the target's state value at time k-1. The specific method is as follows: The discretized representation of the pure azimuth target tracking model is as follows: （12） in and These represent the target's motion state values ​​at time k and time k+1, respectively. Represents the measured value of the target. This represents noise during the target's motion process, used to simulate the disturbance effect during real motion. This represents measurement noise, used to describe the measurement error of the sensor; The state transition equation for the target is determined by the target's motion. Represent the sensor measurement equation; Assuming the target is observed by n sensors, the position coordinates of the i-th sensor are... The target position coordinates at time k are The measurement value obtained by the multi-sensor pure azimuth target tracking system at time k is shown in the following formula: （13） in The measurement error vector consists of the independent errors of n sensors, i.e., in equation (2). composition; The motion state of the target at time k in a two-dimensional plane. for When the target is moving at a constant velocity in a straight line or turning at a constant velocity, the motion model is represented as follows: （14） in The noise-driven equation is expressed as: （15） T is the sampling interval, which can be obtained from the physical laws of uniform linear motion and uniform turning motion: （16） （17） , Let F represent the state transition matrix F in the target motion model during CT and CV motion, respectively; Given the target state value at time k-1 If we perform a one-step prediction of the target state at time k, the predicted value of the target state is calculated as follows: （18） To perform optimal geometric configuration matching and complete real-time sensor optimization selection, the specific method is as follows: Based on the one-step predicted position coordinates at time k, the maximum and minimum observation radii R and r of the target, sensors within the observation ring are initially selected; if there are no sensor nodes within the current ring, then... With the minimum radius unchanged, increase it; or with r unchanged, increase it. ; Based on the optimal geometric configuration matching method, the set of sensors that are closest to the optimal geometric configuration within the observation ring at time k is selected as the target observation station at time k, and the pure azimuth target observation value is obtained. The predicted target state value at time k is The predicted position of the target at time k is Based on the target observation radius requirements, the sensors within the observation ring are first selected and considered as approximately distributed on a circle; then, based on the optimal geometric configuration of the sensors, the optimal geometric configuration of the sensor-target at the current moment is matched. The specific steps are as follows: Step 1: First, establish a rectangular coordinate system and determine the predicted position of the target at time k. The number M of sensors on the circumference and the position of each sensor Each sensor is numbered. Step 2: With With the origin as the line passing through sensor 1, the line is... Establish a right-handed coordinate system based on the axes. Rotation normalization is performed on the position vectors of all sensors; The equations of rotation for the coordinate system are as follows: （19） in , , Indicates the sensor position coordinates. Indicates the target's location coordinates; Then the i-th sensor is Coordinates in a coordinate system ; Step 3: Based on the analytical expression of the optimal geometric configuration, give the optimal mode for n sensors; considering the symmetry of the optimal geometric configuration, there are n-1 optimal modes for n sensors. The unit direction vector of the q-th optimal sensor position relative to the target in the optimal mode is represented as: , Based on equation (11) and its necessary and sufficient conditions, the unit direction vector of the q-th sensor position in the k-th optimal mode is obtained as follows: （20） for At this point, there are two optimal modes, and their vector representations are as follows: Pattern a: （21） Pattern b: （22） Solve sequentially for the direction vectors of the M sensors relative to the target. The angle between : （23） in, Let represent the cosine value between the direction vector of the i-th sensor among the candidate sensors and the q-th vector in the optimal mode. ; Find the n sensors whose direction vectors have the smallest angles with the sensor direction vectors in the optimal mode. Record the minimum angle differences as follows: （24） Find the root mean square error of the n smallest included angles, denoted as . : （25） The sensor numbers corresponding to the n smallest included angles are denoted as follows: ; Step 4: Traverse the M sensors, i.e. Let the origin be the line connecting it to the m-th sensor. axis, Construct a right-handed coordinate system Repeat Steps 2 and 3 to find the cause. The smallest group of sensors is numbered as follows: ; （26） Step 5: For the next optimal pattern, repeat Steps 2 through 4 to find the optimal set. ; Step 6: Comparison ,Pick The smallest set of sensors is optimal, and the numbers of the n selected sensors are obtained in the end; Filter and estimate the target state; Based on the target state at time k-1 and the sensor's observation of the target at time k, the UKF filtering algorithm is used for centralized filtering to update the state estimate at time k. Based on the Kalman filter, the UKF filter obtains a set of sigma points through the UT transform to convey the mean and covariance characteristics of the nonlinear system. The specific calculation steps are as follows: (1) Generate sigma point set Sigma point set: obtained by UT transformation, selecting a set of sampling points whose mean and covariance are consistent with the original state distribution; known Time-state estimate and estimation error covariance matrix , The following 2n+1 sigma points and their corresponding weights are obtained through UT transformation. （27） （28） In the formula, The i-th column represents the square root of the matrix, and n is the dimension of the state vector; This is a scaling parameter used to reduce the overall prediction error. Where 'a' controls the distribution of sampling points. As a scalar, it controls the distance of each point from the state mean. is a non-negative weighting coefficient, where the subscript i represents the sampling point, the superscript m represents the mean, and the superscript c represents the covariance; (2) Perform one-step state value prediction and covariance prediction （29） （30） （31） (3) Generate the sigma point set again from the predicted state values ​​and covariance in one step. （32） (4) Prediction of measured values ​​and system covariance （33） （34） （35） （36） (5) Calculate the Kalman gain （37） (6) Filtering update: Correct the predicted state value using the measured value at the current time. （38） （39） Determine whether the filtering process has ended.

2. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method as described in claim 1.

3. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the method as described in claim 1.

4. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method of claim 1.

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