A long baseline positioning algorithm and system for automatic tracking management decision-making

Abstract

The present invention provides a long baseline positioning algorithm and system for automatic tracking management decision-making, which relates to the field of underwater target positioning technology, including defining indicator variables, gridding the positioning area, calculating the likelihood value of each resolution unit, and initializing particles; updating the indicator variables based on the Markov transition matrix, and updating the particle state based on the indicator variables; constructing the likelihood ratio function of the particles, and calculating the particle weight according to the likelihood ratio function; resampling, calculating the number of existing particles, and when the ratio of the number of existing particles to the number of particles in the gridded positioning area is greater than 0.6, calculating the target state, and using a segmented threshold to mark the target position estimated by the algorithm. The present application updates the indicator variables based on the Markov transition matrix, updates the particle state based on the indicator variables, calculates the target state based on the ratio of the number of existing particles to the number of particles in the gridded positioning area, and marks the target, and is suitable for situations where the tracked target enters and exits the positioning area.

Description

Technical Field

[0001] The present application relates to the technical field of underwater target positioning, and more specifically, to a long baseline positioning algorithm and system for automatic tracking management decision-making. Background Art

[0002] Long baseline positioning technology plays an important role in the field of underwater target positioning. Due to the complexity of the underwater environment and the particularity of signal propagation, traditional positioning methods often cannot meet the needs of accurate positioning. Long baseline positioning technology can achieve high-precision underwater target positioning by measuring the signal propagation time difference or phase difference from underwater targets to multiple base stations, as well as the location information of the base stations. In the prior art, underwater target positioning algorithms based on long baseline positioning technology include:

[0003] (1) The Chinese invention patent with publication number CN116660911A, a method for underwater target positioning based on ranging error matching, discloses using the traditional long baseline positioning method, combined with the spatial intersection model, to calculate the initial position of the target to be positioned; combining the hydroacoustic ranging results, constructing a ranging error probability model; using the ranging error probability model, constructing a ranging error fitness function; correcting the initial positioning position through a positioning algorithm based on ranging error matching, and outputting the positioning result. Taking advantage of the positive correlation between the hydroacoustic ranging error and the true distance, the ranging error probability model and fitness function are constructed to correct the traditional long baseline positioning results and improve the positioning accuracy.

[0004] (2) Chinese invention patent with publication number CN109541546A, a method for underwater long baseline acoustic positioning based on TDOA, discloses deploying a positioning base station array consisting of several base stations and a survey ship for receiving data in the target sea area; establishing a positioning model based on the TDOA method to obtain the distance value between the i-th base station and the positioning target based on the TDOA method; using the Chan algorithm to obtain the initial position of the positioning target based on the distance value; using the Taylor algorithm to iterate the initial position of the positioning target to obtain a more accurate result; and performing a threshold judgment on the result. If the result is less than the set threshold, the final result is output; otherwise, the threshold judgment is continued until the result is less than the threshold.

[0005] It can be seen that the long baseline underwater target positioning algorithm in the prior art focuses on improving positioning accuracy, but does not consider the situation where the tracked target leaves or enters the positioning area. In actual applications, the number of tracked targets is unknown and changes over time. Summary of the invention

[0006] To solve the above problems, the technical solution adopted in this application is a long baseline positioning algorithm for automatic tracking management decisions, including the following steps:

[0007] S1: Define indicator variables, grid the positioning area, calculate the likelihood value of each resolution unit, and initialize the particles;

[0008] S2: Update the indicator variable based on the Markov transition matrix, and update the particle state based on the indicator variable.

[0009] S3: construct the likelihood ratio function of the particle and calculate the particle weight based on the likelihood ratio function;

[0010] S4: Resampling is performed to calculate the number of existing particles. When the ratio of the number of existing particles to the number of particles in the gridded positioning area is greater than 0.6, the target state is calculated and the target position estimated by the algorithm is marked using a segmentation threshold.

[0011] Preferably, defining the indicator variable is to define the indicator variable of the particle as ,by and Respectively represent the presence and absence of the target; the indicator variable of the particle is sampled from a 0-1 distribution with a probability of 0.5.

[0012] Preferably, the particle is initialized by using a distance-azimuth polar coordinate system with the maximum likelihood value position as the origin to initialize the particle position; using Initialize the particle speed in the velocity-course angle polar coordinate system of the origin; the distance is evenly distributed in The speed is evenly distributed between The azimuth and heading angles are evenly distributed between between, To preset the maximum distance, The maximum speed is preset.

[0013] Preferably, the particle state is updated based on the indicator variable as The particle's state is updated as follows:

[0014]

[0015] in, is the indicator variable of the nth particle at time t, is the indicator variable of the nth particle at time t-1, is the state of the nth particle at time t, is the state of the nth particle at time t-1, ,in and Respectively represent the horizontal and vertical position and velocity of the nth particle at time t, represents the transpose of a matrix, is the control input at time t, is the process noise at time t;

[0016] For other particles, the state update of the particles follows the process of initializing the particles in step S1.

[0017] Preferably, constructing a likelihood ratio function of a particle includes:

[0018] S3-1: Calculate the direct sound arrival time of the particle. For the mth buoy, the particle The TOA value is:

[0019] ;

[0020] in, and is the known position of the mth buoy, is the estimated speed of sound.

[0021] S3-2: Calculate the index value of the received signal after the buoy matched filtering, The index value of the received signal after matching filtering of the corresponding mth buoy is:

[0022] ;

[0023] in, means rounding towards negative infinity, is the sampling frequency.

[0024] For particles , define the matched filter output of all buoys in the buoy combination as a vector .definition The received signal after matching filtering for the mth buoy is at index value The amplitude at .

[0025] Preferably, the likelihood ratio function is defined as follows:

[0026]

[0027] In the formula, The received signal after matching filtering for the mth buoy is at index value The amplitude at is the target observation value at time t, For particles The likelihood ratio function of is the likelihood function of the particle not existing, is the likelihood function of the particle existence. Arrange all the likelihood values ​​in step S1 in descending order, and then calculate the Z score of each data in descending order. Take the first original data with a Z score not greater than 2 as The value of .

[0028] Preferably, the target position estimated by the algorithm is marked using a segmented threshold: when the proportion of particles is greater than 0.8, it means that the positioning target exists and the estimated positioning accuracy of the target position meets the positioning requirements, and when the proportion of particles is greater than 0.6 and less than or equal to 0.8 after convergence, it means that the positioning target exists but the estimated positioning accuracy of the target position does not meet the positioning requirements. When the proportion of particles is less than or equal to 0.6, it means that the positioning target does not exist.

[0029] Preferably, the target state is calculated according to the following formula:

[0030]

[0031] In the formula, is the number of particles present, is the number of particles in the gridded positioning area, is the target state.

[0032] Preferably, the weight calculation is performed according to the following formula:

[0033] ;

[0034] In the formula, is the unnormalized weight of the particle, is the state of the jth particle at time t, is the indicator variable of the jth particle at time t.

[0035] The present application also provides a long baseline positioning system for automatic tracking management decisions, including:

[0036] Initialization module: used to define indicator variables, grid the positioning area, calculate the likelihood value of each resolution unit, and initialize the particles;

[0037] State prediction module: used to update the indicator variables based on the Markov transition matrix and update the particle state based on the indicator variables.

[0038] Likelihood ratio function module: constructs the likelihood ratio function of particles and calculates particle weights based on the likelihood ratio function;

[0039] Target state estimation module: used for resampling and calculating the number of existing particles. When the ratio of the number of existing particles to the number of particles in the gridded positioning area is greater than 0.6, the target state is calculated and the segmented threshold is used to mark the target position estimated by the algorithm.

[0040] The beneficial effects of the present invention are:

[0041] 1. Update the indicator variable based on the Markov transition matrix, update the particle state based on the indicator variable, calculate the target state based on the ratio of the number of existing particles to the number of particles in the gridded positioning area and mark the target. It can be applied to the situation where the tracked target leaves or enters the positioning area. Since the pre-detection tracking method based on particle filtering takes a certain amount of time to converge to the true position of the target, this algorithm uses a segmented threshold to mark the target position estimated by the algorithm, so as to achieve the purpose of estimating the convergence time, and can distinguish the positioning results before and after the target convergence. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following briefly introduces the drawings required for use in the embodiments or descriptions of the prior art.

[0043] Figure 1 Schematic diagram of likelihood values ​​of each resolution unit;

[0044] Figure 2 Schematic diagram of error distribution at different target positions;

[0045] Figure 3 Schematic diagram of the target's actual trajectory and the target position estimated by the algorithm of this application;

[0046] Figure 4 Schematic diagram of the target's true trajectory and the target position estimated by the TOA algorithm;

[0047] Figure 5 Schematic diagram of positioning error of each algorithm at different times;

[0048] Figure 6 This is a schematic diagram of the comparison between the real trajectory and the positioning trajectory of multiple targets;

[0049] Figure 7 Schematic diagram of the relationship between the proportion of particles with an indicator variable of 1 and the signal-to-noise ratio before and after convergence; DETAILED DESCRIPTION

[0050] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0051] Example 1

[0052] S1: Define indicator variables, grid the positioning area, calculate the likelihood value of each resolution unit, and initialize the particles.

[0053] Defining indicator variables , and In the absence of any prior knowledge, the indicator variable of the particle is sampled from a 0-1 distribution with a probability of 0.5.

[0054] like Figure 1 As shown in the figure, the positioning area is gridded according to a certain grid size. After grid division, according to Calculate the likelihood value of each resolution unit and record the position of the resolution unit with the largest likelihood value as .

[0055] In order to uniformly initialize particles near the maximum likelihood position, we use Initialize the particle position using the distance-azimuth polar coordinate system with the origin as The velocity of the particle is initialized by the velocity-course angle polar coordinate system of the origin. The distance is evenly distributed in The speed is evenly distributed between The azimuth and heading angles are evenly distributed between between.

[0056] S2: Update the indicator variable based on the Markov transition matrix, and update the particle state based on the indicator variable.

[0057]

[0058] for The particle's state is updated as follows:

[0059]

[0060] in, is the state of the nth particle at time t, , and Respectively represent the horizontal and vertical position and velocity of the nth particle at time t, Represents the transpose of a matrix. is the control input at time t. is the process noise at time t, usually assumed to be zero-mean Gaussian noise.

[0061] For other particles, the particle state update follows the process in A initialization.

[0062] The transition of the indicator variable E is a Markov process, and the Markov transition matrix is:

[0063]

[0064] In the Markov transition matrix, Represents the probability that the target changes from non-existence to existence. Represents the probability of the target changing from existence to non-existence.

[0065]

[0066] S3: constructing a likelihood ratio function of the particle, and calculating the particle weight according to the likelihood ratio function.

[0067] S3-1: Calculate the direct sound arrival time of the particle. For the mth buoy, the particle The TOA value is:

[0068] ;

[0069] in, and is the known position of the mth buoy, is the estimated speed of sound.

[0070] S3-2: Calculate the index value of the received signal after the buoy matched filtering, The index value of the received signal after matching filtering of the corresponding mth buoy is:

[0071] ;

[0072] in, means rounding towards negative infinity, is the sampling frequency.

[0073] For particles , define the matched filter output of all buoys in the buoy combination as a vector .in It means the received signal after matching filtering of the mth buoy is at index value The amplitude at . The likelihood function The definition is as follows:

[0074]

[0075] Among them, for , calculate the likelihood value of each resolution unit in the gridded positioning area during initialization, and arrange all likelihood values ​​in order from large to small. Next, calculate the Z score of each data in order from large to small, and take the first original data with a Z score not greater than 2 as The value of .

[0076] (1) The Z-score standardizes the original data to make it comparable and universal. Regardless of the original distribution of the data, the Z-score reflects the relative position of the data points around the mean.

[0077] (2) Based on the characteristics of the normal distribution, in a normal distribution, about 95% of the data have a Z score between -2 and 2. Selecting a Z score no greater than 2 can eliminate the influence of outliers or extreme values ​​to a certain extent.

[0078] Through standardization, data of different scales and units can be compared and judged under the same standard. By utilizing the common characteristics of the normal distribution, a Z score of 2 can be used as a relatively clear and interpretable threshold, which helps to improve the consistency and repeatability of judgments and simplifies the judgment process because the calculation and comparison of Z scores are relatively intuitive and simple.

[0079] Determine whether resampling is needed according to the following formula:

[0080] ;

[0081] In the formula, is the unnormalized weight of the particle, is the state of the jth particle at time t, is the indicator variable of the jth particle at time t.

[0082] ;

[0083] Where n p is the total number of particles, Indicates the number of effective particles. Less than , resampling is performed.

[0084] S4: Determine whether resampling is required according to step S3, and then calculate the number of existing particles. When the ratio of the number of existing particles to the number of particles in the gridded positioning area is greater than 0.6, calculate the target state and use the segmentation threshold to mark the target position estimated by the algorithm.

[0085] Because the detection-before-tracking method based on particle filtering takes a certain amount of time to converge to the true position of the target. Because this algorithm innovatively uses segmented thresholds to mark the target position estimated by the algorithm, it can achieve the purpose of estimating the convergence time. This algorithm uses 0.8 and 0.6 as the interval boundaries. When the proportion of particles is greater than 0.8, it means that the positioning target exists at this time and the estimated target position positioning accuracy is high, which meets the positioning requirements. When the proportion of particles is greater than 0.6 and less than or equal to 0.8, it means that the positioning target exists but the estimated target position positioning accuracy is low, which does not meet the positioning requirements. When the proportion of particles is less than or equal to 0.6, it means that the positioning target does not exist at this time.

[0086] The upper and lower interval limits are the thresholds of particle convergence and particle existence, respectively. The thresholds are calculated according to the following formula:

[0087] (1) The threshold used to determine whether a target exists is 0.6

[0088] The optimal threshold is calculated using the Neyman-Pearson criterion, assuming that the received signal is , under two assumptions (no target) and (Existence target) The probability density functions are and .

[0089] ①First, set the upper limit of the false alarm probability ;

[0090] ②Calculate the false alarm probability ,in is the detection threshold to be determined;

[0091] ③To find satisfaction Threshold , the above integral needs to be solved;

[0092] ④Calculate the detection probability ;

[0093] ⑤In satisfaction Under the condition of Make The largest at this time is the optimal threshold.

[0094] (2) Threshold 0.8 for judging whether the target converges or not

[0095] like Figure 7 As shown in FIG. 1 , the optimal threshold for judging whether the target converges or not is determined according to the ratio of the number of particles whose indicator variable is 1 to the number of all particles before and after convergence under different signal-to-noise ratios.

[0096] The signal-to-noise ratio is set between -12dB and -3dB, with a step of 1, and 10,000 simulation tests are performed. The average of the proportion of particles with an indicator variable of 1 before and after convergence of all tests is calculated, so as to obtain the relationship between the proportion of particles with an indicator variable of 1 before and after convergence and the signal-to-noise ratio. In order to ensure that the threshold used to determine whether the target converges or not is applicable to various environments, the threshold is selected as 0.8.

[0097] The above is only an example of calculation under the above conditions. When the upper limit of the false alarm probability is When the actual value of the signal-to-noise ratio changes, the threshold is also calculated and determined according to the above formula.

[0098] Resample and calculate The number of particles .when When it is greater than 0.6, the target state is calculated.

[0099]

[0100] Algorithm performance analysis

[0101] The long baseline underwater positioning system consists of four positioning buoys. The four buoys form a square with a side length of 1 km. Their coordinates are (0,0), (1000,0), (1000,1000) and (0,1000). The simulation parameters used in the algorithm performance analysis are shown in Table 1.

[0102] Table 1: Simulation parameters

[0103] Number of particles Target location Speed ​​of sound 2500 (100m,100m) 1500m / s Standard deviation of TOA error Standard deviation of sound velocity error Standard deviation of buoy position error 0.5ms 1.5m / s 1m

[0104] from Figure 2 It can be seen that the positioning error in most areas of the positioning area is less than 2m. The positioning accuracy of the center point of the positioning area is the highest, and the positioning accuracy gradually decreases as it spreads outward.

[0105] First, the hydroacoustic channel, transmitting signal, acoustic beacon and receiver are defined. In a shallow water environment, there are multiple propagation paths between the sound source and the target. Ten propagation paths are set in the hydroacoustic channel with a constant sound velocity of 1520m / s. A bottom loss of 0.5dB is used to highlight the effect of multiple paths. The transmitting signal is a rectangular pulse with the following parameters: signal carrier frequency is 37.5kHz, pulse width is 0.01s, and period is 1s. In the complete positioning area, the proposed algorithm uses 2500 particles. An isotropic sound transducer and a narrowband signal radiator are defined in the acoustic beacon. The receiver consists of an isotropic hydrophone, a narrowband signal collector and an amplifier. The hydrophone is a single isotropic element with a frequency range of 0 to 30kHz, which contains the operating frequency of the multipath channel. The hydrophone voltage sensitivity is specified as -140dB. The hydrophone receiving signal data is generated by simulating a long baseline hydroacoustic positioning system.

[0106] The algorithm provided in this application is compared with the classic TOA (Time of Arrival) algorithm. The TOA algorithm uses a two-step paradigm to estimate the position of the target: (1) First, the distance between the positioning target and each buoy is calculated by estimating the direct sound arrival time and sound speed. (2) Then, the position of the target is solved based on the spherical intersection principle and the least squares method.

[0107] Figure 3 and Figure 4The actual trajectory of the target, the target position estimated by the proposed algorithm, and the target position estimated by the TOA algorithm are shown. As can be seen from the figure, the positioning performance of the proposed algorithm is better than that of the TOA algorithm. Moreover, since the constructed segmentation threshold can mark the positioning results, the positioning results before and after the target convergence can also be distinguished.

[0108] Figure 5 The positioning error comparison chart of the proposed algorithm and the TOA algorithm under different signal-to-noise ratios is shown. The positioning error of the algorithm during 40s of movement is compared for the signal-to-noise ratios of -12dB, -10dB, -8dB, -6dB and -4dB. It can be seen from the figure that no matter what the situation is, the positioning error of the proposed algorithm is lower than the positioning error of the TOA algorithm. The positioning error of the proposed algorithm is always less than 1m, while the positioning error of the TOA algorithm exceeds 3.5m when the signal-to-noise ratio is low. This proves the accuracy and effectiveness of the long baseline positioning algorithm for automatic tracking management decision-making provided by this application.

[0109] Example 2

[0110] A long baseline positioning system for automatic tracking management decision-making, characterized by comprising:

[0111] Initialization module: used to define indicator variables, grid the positioning area, calculate the likelihood value of each resolution unit, and initialize the particles;

[0112] State prediction module: used to update the indicator variables based on the Markov transition matrix and update the particle state based on the indicator variables.

[0113] Likelihood ratio function module: constructs the likelihood ratio function of particles and calculates particle weights based on the likelihood ratio function;

[0114] Target state estimation module: used for resampling and calculating the number of existing particles. When the ratio of the number of existing particles to the number of particles in the gridded positioning area is greater than 0.6, the target state is calculated and the segmented threshold is used to mark the target position estimated by the algorithm.

[0115] Example 3

[0116] like Figure 6 As shown, when the initial state of the cooperative target is known, the long baseline positioning algorithm for automatic tracking management decision-making provided by the present application can be applied to multi-target tracking scenarios in cooperative situations.

[0117] The embodiments described above are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, a person skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A long baseline positioning algorithm for automatic tracking management decisions, It is characterized in that The following steps are involved: S1: Define indicator variables, grid the positioning area, calculate the likelihood value of each resolution unit, and initialize the particles; S2: updating the indicator variable based on the Markov transition matrix, and updating the particle state based on the indicator variable; S3: constructing a likelihood ratio function of the particle, and calculating the particle weight according to the likelihood ratio function; S4: resampling, calculating the number of existing particles, and when the ratio of the number of existing particles to the number of particles in the gridded positioning area is greater than 0.6, calculating the target state, and using a segmentation threshold to mark the target position estimated by the algorithm; The target position estimated by the algorithm is marked by using a segmented threshold: when the proportion of particles is greater than 0.8, it means that the positioning target exists and the estimated positioning accuracy of the target position meets the positioning requirements; when the proportion of particles is greater than 0.6 and less than or equal to 0.8 after convergence, it means that the positioning target exists but the estimated positioning accuracy of the target position does not meet the positioning requirements; when the proportion of particles is less than or equal to 0.6, it means that the positioning target does not exist; The target state is calculated according to the following formula: In the formula, is the number of particles present, is the number of particles in the gridded positioning area, is the target state, is the indicator variable of the nth particle at time t, is the state of the nth particle at time t.

2. The long baseline positioning algorithm for automatic tracking management decision making as claimed in claim 1, Features: The definition of indicator variables is to define the indicator variables of the particles as ,by and Respectively characterize the presence and absence of the target; the indicator variable of the particle is sampled according to a 0-1 distribution with a probability of 0.

5.

3. The long baseline positioning algorithm for automatic tracking management decision making as claimed in claim 1, Features: The particle initialization is to use the distance-azimuth polar coordinate system with the maximum likelihood value position as the origin to initialize the particle position; Initialize the particle speed in the velocity-course angle polar coordinate system of the origin; the distance is evenly distributed in The speed is evenly distributed between The azimuth and heading angles are evenly distributed between between, To preset the maximum distance, The maximum speed is preset.

4. The long baseline positioning algorithm for automatic tracking management decision making as claimed in claim 2, Features: The particle state is updated based on the indicator variable as follows: for The particle's state is updated as follows: in, is the indicator variable of the nth particle at time t, is the indicator variable of the nth particle at time t-1, is the state of the nth particle at time t, is the state of the nth particle at time t-1, ,in and Respectively represent the horizontal and vertical position and velocity of the nth particle at time t, represents the transpose of a matrix, is the control input at time t, is the process noise at time t; For other particles, the state update of the particles follows the process of initializing the particles described in step S1.

5. The long baseline positioning algorithm for automatic tracking management decision making as claimed in claim 2, Features: The likelihood ratio function of constructing the particle includes: S3-1: Calculate the direct sound arrival time of the particle. For the mth buoy, the particle The TOA value is: ； in, and is the known position of the mth buoy, is the estimated speed of sound; S3-2: Calculate the index value of the received signal after the buoy matched filtering, The index value of the received signal after matching filtering of the corresponding mth buoy is: ； in, means rounding towards negative infinity, is the sampling frequency; For particles , define the matched filter output of all buoys in the buoy combination as a vector ,definition The received signal after matching filtering for the mth buoy is at index value The amplitude at .

6. The long baseline positioning algorithm for automatic tracking management decision making as claimed in claim 3, Features: The likelihood ratio function is defined as follows: In the formula, The received signal after matching filtering for the mth buoy is at index value The amplitude at is the target observation value at time t, For particles The likelihood ratio function of is the likelihood function of the particle not existing, is the likelihood function of the particle existence. Arrange all the likelihood values ​​in step S1 in descending order, and then calculate the Z score of each data in descending order. Take the first original data with a Z score not greater than 2 as The value of .

7. The long baseline positioning algorithm for automatic tracking management decision making as claimed in claim 5, Features: The weight calculation is performed according to the following formula: ； In the formula, is the unnormalized weight of the particle, is the state of the jth particle at time t, is the indicator variable of the jth particle at time t.

8. A long baseline positioning system for automatic tracking management decisions, It is characterized in that include: Initialization module: used to define indicator variables, grid the positioning area, calculate the likelihood value of each resolution unit, and initialize the particles; State prediction module: used to update indicator variables based on the Markov transition matrix, and update particle states based on the indicator variables; Likelihood ratio function module: constructs the likelihood ratio function of the particle and calculates the particle weight according to the likelihood ratio function; Target state estimation module: used for resampling, calculating the number of existing particles, and when the ratio of the number of existing particles to the number of particles in the gridded positioning area is greater than 0.6, calculating the target state and marking the target position estimated by the algorithm using a segmentation threshold; The target position estimated by the algorithm is marked by using a segmented threshold: when the proportion of particles is greater than 0.8, it means that the positioning target exists and the estimated positioning accuracy of the target position meets the positioning requirements; when the proportion of particles is greater than 0.6 and less than or equal to 0.8 after convergence, it means that the positioning target exists but the estimated positioning accuracy of the target position does not meet the positioning requirements; when the proportion of particles is less than or equal to 0.6, it means that the positioning target does not exist; The target state is calculated according to the following formula: In the formula, is the number of particles present, is the number of particles in the gridded positioning area, is the target state, is the indicator variable of the nth particle at time t, is the state of the nth particle at time t.

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