A positioning batch number association method for multi-station joint observation of a non-cooperative target

Abstract

A method for batch number association of positioning for non-cooperative targets observed jointly by multiple stations is disclosed, relating to the field of multi-station joint observation information association. This invention aims to address the problem that existing batch number association methods for multi-station measurement information struggle to provide stable and effective association results, leading to a decrease in subsequent positioning and tracking accuracy. The invention includes: acquiring the measurement set obtained from observation station s to obtain the target's azimuth measurement power spectrum distribution function and line spectrum frequency; and using this information to obtain the azimuth feature subset Θ of the associated set. s‑1,q The spatial fuzzy relation matrix of the azimuth features to be associated is obtained by using the continuous spectrum feature subset of the already associated set and the continuous spectrum feature fuzzy relation matrix of the features to be associated. The line spectrum feature subset of the already associated set is then used to obtain the fuzzy relation matrix of the line spectrum features to be associated. A comprehensive fuzzy relation matrix is ​​constructed and two-dimensional association is performed to obtain the batch number association result. This invention is used to associate batch numbers of multi-station observation targets.

Description

Technical Field

[0001] This invention relates to the field of information association from multi-station joint observations, and in particular to a method for associating the location batch numbers of non-cooperative targets in multi-station joint observations. Background Technology

[0002] Multi-station joint non-cooperative localization methods possess advantages such as good scalability and strong concealment, making them suitable for underwater target localization where it is inconvenient to install cooperative beacons. An important type of information from non-cooperative observations is broadband radiated noise information, which may originate from the passive radiation or active acoustic emission of underwater targets, carrying various features including spectral information. Fully utilizing these features for target localization is a key issue in multi-station joint non-cooperative localization methods. In complex environments, algorithms based on Direction of Arrival (DOA) are effective for distinguishing target measurements. With the development of high-resolution orientation technology, DOA-based algorithms have become even more advantageous in the application of multi-station joint non-cooperative localization problems.

[0003] For non-cooperative target localization, fully utilizing historical information is crucial. However, in the initial observation phase, due to the lack of effective historical information, target localization can only be achieved directly using measurement data. After acquiring target measurement data, it is necessary to correlate information emitted by the same target at the same time to achieve accurate localization. Therefore, the correlation problem in multi-station joint localization can be divided into two categories: one is to correlate measurement data from multiple stations by batch number, and the other is to correlate information of the same target at the same time in a spatiotemporal manner. When the target is moving at low speed, the spatiotemporal correlation problem can be ignored; we focus on the target batch number correlation problem.

[0004] Currently, spatial measurement information is mainly used to solve the target association problem by associating measurement information from multiple stations in batches. Typical algorithms include multi-dimensional allocation and divide-and-conquer greedy algorithms. These algorithms associate measurements based on the minimum cost or distance of the target in space, performing well when the number of targets is small, but degrading as the number of targets increases. Besides spatial information, some literature proposes using additional feature information to solve the target batch association problem. Swartling proposed using blind source separation to extract features to associate DOAs of different arrays, but this algorithm only works in scenarios with two observation stations. To address the limitation on the number of observation stations, Alexandridis proposed a greedy association algorithm based on histogram features, clustering similar features obtained from different observation stations into groups, but this method is still sensitive to false alarms. Dang, building on Alexandridis' work, proposed a two-dimensional allocation method based on histogram features, which performs well in false alarm scenarios. These feature-based algorithms are all proposed for indoor acoustic scenarios, but due to the complex time- and space-varying characteristics of underwater acoustic channels, the performance of association algorithms using these features degrades. For underwater acoustic positioning scenarios, Qu Guangyu proposed an association algorithm that utilizes power spectrum features or time-frequency window features. This algorithm performs well when the features are stable, but its performance degrades as the number of targets increases. Therefore, the existing batch association method for multi-station measurement information still has the problem of not being able to provide stable and effective association results when observing multiple targets, which will lead to a decrease in subsequent positioning accuracy. Summary of the Invention

[0005] The purpose of this invention is to solve the problem that existing batch number association methods for multi-station measurement information are difficult to provide stable and effective association results, leading to a decrease in the accuracy of subsequent positioning and tracking. Therefore, this invention proposes a positioning batch number association method for multi-station joint observation of non-cooperative targets.

[0006] The specific process of a method for associating location batch numbers of non-cooperative targets in multi-station joint observation is as follows:

[0007] Step 1: Obtain the measurement set obtained by observation station s Thus, the azimuth measurement of the target is obtained. Then Obtain the power spectral distribution function and line spectrum frequency

[0008] Step 2: Using the information obtained in Step 1 Obtain the directional feature subset Θ of the associated set. s-1,q and Spatial fuzzy relation matrix

[0009] Step 3: Utilize the information obtained in Step 1 By obtaining fuzzy relationships between continuous spectral features measured at different observation stations, a subset of continuous spectral features of the associated set can be obtained. and features of the continuous spectrum to be correlated Continuous spectrum fuzzy relation matrix

[0010] Step 4: Utilize the information obtained in Step 1 By obtaining the fuzzy relationships between the line spectral features measured at different observation stations, a subset of the line spectral features of the associated set can be obtained. and the spectral features to be correlated Fuzzy relation matrix

[0011] Step 5: Utilize the results obtained in Steps 2 to 4 A comprehensive fuzzy relation matrix is ​​constructed, and the comprehensive fuzzy relation matrix is ​​used to perform two-dimensional association of target location batch numbers to obtain batch number association results.

[0012] Furthermore, in step one, the measurement set obtained by the observation station s... As shown in the following formula:

[0013]

[0014] Where S is the total number of observation stations, n s i is the number of targets observed by observation station s. s ∈{i1,i2,...,i S}, i s Let i be the i-th target observed by observation station s, where i ∈ [1, N] and N is the total number of targets in the environment. It is the i-th observation station of the s-th observation station. s A set of measurements, The azimuth measurement of the target is the azimuth feature to be associated.

[0015] Furthermore, in step two, the information obtained in step one... Obtain the directional feature subset Θ of the associated set. s-1,q and Spatial fuzzy relation matrix This includes the following steps:

[0016] Step 2.1: Define an S-tuple to represent all the association results of the target azimuth measurement set obtained by the observation station, and obtain the azimuth association cost corresponding to the S-tuple. As shown in the following formula:

[0017]

[0018] Where S = {i1i2…i} S}, It is the target detection probability; Φ s Indicates the false alarm distribution; σ s This represents the standard deviation of the azimuth measurement. It is the azimuth measurement of the target estimated by the S-tuple; u(i s () represents a binary correlation variable, i.e., when observation station s has a missed report. s =0 when u(i s )=0, otherwise u(i s ) = 1;

[0019] Step 22: Utilize the location correlation cost obtained in Step 21 Get the associated set Z s-1,q The azimuth feature subset Θ s-1,q and location features to be associated The cost of association between them As shown in the following formula:

[0020]

[0021] Among them, l s-1,q This represents the index of the qth associated set among the first s-1 observation stations. After indexing is created ∧ is Zadeh's small operator;

[0022] Steps 2 and 3: Define the fuzzy membership function M of the spatial fuzzy relation. K (k)∈[0,1], and the result obtained in step two is... Substitute M K In (k), the spatial fuzzy relation matrix is ​​obtained. As shown in the following formula:

[0023]

[0024]

[0025] in, This is a conservative threshold for orientation ambiguity. The threshold for ambiguity segmentation is k, where k is a parameter variable. It is a column label in ρ. yes Arrange the vectors in ascending order;

[0026] Step Two Four: Utilizing the information obtained in Step Two Three When obtaining the location feature subset Θ of the already associated set for observation station s, s-1,q and location features to be associated Spatial fuzzy relation matrix

[0027] Where Q is the total number of associated sets.

[0028] Furthermore, in step three, the information obtained in step one... To obtain the fuzzy relationships between continuous spectral features measured at different observation stations, thereby obtaining a subset of continuous spectral features from the associated set. and features of the continuous spectrum to be correlated Continuous spectrum fuzzy relation matrix This includes the following steps:

[0029] Step 3.1: Obtain the i-th data obtained from observation station s. s The directional power spectrum distribution function corresponding to each target is: Then use Obtain the set of all continuous spectra obtained from observation station s

[0030] in, These are the features of the continuous spectrum to be correlated;

[0031] Step 3.2: Define the associated set Z s-1,q The continuous spectrum feature subset in is ,Establish and Fuzzy membership functions between

[0032] Step 33, Utilize Obtain the fuzzy relation matrix of the continuous spectrum As shown in the following formula:

[0033]

[0034] Step 3-4: Using the information obtained in Step 3-3 When obtaining the continuous spectrum feature subset of the already correlated set of observation station s, and features of the continuous spectrum to be correlated The fuzzy relation matrix of the continuous spectrum is

[0035] Furthermore, the aforementioned and Fuzzy membership functions between As shown in the following formula:

[0036]

[0037] in, It is established and The Wasserstein distance between them, Th C1 As a conservative threshold for continuous spectrum ambiguity, ThC2 It is the threshold for segmenting continuous spectrum ambiguity.

[0038] Furthermore, in step four, the information obtained in step one... By obtaining the fuzzy relationships between line spectral features measured at different observation stations, a subset of line spectral features of the associated set can be obtained. and the spectral features to be correlated Fuzzy relation matrix This includes the following steps:

[0039] Step 41: Extend the line spectrum according to the relative Doppler frequency shift to obtain the line spectrum feature set.

[0040] in, It is a characteristic of the line spectrum;

[0041] Step 42: Utilize the line spectrum features obtained in Step 41 Construct a subset of the line spectral features of the associated set as and Fuzzy membership function As shown in the following formula:

[0042]

[0043]

[0044] Among them, Th L1 ,Th L2 These are the conservative threshold and the segmentation threshold for ambiguity, respectively. yes and The maximum overlap similarity is determined by ∨, which is the largest operator. yes The j-th element, yes and The overlap similarity;

[0045] Step 43: Using the information obtained in Step 42 Obtaining the elements of the line spectrum fuzzy relation matrix Then use Obtain the spectral feature subset of the associated set and the spectral features to be correlated The fuzzy relation matrix is

[0046] Furthermore, line spectrum features

[0047]

[0048] in, It is an extended spectral range. It is a spectral characteristic, Δf is Maximum tolerable frequency deviation.

[0049] Furthermore, in step five, the information obtained from steps two to four... Constructing a comprehensive fuzzy relation matrix and performing two-dimensional association to obtain batch number association results includes the following steps:

[0050] Step 51, Utilize Construct a comprehensive fuzzy relation matrix between the measurements to be associated and the already associated sets;

[0051] Step 5.2: Define binary association decision variables

[0052] The Used to determine if the set Z is already associated. s-1,q and measurements to be correlated Whether they come from the same target is determined by the following formula:

[0053]

[0054] Step 53: Use the elements in the comprehensive fuzzy relation matrix obtained in Step 51 and the elements obtained in Step 52... Define the target batch number association problem and constraints of multi-station joint observation non-cooperative positioning:

[0055] The target batch number association problem in the multi-station joint observation non-cooperative positioning is as follows:

[0056]

[0057] The constraints for the target batch number association problem in multi-station joint observation non-cooperative positioning are as follows:

[0058]

[0059]

[0060] Step 54: Use the Hungarian algorithm to solve the target batch number association problem established in Step 53 for multi-station joint observation non-cooperative positioning, and thus perform target batch number association.

[0061] Furthermore, the utilization in step five-one... Construct a comprehensive fuzzy relation matrix between the measurements to be associated and the already associated sets, as shown in the following formula:

[0062]

[0063]

[0064] in, It is an element of a comprehensive fuzzy relation matrix.

[0065] Furthermore, in step five-four, the Hungarian algorithm is used to solve the target batch number association problem established in step five-three for multi-station joint observation non-cooperative positioning, thereby performing target batch number association and obtaining batch number association results. Specifically:

[0066] First, the measurements from the first observation station are placed into the associated set. Then, the measurements from the second observation station are associated with the first observation station. At this point, s = 2, and the number of associated sets is equal to the number of measurements from the first observation station, i.e., Q = n1. The associated sets and index sets are then as follows:

[0067]

[0068] Then, the remaining station measurements are sequentially correlated with the station data to obtain the correlation results, and the correlated set and index set are updated, as follows:

[0069] 1) If the association result and Then the associated set and index set will be updated as follows:

[0070]

[0071] Where δ is the preset membership threshold;

[0072] 2) If the association result and If the association fails, the association decision variable will be reset, as shown in the following formula:

[0073]

[0074] 3) If This indicates that there are no measurements at observation station s related to Z. s-1,q If a relationship is established, then the associated set and the index set are updated, as follows:

[0075] Z s,q ={Z s-1,q};l s,q ={l s-1,q ,0}

[0076] 4) If This indicates that there are no associated sets and measurements. If a relationship is established, the number of associated sets is increased, and the associated sets and index sets are updated, as follows:

[0077]

[0078] Among them, O 1×(s-1)The default value is a 0 matrix;

[0079] After correlating all measurements acquired from the S observation stations, Q correlated sets Z are obtained from the S observation stations. S,q and index set l S,q q = 1, ..., Q, and the associated set is the batch number association result.

[0080] The beneficial effects of this invention are as follows:

[0081] To address the batch number association problem in multi-station joint positioning, this invention proposes a batch number association algorithm for non-cooperative targets observed jointly by multiple stations. Based on fully utilizing target feature information and considering unfavorable conditions such as missed detections and false alarms within the scene, this invention utilizes fuzzy mathematics theory to construct fuzzy relation matrices between azimuth information, continuous spectrum features, and line spectrum features of measurements from different observation stations. By synthesizing the fuzzy relation matrices, the measurement with the highest fuzzy membership degree among different observation stations—that is, the clearest measurement—is found, and a two-dimensional association is used for solution. This invention designs a multi-observation station association strategy using rough set theory, maximizing the use of information provided by the detection end, improving the accuracy of multi-observation station association, and thus enhancing subsequent positioning performance. Attached Figure Description

[0082] Figure 1 This is a flowchart of the present invention;

[0083] Figure 2(a) is a schematic diagram of the power spectrum of a motorboat;

[0084] Figure 2(b) is a schematic diagram of the power spectrum of fishing vessels;

[0085] Figure 2(c) is a schematic diagram of the power spectrum of the cruise ship;

[0086] Figure 2(d) is a schematic diagram of the power spectrum of a roll-on / roll-off ship;

[0087] Figure 2(e) is a schematic diagram of the power spectrum of the pilot ship;

[0088] Figure 2(f) is a schematic diagram of the power spectrum of the sailboat;

[0089] Figure 3 A schematic diagram showing the deployment of observation stations and targets;

[0090] Figure 4 A schematic diagram of the target location association results. Detailed Implementation

[0091] Specific implementation method one: as follows Figure 1 As shown in the figure, the specific process of the method for associating the location batch number of a non-cooperative target in multi-station joint observation in this embodiment is as follows:

[0092] Step 1: Consider the multi-station joint observation underwater acoustic non-cooperative target localization problem consisting of S observation stations. The locations of the observation stations are known. Assume that there are N targets in the environment simultaneously, where N is unknown. The observation azimuths of the targets do not overlap at different observation stations. Obtain the measurement set obtained by the observation stations s∈{1,2,…,S}. As shown in the following formula:

[0093]

[0094] Where S is the total number of observation stations, n s i is the number of targets observed by observation station s. s Let i be the i-th target observed by observation station s, where i ∈ [1, N] and N is the total number of targets in the environment. It is the i-th observation station of the s-th observation station. s A set of measurements, The azimuth measurement of the target is the azimuth feature to be associated. and They represent the directions respectively. The power spectral distribution function and line spectral frequencies were obtained from the above.

[0095] Define Z s-1,q ,s=1,2,…,S; q=1,…,Q,Z s-1,q Let Z be the q-th associated measurement set, where Q is the number of associated sets. 0,q It is an empty set.

[0096] Step 2: Using the information obtained in Step 1 Obtain data from all observation stations. The spatial fuzzy relations of the observed information are traversed and calculated to obtain the azimuth feature subset Θ of the associated set. s-1,q and location features to be associated Spatial fuzzy relation matrix This includes the following steps:

[0097] Step 2.1: Establish S = {i1i2...i...} S The tuple represents all possible associations of the target azimuth measurement set obtained from the observation station, and uses the mapping g K (·) Define the orientation association cost for each S-tuple. As shown in the following formula:

[0098]

[0099] Among them, i s ∈{i1,i2,...,i S}, where S is the total number of observation stations. The same S tuple cannot contain multiple measurements from the same observation station. Furthermore, if it does not contain any measurements from observation station s, then a dummy measurement corresponds to i. s =0, i.e. i s =0 when θ s,0 These are virtual measurements, and each virtual measurement in the S-tuple comes from a different observation station; It is the target detection probability; Φ s It is a false alarm distribution; σ s It is the standard deviation of the orientation measurement; It is the measurement of the target's orientation. Represents the azimuth measurement of the target estimated by the S-tuple; u(i s () represents a binary correlation variable, i.e., when observation station s has a missed report. s =0 when u(i s )=0, otherwise u(i s ) = 1.

[0100] Step 22, The vector ρ is obtained by arranging the vectors from smallest to largest:

[0101]

[0102] in,

[0103] Step 23: Using the Zadeh minimization operator ∧ in fuzzy mathematics, and utilizing the orientation association cost obtained in Step 21, obtain the associated set Z. s-1,q The azimuth feature subset Θ s-1,q and location features to be associated The cost of association between them is As shown in the following formula;

[0104]

[0105] Among them, l s-1,q This represents the index of the qth associated set among the first s-1 observation stations. After indexing is created

[0106] Step 24: Utilizing the concepts of fuzzy mathematics, introduce the concept of fuzzy membership function and define the fuzzy membership function M of spatial fuzzy relations. K (k)∈[0,1], and the results obtained in steps two and three are... Substitute M K In (k), the spatial fuzzy relation matrix is ​​obtained.

[0107]

[0108]

[0109] in, This is a conservative threshold for orientation ambiguity. The threshold for ambiguity segmentation is k, where k is a parameter variable. It is a column label in ρ.

[0110] Step 2.5: When associating observation station s, the azimuth feature subset Θ of the already associated set... s-1,q and location features to be associated The spatial fuzzy relation matrix is

[0111] Where Q is the total number of associated sets.

[0112] Step 3: Calculate the fuzzy relationships between the continuous spectral features measured at different observation stations, and obtain the continuous spectral feature subset of the associated set. and features of the continuous spectrum to be correlated The continuous spectrum fuzzy relation matrix is ​​obtained by the following steps:

[0113] Step 3.1: Obtain the i-th data obtained from observation station s. s The directional power spectrum distribution function corresponding to each target is: Then use The set of all continuous spectra obtained from observation station s is obtained as follows:

[0114]

[0115]

[0116] Step 3.2: Define the fuzzy membership function M for the fuzzy relation of the continuous spectrum. C (U,v), defining the associated set Z s-1,q The continuous spectrum feature subset in is Since the continuous spectral distributions of the same target at different observation stations have structurally similar characteristics, the Wasserstein distance is used to construct a continuous spectral feature subset to represent the associated set. and features of the continuous spectrum to be correlated Fuzzy membership function of the degree of membership between

[0117]

[0118] Where, d C (U,v) is the minimum Wasserstein distance d between the distribution set U = {u1, u2, ...} and the distribution v. C (U,v), d W(u,v) is the Wasserstein distance between distributions u and v; u and v are two hypothetical distributions; in formula (8) Th C1 (=3), Th C2 (=10) are the conservative threshold and the segmentation threshold for continuous spectrum ambiguity, respectively;

[0119] Among them, due to the minimum Wasserstein distance d C The range of variation of (U,v) is relatively small, and the smaller the value, the more similar the continuous spectrum. Therefore, the fuzzy membership function of the continuous spectrum feature is constructed into a small, gently shaped function. Thus, the fuzzy membership function M of the continuous spectrum feature is defined. C (U,v)∈[0,1]

[0120] Step 33: Using the information obtained in Step 32 Obtain the fuzzy relation matrix of the continuous spectrum As shown in the following formula:

[0121]

[0122] Steps three and four: When correlation is performed on observation station s, the continuous spectrum feature subset of the correlated set is... and features of the continuous spectrum to be correlated The fuzzy relation matrix of the continuous spectrum is

[0123] Step 4: Obtain the fuzzy relationships between the line spectrum features measured at different observation stations, and obtain the subset of line spectrum features of the associated set. and the spectral features to be correlated The fuzzy relation matrix includes the following steps:

[0124] Step 4.1 If observation station s is at the i-th... s Obtain from each direction Root line spectrum, Let f represent the frequency of the m-th line spectrum. Since the line spectra obtained from different observation stations are affected by the Doppler frequency shift, the line spectrum is extended according to the relative Doppler frequency shift, denoted as Δf. Maximum tolerance frequency offset, obtaining line spectrum features Thus, the set of all spectral features is obtained as follows:

[0125]

[0126]

[0127]

[0128] in, It is an extended spectral range. It is a characteristic of the line spectrum;

[0129] Step 42: Utilize the line spectrum features obtained in Step 41 Construct a subset of line spectral features to represent the associated set. and the spectral features to be correlated Fuzzy membership function of the degree of membership between This includes the following steps:

[0130] First, define set A. j The overlap similarity between set B and set B is d. O (A j B), using the maximum operator ∨, we define the maximum value d of the overlap similarity between the multiset Ξ={A1,A2,…} and set B. L (Ξ,B) represents:

[0131]

[0132] Among them, A j It is the j-th element in Ξ;

[0133] Then, due to the maximum overlap similarity d L A larger value for (Ξ,B) indicates a greater likelihood that the measurements originate from the same target. Therefore, the fuzzy membership function of the line spectrum feature is constructed as a relatively large, gently shaped function. The fuzzy membership function M of the line spectrum feature... L (Ξ,B)∈[0,1] is defined as:

[0134]

[0135] Among them, Th L1 (=0.2), Th L2 (=0.8) are the conservative threshold and segmentation threshold for ambiguity, respectively;

[0136] Step 43, The j-th element and Substitute the fuzzy membership function to calculate the elements of the line spectrum fuzzy relation matrix. This allows us to obtain the spectral feature subset of the correlated set when the observation station s is correlated. and the spectral features to be correlated The fuzzy relation matrix is

[0137]

[0138] Step 5: Utilize the information obtained in Step 2 The result obtained in step three The result obtained in step four A comprehensive fuzzy relation matrix is ​​constructed, and the comprehensive fuzzy relation matrix is ​​used to perform two-dimensional association of target location batch numbers to obtain batch number association results. The steps include:

[0139] Step 51: After obtaining the fuzzy relation matrix of spatial information and spectral features, determine the comprehensive fuzzy relation matrix between the measurement to be correlated and the already correlated set:

[0140]

[0141]

[0142] in, These are elements of a comprehensive fuzzy relation matrix;

[0143] Step 5.2: Define binary association decision variables , used to represent the associated set Z s-1,q and measurements to be correlated The determination result of whether they come from the same target is defined as follows:

[0144]

[0145] The others in formula (18) are considered failed associations;

[0146] Step 53: Using the elements in the comprehensive fuzzy relation matrix obtained in Step 51 and the elements obtained in Step 52... Define the target batch number association problem and its constraints in multi-station joint observation non-cooperative positioning:

[0147] The target batch number association problem in multi-station joint observation and non-cooperative positioning can be defined as:

[0148]

[0149] The constraints are:

[0150]

[0151] In formula (20), the first condition indicates that at most one measurement at observation station s is associated with the already associated set Z. s-1,q Association; the second condition indicates that there is at most one associated set Z. s-1,q With measurement Related.

[0152] The constraint stems from the fact that both associated sets and unassociated measurements can be associated at most once.

[0153] Step 54: Use the Hungarian algorithm to solve the target batch number association problem established in Step 53 for multi-station joint observation non-cooperative positioning, and then associate the target batch numbers as follows:

[0154] In the first step of association, the measurements from the first observation station are added to the associated set, and the measurements from the second observation station are associated with the first observation station. At this point, s = 2, and the number of associated sets equals the number of measurements from observation station 1, i.e., Q = n1. The associated set and the index set can be represented as:

[0155]

[0156] In subsequent associations, the associated set and index set are updated as follows:

[0157] 1) If the association result and (δ is the defined membership threshold), associated sets and index sets are more...

[0158] new:

[0159]

[0160] 2) If the association result and If the association fails, the association decision variable will be reset.

[0161]

[0162] 3) If This indicates that there are no measurements at observation station s related to Z. s-1,q Associations, associated sets and index sets

[0163] renew:

[0164] Z s,q ={Z s-1,q};l s,q ={l s-1,q ,0} (24)

[0165] 4) If This indicates that there are no associated sets and measurements. Association, the number of associated sets increases:

[0166]

[0167] Among them, O 1×(s-1) The default value is 0;

[0168] After correlating the measurements from all the observation stations, we obtained Q correlated sets Z from the S observation stations. S,q and index set l S,q(q = 1, ..., Q). The measurement set explains the most likely combination of orientation and characteristic measurements. Estimating a single target in two-dimensional space requires at least two orientation measurements, so the associated set of measurements from at least two observation stations is used for localization, and the final estimated number of targets equals the number of sets.

[0169] Example:

[0170] To verify the beneficial effects of the present invention, simulation experiments were conducted to illustrate its features:

[0171] Consider a multi-station joint non-cooperative localization scenario with a square topology of 4 stations and a side length of 4km. Each station independently observes targets within its area and extracts the azimuth information, continuous spectrum structure, and line spectrum frequency of the detected targets. Angle measurements follow a Gaussian distribution with a mean of 0° and a standard deviation of 1°. The number of false alarms follows a Poisson distribution with an expectation of λ. False alarms are uniformly distributed within the observation angle [0, π / 2) of each station. The ambiguity membership threshold is δ = 0.3. The maximum likelihood algorithm is used in the localization process. Target radiated noise is taken from the ShipsEar underwater ship noise database. First, six types of ship noise are selected, and their continuous spectrum and line spectrum features are extracted to construct the target radiated noise signal used in this example. Then, the signal is transmitted to the station through a shallow sea acoustic channel according to the deployment location, and -5dB Gaussian white noise is added. Finally, the azimuth measurement and feature extraction of the received ship radiated noise are performed to obtain the measurement set of the station. The power spectra of the radiated noise signals from the targets correspond to motorboats, fishing boats, mail ships, roll-on / roll-off ships, pilot boats, and sailboats, respectively. The deployment of targets and observation stations is as follows: Figure 3 As shown, the power spectra corresponding to targets 1-6 are divided into Figures 2(a)-2(f) .

[0172] Figure 4 This displays the association and localization results in this embodiment when all observation stations have a target detection probability of 1 and a false alarm expectation of 0. From Figure 4 As can be seen from the simulation results, under the set simulation conditions, the algorithm in this example can accurately estimate the number of targets in space, indicating that the algorithm in this example can effectively achieve target association and localization when the information provided by the observation station is accurate.

[0173] This invention may have other embodiments. Without departing from the spirit and essence of this invention, those skilled in the art can make various corresponding changes and modifications according to this invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. A method for associating location batch numbers of non-cooperative targets in multi-station joint observation, characterized in that... The specific process of the method is as follows: Step 1: Obtain the measurement set obtained by observation station s Thus, the azimuth measurement of the target is obtained. Then Obtain the power spectral distribution function and line spectrum frequency ; Step 2: Using the information obtained in Step 1 Obtain the location feature subset of the associated set. and Spatial fuzzy relation matrix ; Definition of the first A set of already associated measurements , It is the number of associated sets. It is an empty set. It is the station number. This is the total number of observation stations; Step 3: Utilize the information obtained in Step 1 By obtaining fuzzy relationships between continuous spectral features measured at different observation stations, a subset of continuous spectral features of the associated set can be obtained. and features of the continuous spectrum to be correlated Continuous spectrum fuzzy relation matrix ; Step 4: Utilize the information obtained in Step 1 By obtaining the fuzzy relationships between the line spectral features measured at different observation stations, a subset of the line spectral features of the associated set can be obtained. and the spectral features to be correlated Fuzzy relation matrix ; Step 5: Utilize the results obtained in Steps 2 to 4 , , A comprehensive fuzzy relation matrix is ​​constructed, and the comprehensive fuzzy relation matrix is ​​used to perform two-dimensional association of target location batch numbers to obtain batch number association results.

2. The method for associating location batch numbers of non-cooperative targets in multi-station joint observation according to claim 1, characterized in that: The measurement set obtained from observation station s in step one As shown in the following formula: (1) in, It is the total number of observation stations. It is an observation station The number of targets observed , It is an observation station The i-th observed target, N is the total number of targets in the environment. It is the first The first observation station A set of measurements, The azimuth measurement of the target is the azimuth feature to be associated.

3. The method for associating location batch numbers of non-cooperative targets in multi-station joint observation according to claim 2, characterized in that: The second step utilizes the information obtained in the first step. Obtain the location feature subset of the associated set. and Spatial fuzzy relation matrix This includes the following steps: Step Two: Definition The tuple represents all the associated results of the target azimuth measurement set obtained by the observation station, and obtains Location association cost corresponding to the tuple As shown in the following formula: （2） in, , It is the target detection probability; Indicates the distribution of false alarms; This represents the standard deviation of the azimuth measurement. It is the orientation measurement of the target estimated by the S-tuple; This represents a binary correlation variable, indicating that when observation station s experiences a missed report... hour ,otherwise ; Step 22: Utilize the location correlation cost obtained in Step 21 Get associated sets The directional feature subset in and location features to be associated The cost of association between them As shown in the following formula: （3） in, Indicates the preceding The first observation station An index of an already associated set, After indexing is created , Zadeh takes the smaller operator; Steps 2 and 3: Define the fuzzy membership function of spatial fuzzy relations. and the results obtained in step two. Substitution In the process, the spatial fuzzy relation matrix is ​​obtained. As shown in the following formula: （4） （5） in, This is a conservative threshold for orientation ambiguity. The threshold for ambiguity segmentation is k, where k is a parameter variable. , yes A column of labels in yes Arrange the vectors in ascending order; Step Two Four: Utilizing the information obtained in Step Two Three When obtaining the location feature subset of the already associated set for observation station s, and location features to be associated Spatial fuzzy relation matrix ; Where Q is the total number of associated sets.

4. The method for associating location batch numbers of non-cooperative targets in multi-station joint observation according to claim 3, characterized in that: Step three utilizes the information obtained in step one. By obtaining fuzzy relationships between continuous spectral features measured at different observation stations, a subset of continuous spectral features of the associated set can be obtained. and features of the continuous spectrum to be correlated Continuous spectrum fuzzy relation matrix This includes the following steps: Step 3.1: Obtain the first... The directional power spectrum distribution function corresponding to each target is: Then use Obtain the set of all continuous spectra obtained from observation station s ; in, These are the features of the continuous spectrum to be correlated; Step 3.2: Define the associated set The continuous spectrum feature subset in is ,Establish and Fuzzy membership functions between ; Step 33, Utilize Obtain the fuzzy relation matrix of the continuous spectrum As shown in the following formula: Step 3-4: Using the information obtained in Step 3-3 When obtaining the continuous spectrum feature subset of the already correlated set of observation station s, and features of the continuous spectrum to be correlated The fuzzy relation matrix of the continuous spectrum is .

5. The method for associating location batch numbers of non-cooperative targets in multi-station joint observation according to claim 4, characterized in that: The and Fuzzy membership functions between As shown in the following formula: in, It is established and Wasserstein distance between them This is a conservative threshold for continuous spectrum ambiguity. It is the threshold for segmenting continuous spectrum ambiguity.

6. The method for associating location batch numbers of non-cooperative targets in multi-station joint observation according to claim 5, characterized in that: Step four utilizes the information obtained in step one. By obtaining the fuzzy relationships between line spectral features measured at different observation stations, a subset of line spectral features of the associated set can be obtained. and the spectral features to be correlated Fuzzy relation matrix This includes the following steps: Step 41: Extend the line spectrum according to the relative Doppler frequency shift to obtain the line spectrum feature set. ; in, It is a characteristic of the line spectrum; Step 42: Utilize the line spectrum features obtained in Step 41 Construct a subset of the line spectrum features of the associated set as and Fuzzy membership function As shown in the following formula: in, , These are the conservative threshold and the segmentation threshold for ambiguity, respectively. yes and The maximum overlap similarity. It is to take the larger number. yes The j-th element, yes and The overlap similarity; Step 43: Using the information obtained in Step 42 Obtaining the elements of the line spectrum fuzzy relation matrix Then use Obtain the spectral feature subset of the associated set and the spectral features to be correlated The fuzzy relation matrix is .

7. The method for associating location batch numbers of non-cooperative targets in multi-station joint observation according to claim 6, characterized in that: Line spectral characteristics ; ； in, It is an extended spectral range. It is a spectral feature. yes Maximum tolerable frequency deviation.

8. The method for associating location batch numbers of non-cooperative targets in multi-station joint observation according to claim 7, characterized in that: The fifth step utilizes the information obtained from steps two to four. , , Constructing a comprehensive fuzzy relation matrix and performing two-dimensional association to obtain batch number association results includes the following steps: Step 51, Utilize , , Construct a comprehensive fuzzy relation matrix between the measurements to be associated and the already associated sets; Step 5.2: Define binary association decision variables ; The Used to determine if a set is already associated. and measurements to be correlated Whether they come from the same target is determined by the following formula: Step 53: Use the elements in the comprehensive fuzzy relation matrix obtained in Step 51 and the elements obtained in Step 52... Define the target batch number association problem and constraints of multi-station joint observation non-cooperative positioning: The target batch number association problem in the multi-station joint observation non-cooperative positioning is as follows: The constraints for the target batch number association problem in multi-station joint observation non-cooperative positioning are as follows: Step 54: Use the Hungarian algorithm to solve the target batch number association problem established in Step 53 for multi-station joint observation non-cooperative positioning, and thus perform target batch number association.

9. The method for associating location batch numbers of non-cooperative targets in multi-station joint observation according to claim 8, characterized in that: The utilization in step five one , , Construct a comprehensive fuzzy relation matrix between the measurements to be associated and the already associated sets, as shown in the following formula: in, It is an element of a comprehensive fuzzy relation matrix.

10. The method for associating location batch numbers of non-cooperative targets in multi-station joint observation according to claim 9, characterized in that: Step 54 involves using the Hungarian algorithm to solve the target batch number association problem established in Step 53 for multi-station joint observation non-cooperative positioning, thereby associating target batch numbers and obtaining batch number association results. Specifically: First, the measurements from the first observation station are placed into the associated set. Then, the measurements from the second observation station are associated with the first observation station. At this point, s=2, and the number of associated sets equals the number of measurements from the first observation station. At this point, the associated set and index set are as follows: Then, the remaining station measurements are sequentially correlated with the station data to obtain the correlation results, and the correlated set and index set are updated, as follows: 1) If the association result and Then the associated set and index set will be updated as follows: in, It is a preset membership threshold; 2) If the association result and If the association fails, the association decision variable will be reset, as shown in the following formula: 3) If This indicates that there are no measurements or data at observation station s. If a relationship is established, then the associated set and the index set are updated, as follows: 4) If This indicates that there are no associated sets and measurements. If a relationship is established, the number of associated sets is increased, and the associated sets and index sets are updated, as follows: in, The default value is a 0 matrix; After correlating the measurements obtained from all observation stations, then measurements were obtained from S observation stations. A set of already associated and index set , =1,…, The associated set is the batch number association result.

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