Multi-array fusion positioning method based on maximum likelihood criterion
By adopting a fusion positioning method based on the maximum likelihood criterion in the multi-array positioning method, combined with low-rank matrix reconstruction and distribution modeling, the problem of imbalance in positioning accuracy and calculation complexity in the prior art is solved, and efficient multi-array fusion positioning is achieved.
Patent Information
- Application Number
- CN202510001404.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-01-02
- Publication Date
- 2025-06-03
AI Technical Summary
The existing multi-array positioning methods cannot balance the positioning accuracy and computational complexity, and are limited by the unbalanced bandwidth of the received array communication, so they cannot use intermediate parameters and observation data for fusion positioning at the same time.
Using a multi-array fusion positioning method based on the maximum likelihood criterion, the angular parameters and observation data transmitted by the received array are fused through low-rank matrix reconstruction technology, the von Misess distribution and Gaussian distribution are established, and the combined likelihood function is formed, and the processing is simplified through least squares and eigenvalue decomposition is introduced, and the weight factor and normalization are introduced to improve the fusion effect.
It achieves higher positioning accuracy and lower calculation complexity, balances positioning accuracy and calculation complexity, and can adjust the weight factor according to the communication environment of the receiving array, breaking through the limitation of unbalanced communication bandwidth, and can use angle parameters and observation data for fusion positioning at the same time.
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Figure CN120086785A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of signal processing. Specifically, in array signal processing, it is a multi-array fusion positioning method, and more specifically, it relates to a multi-array fusion positioning method based on the maximum likelihood criterion. Background Art
[0002] The multi-array positioning technology is a technology that estimates the target position jointly according to the received measurement information by multiple distributed receiving arrays working together. Traditional multi-array positioning methods can be divided into the direct positioning method (DPD, direct position determination) and the two-step method. The direct positioning method refers to the method that the fusion center directly processes the observed data information transmitted by the receiving array to estimate the source position. In this method, there is no need to estimate the intermediate result first during the signal processing, but the final source position information is obtained through optimization and other means; the two-step method is a method that divides the positioning process into two independent steps. The first step estimates certain parameters containing the source position information, such as AOA (Angle of Arrival), TOA (Time of Arrival), etc. The second step estimates the source position through methods such as exhaustive search method, least squares method, pseudo-linear and gradient combination method, etc. In this patent, the two-step method based on AOA is mainly considered.
[0003] The direct positioning method and the two-step method each have their own advantages and disadvantages. For example, in terms of accuracy, the direct positioning method directly realizes positioning through the observed data, and the positioning accuracy is relatively high. While the two-step method decomposes the positioning process into two steps, which may lead to the accumulation of errors and the positioning accuracy is relatively poor; in terms of computational complexity, the direct positioning method usually needs to directly deduce the position of the signal source from the observed data, and the computational complexity is relatively large. While the two-step method is based on angle parameters for positioning, and the computational complexity is relatively small; in terms of communication bandwidth, the direct positioning method needs to directly process the received original signal, so all receiving arrays need to transmit the observed data, and the bandwidth requirement is large. In the two-step method, the receiving array only needs to transmit the angle parameters, and the bandwidth requirement is small.
[0004] In the actual process, whether the direct positioning method or the two-step method is selected, it is impossible to achieve a balance between positioning accuracy and computational complexity. One can only choose the direct positioning method with higher positioning accuracy but also higher computational complexity or the two-step method with lower computational complexity but also lower positioning accuracy. The uneven communication bandwidth of the receiving arrays in the case of multiple arrays will also limit the choice of methods. The methods currently adopted by researchers are either to perform hybrid positioning on various intermediate parameters. For example, RSS and AOA are jointly used for positioning, or to implement improvements on the basis of the direct positioning method. For example, the minimum variance distortionless response method is used to construct a cost function. However, the above methods essentially still combine parameter with parameter and observation data with observation data, and it is impossible to perform fusion positioning by simultaneously using intermediate parameters and observation data.
[0005] Summarizing the existing multi-array positioning methods, there are the following main problems: (1) For the existing multi-array positioning methods, whether using the two-step method or the direct positioning method, it is impossible to achieve a balance in computational accuracy and computational complexity.
[0006] (2) The existing multi-array positioning methods are limited by the uneven communication bandwidth of the receiving arrays. The direct positioning method is difficult to use because it depends on all receiving arrays to provide complete observation data.
[0007] (3) The existing multi-array positioning methods cannot perform fusion positioning by simultaneously using intermediate parameters and observation data, and still need to use the same type of parameters for positioning. Summary of the Invention
[0008] The main purpose of the present invention is to overcome the shortcomings and deficiencies of the existing multi-array positioning technology, and provide a multi-array fusion positioning method based on the maximum likelihood criterion.
[0009] To achieve the above purpose, the present invention adopts the following technical solutions: A positioning method for an underwater acoustic wideband scattering source based on low-rank matrix reconstruction, the positioning method comprising the following steps: S1. Initialize parameters, set the number of signal sources K, the signal center frequency of the k-th signal source as , 1 ≤ k ≤ K, the propagation speed is the speed of light c, the wavelength corresponding to the signal center frequency of the k-th signal source is , the position of the k-th signal source is , are respectively the x-axis and y-axis coordinate values of the position of the k-th signal source, the signal source position matrix is , the signal waveform of the k-th signal source at time t is , the number of receiving arrays L, the position of the l-th receiving array is , 1 ≤ l ≤ L, are the x-axis and y-axis coordinate values of the l-th receiving array respectively. The receiving array is a linear array, with the number of elements M and the element spacing d in the receiving array. To avoid phase ambiguity, the element spacing should not exceed half the wavelength of the received signal. Among the L receiving arrays, there are L a receiving arrays that send angle parameter information to the fusion center, and the remaining L - L a receiving arrays send observation data information to the fusion center. The sampling frequency of the receiving array is , and the number of snapshots of the observation data is N s , the search area of interest; S2. Establish a model for the received observation data , and assume that the noise of the observation data is Gaussian noise, and represent the observation data and the noise of the l-th receiving array at time t respectively, where 1 ≤ t ≤ N s , L a receiving arrays use the MUSIC method for estimation and positioning, and obtain the result and transmit it to the fusion center, represents the angle parameter vector estimated by the l-th receiving array, and the expression is , represents the angle parameter estimated by the l-th receiving array for the k-th signal source; the remaining L - L a receiving arrays do not perform processing and directly transmit the observation data to the fusion center, where represents the observation data transmitted by the l-th receiving array; S3. The fusion center establishes a von Mises distribution for the angle parameters a received by the L receiving arrays. The probability density function of the angle parameter is . In the formula, represents the product of multiple terms, represents the theoretical angle direction value from the k-th signal source to the l-th receiving array, and the expression is , represents the concentration parameter of the l-th receiving array, is the modified Bessel function of the 0th order, and the expression is ; the fusion center establishes a Gaussian distribution for the observation data a received by the remaining L - L receiving arrays. The probability density function of the observation data is . In the formula, represents the standard deviation of the observation data transmitted by the l-th receiving array, Represents the theoretical observed data value of the l-th receiving array; S4. According to the angle parameters received by the fusion center and the probability distribution function of the observed data to establish the first likelihood function corresponding to the probability distribution function of the angle parameter and the second likelihood function corresponding to the probability distribution function of the observed data where c and c represent the first and second likelihood constants greater than zero respectively, 1 c 2 ; , ; S5. Establish the joint likelihood function to form a maximum likelihood problem: . where () is the maximum value function, () is the minimum value function, and the parameter noises transmitted by different receiving arrays are regarded as independently and identically distributed, that is , , , then the above formula is transformed into:
[0010] Introduce the weight factor , and the above formula is further transformed into:
[0011] S5. Use the least squares method and eigenvalue decomposition to simplify the part related to the observed signal in the joint likelihood function; S6. Introduce normalization to process the joint likelihood function; S7. Search for the joint likelihood function to obtain the source position matrix corresponding to the extreme point .
[0012] Furthermore, in the step S2, the observed data model received by the l-th receiving array is:
[0013] where is the array manifold matrix from the k-th source to the l-th receiving array, , and this array manifold matrix is a common linear array arrangement.
[0014] Furthermore, the process of using the least squares method to simplify the part related to the observed signal in the objective function in the step S5 is: Based on the least squares criterion, establish the cost function for the \(l\)th receiving array:
[0015] Expand the cost function:
[0016] Remove the constant term and find that minimizing is equivalent to minimizing for the minimum value Express the cost function as:
[0017] This term represents the matching degree between the observed data of the receiving array and the array manifold matrix. The greater the matching degree, the larger the cost function value.
[0018] Make a general assumption that at the \(l\)th receiving array, there is
[0019] By introducing the covariance matrix, express the cost function as:
[0020] In the formula , , is the covariance matrix of the observed data, and the joint likelihood function is expressed as:
[0021] Furthermore, the joint likelihood function in step S6 is expressed as:
[0022] Define , , and the joint likelihood function can be expressed as:
[0023] The normalization process is:
[0024]
[0025] In the formula, and respectively represent and the maximum values in the region of interest search area. After normalization, the joint likelihood function is expressed as: .
[0026] Through this normalization process, the influence caused by the angular parameters and the observation data can be utilized more fairly, improving the fusion effect. Otherwise, the influence of one type of data will completely cover the influence of the other type of data.
[0027] Furthermore, the search process in step S6 is as follows: first, a coarse grid search is performed on the search area of interest, and the maximum value of the coarse grid search is used as the basis for normalization. A fine grid search is then performed near the minimum value of the coarse grid search. Through this combination of coarse and fine grid searches, the search efficiency can be greatly improved, avoiding the situation of long search time caused by a large-scale fine-precision search. Moreover, the normalization process can directly utilize the results of the coarse grid search to improve efficiency.
[0028] Compared with the prior art, the present invention has the following advantages and beneficial effects: (1) The multi-array positioning method disclosed in the present invention achieves higher positioning accuracy than the two-step method and lower computational complexity than the direct positioning method, achieving a balance of performance between positioning accuracy and computational complexity. Moreover, the weight factor can be adjusted according to the communication environment of the receiving array to improve the fusion effect.
[0029] (2) The multi-array positioning method disclosed in the present invention can adjust the type of transmitted data according to the communication bandwidth of different receiving arrays, breaking through the limitation of unbalanced communication bandwidth of the receiving arrays.
[0030] (3) The positioning method disclosed in the present invention can receive the angular parameters and observation data of different receiving arrays for fusion positioning. Since the present invention is based on the maximum likelihood criterion, it has a good positioning effect and is suitable for the environment where different data types are transmitted by multiple arrays. BRIEF DESCRIPTION OF THE DRAWINGS
[0031] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.
[0032] Figure 1 is a flowchart of the multi-array fusion positioning method based on the maximum likelihood criterion disclosed in the present invention; Figure 2a is a comparison diagram of the estimation performance of the present invention, the direct positioning method, and the two-step method in the same environment; Figure 2b is a comparison diagram of the estimation performance of the present invention under different weight factors; Figure 2c is a comparison diagram of the estimation performance of the present invention with and without normalization processing; Figure 3a and Figure 3b are the positioning estimation diagrams of the present invention under two different signal source conditions respectively. Specific implementation manners
[0033] In order to enable those skilled in the art of this technology to better understand the solution of this application, the technical solutions in the embodiments of this application will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of this application. Obviously, the described embodiments are only a part of the embodiments of this application, rather than all the embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative efforts belong to the scope of protection of this application.
[0034] Embodiment 1 Figure 1 is a flowchart of the multi-array fusion positioning method based on the maximum likelihood criterion disclosed in this embodiment, and specifically includes the following steps: S1. Initialize parameters, set the number of signal sources K, the signal center frequency of the kth signal source as , 1 ≤ k ≤ K, the propagation speed is the speed of light c, the wavelength corresponding to the signal center frequency of the kth signal source is , the position of the kth signal source is , are respectively the x-axis and y-axis coordinate values of the position of the kth signal source, the signal source position matrix is , the signal waveform of the kth signal source at time t is , the number of receiving arrays L, the position of the lth receiving array is , 1 ≤ l ≤ L, are respectively the x-axis and y-axis coordinate values of the lth receiving array, the receiving array is a linear array, the number of array elements of the receiving array is M, the element spacing is d, among the L receiving arrays, there are L a receiving arrays send angle parameter information to the fusion center, and the remaining L - L a receiving arrays send observation data information to the fusion center, the sampling frequency of the receiving array is , the number of snapshots of the observation data is N s , the search area of interest; S2. Establish a model for the received observation data , and assume that the noise of the observation data is Gaussian noise, and respectively represent the observation data and the noise of the lth receiving array at time t, 1 ≤ t ≤ N s , L a receiving arrays use the MUSIC method for estimation and positioning, and the result is obtained and transmitted to the fusion center. Denote the angle parameter vector estimated by the \(l\)th receiving array, and the expression is , which represents the angle parameter estimated by the \(l\)th receiving array for the \(k\)th signal source; the remaining \(L - l\) a receiving arrays do not perform processing and directly transmit the observation data to the fusion center, where represents the observation data transmitted by the \(l\)th receiving array; S3. The fusion center establishes a von Mises distribution for the angle parameters a received by the \(L\) receiving arrays. The probability density function of the angle parameter is , where represents the product of multiple terms, represents the theoretical angle direction value from the \(k\)th signal source to the \(l\)th receiving array, and the expression is , represents the concentration parameter of the \(l\)th receiving array, is the modified Bessel function of the 0th order, and the expression is ; the fusion center establishes a Gaussian distribution for the observation data a received by the remaining \(L - l\) receiving arrays. The probability density function of the observation data is , where represents the standard deviation of the observation data transmitted by the \(l\)th receiving array, represents the theoretical observation data value of the \(l\)th receiving array; S4. According to the probability distribution function of the angle parameter received by the fusion center and the probability distribution function of the observation data , establish the first likelihood function corresponding to the probability distribution function of the angle parameter and the second likelihood function corresponding to the probability distribution function of the observation data , where \(c\) 1 , \(c\) 2 represent the first and second likelihood constants greater than zero, respectively, , ; S5. Establish the joint likelihood function , forming a maximum likelihood problem: . where () is the maximum value function, () is the minimum value function. The parameter noises transmitted by different receiving arrays are regarded as independently and identically distributed, that is , , then the above formula is transformed into:
[0035] Introduce the weight factor , and the above formula is further transformed into:
[0036] S5. Use the least squares and eigenvalue decomposition to simplify the relevant part of the observed signal in the joint likelihood function; S6. Introduce normalization to process the joint likelihood function; S7. Search the joint likelihood function to obtain the source position matrix corresponding to the extreme point .
[0037] Embodiment 2 This embodiment discloses a multi-array fusion positioning method based on the maximum likelihood criterion. The present invention uses 200 experiments with different weight factors, and compares the performance with the existing direct positioning method and two-step method, which proves the reliability and superiority of the simulation results of the present invention.
[0038] S1. Initialize the parameters, set the number of sources K = 1, the center frequency of the source signal is = 30 kHz, the propagation speed is c (speed of light), the wavelength corresponding to the center frequency of the signal is , the position of the source is , the signal waveform of the kth source at time t is , 1 ≤ k ≤ K, the number of receiving arrays L = 4, and the positions of the receiving arrays are respectively , the receiving array is a linear array, the number of array elements of the receiving array is M = 10, and the element spacing is , among the L receiving arrays, there are L a = 2 receiving arrays that send angle parameter information to the fusion center, and the remaining L - L a = 2 receiving arrays send observation data information to the fusion center. The sampling frequency of the receiving array is = 100 Hz, the number of snapshots of the observation data is = 100, and the search area of interest is ; S2. Establish a model for the observation data received by the lth receiving array, 1 ≤ l ≤ L, and assume that the noise of the observation data is Gaussian noise, and respectively represent Observation data and noise at a moment, L a =2 receiving arrays use the MUSIC (Multiple Signal Classification) method for estimation and positioning to obtain the results and transmit them to the fusion center denotes the angle parameter vector estimated by the l-th receiving array, and the expression is , denotes the -th angle parameter estimated by the l-th receiving array for the k-th signal source; the remaining L-L a =2 receiving arrays do not perform processing and directly transmit the observation data to the fusion center, where denotes the -th observation data transmitted by the l-th receiving array; S3. The fusion center establishes a von Mises distribution for the angle parameters a received by the L receiving arrays. The probability density function of the angle parameter is , where denotes the product of multiple terms denotes the theoretical angle direction value from the k-th signal source to the l-th receiving array, and the expression is , denotes the concentration parameter of the l-th receiving array is the modified Bessel function of the 0th order, and the expression is ; the fusion center establishes a Gaussian distribution for the observation data a received by the remaining L-L receiving arrays. The probability density function of the observation data is , where denotes the standard deviation of the observation data transmitted by the l-th receiving array denotes the theoretical observation data value of the l-th receiving array; S4. According to the probability distribution function of the angle parameter received by the fusion center and the probability distribution function of the observation data , establish the first likelihood function corresponding to the probability distribution function of the angle parameter and the second likelihood function corresponding to the probability distribution function of the observation data , where c 1 , c 2 denotes any first and second likelihood constants greater than zero , ; S5. Establish the joint likelihood function , and form a maximum likelihood problem: . In the formula () is the maximum value function, () is the minimum value function. The parameter noises transmitted by different receiving arrays are regarded as independently and identically distributed, that is , , then the above formula is transformed into:
[0039] Introduce the weight factor , and the above formula is further transformed into:
[0040] S5. Use the least squares method and eigenvalue decomposition to simplify the relevant part of the observed signal in the joint likelihood function; S6. Introduce normalization to process the joint likelihood function; S7. Search the joint likelihood function to obtain the source position matrix corresponding to the extreme point .
[0041] The test results of this embodiment are as shown in Figure 2a , Figure 2b and Figure 2c . All methods perform 200 repeated simulation experiments. Figure 2a is the performance comparison diagram of the fusion positioning RMSE (Root Mean Square Error) with a weight factor of 0.8 and the RMSE of DPD and AOA based on the likelihood function in the same scenario, and is compared with the CRLB (Cramér–Rao Lower Bound) in this scenario. As shown in the figure, it can be seen that the positioning accuracy of multi-array fusion positioning is higher than that of AOA in the case of low signal-to-noise ratio, and the fusion positioning can also achieve performance close to that of DPD and even CRLB in the case of high signal-to-noise ratio, reflecting the advantages of fusion positioning.
[0042] Figure 2b is the comparison diagram of the fusion positioning RMSE under different weight factors. As shown in the figure, the weight factor plays a key role in the fusion positioning algorithm. It determines the contribution degree of different types of data to the positioning result. Different weight factors can achieve different positioning effects. A suitable weight factor can significantly improve the positioning accuracy, while an inappropriate weight factor may lead to an increase in positioning error. The experimental results are in line with expectations. In the actual scenario, the weight can be first allocated based on experience, and then real-time measurement can be carried out for dynamic adjustment to obtain a more accurate weight factor.
[0043] Figure 2c It is a comparison between the fusion positioning RMSE with different weight factors before normalization and the fusion positioning RMSE after normalization, showing the necessity of the normalization process. As shown in the figure, there is no significant difference in the positioning effects of different weight factors before normalization, and the positioning error is much higher than that after normalization. This is because the numerical range of the function part corresponding to the observation data is much larger than that of the function part corresponding to the angle parameter, resulting in the angle parameter hardly participating in the positioning process in fact.
[0044] Example 3 This example discloses a multi-array fusion positioning method based on the maximum likelihood criterion. The present invention in two signal sources corroborates the effectiveness and reliability of the present invention in positioning in a multi-signal source scenario.
[0045] S1. Initialize parameters, set the number of signal sources K = 2, the signal center frequency of signal source 1 is = 30 kHz, the signal center frequency of signal source 2 is = 50 kHz, the propagation speed is c (speed of light), and the wavelength corresponding to the signal center frequency of the kth signal source is , 1 ≤ k ≤ K, the position of the signal source is , , the number of receiving arrays L = 4, and the positions of the receiving arrays are respectively , the receiving array is a linear array, the number of array elements of the receiving array is M = 10, and the element spacing is , among the L receiving arrays, there are L a = 2 receiving arrays that send angle parameter information to the fusion center, and the remaining L - L a = 2 receiving arrays send observation data information to the fusion center, the sampling frequency of the receiving array is = 100 Hz, the number of snapshots of the observation data is = 100, and the interested search area is ; S2. Establish a model for the observation data received by the lth receiving array, 1 ≤ l ≤ L, and assume that the noise of the observation data is Gaussian noise, and respectively represent the observation data and the noise at time t. L a = 2 receiving arrays use the MUSIC (Multiple Signal Classification) method for estimation and positioning, and the result is obtained and transmitted to the fusion center, represents the angle parameter vector estimated by the lth receiving array, and the expression is , Denote the angle parameter estimated by the \(l\)-th receiving array for the \(k\)-th source. Note the corresponding relationship of the angle parameter here, which can be determined by the front and back of the spectral peak appearance; the remaining \(L - L\) a = 2 receiving arrays do not perform processing and directly transmit the observation data to the fusion center, where denotes the observation data transmitted by the \(l\)-th receiving array; S3. The fusion center establishes a von Mises distribution for the angle parameters a received by the \(L\) receiving arrays. The probability density function of the angle parameter is , where denotes the product of multiple terms, denotes the theoretical angle direction value from the \(k\)-th source to the \(l\)-th receiving array, and the expression is , denotes the concentration parameter of the \(l\)-th receiving array, is the modified Bessel function of the zero order, and the expression is ; the fusion center establishes a Gaussian distribution for the observation data a received by the remaining \(L - L\) receiving arrays. The probability density function of the observation data is , where denotes the standard deviation of the observation data transmitted by the \(l\)-th receiving array, denotes the theoretical observation data value of the \(l\)-th receiving array; S4. According to the probability distribution function of the angle parameter received by the fusion center and the probability distribution function of the observation data , establish the first likelihood function corresponding to the probability distribution function of the angle parameter and the second likelihood function corresponding to the probability distribution function of the observation data , where \(c\) 1 , \(c\) 2 denotes the first and second likelihood constants greater than zero, , ; S5. Establish the joint likelihood function , forming a maximum likelihood problem: . where () is the maximum value function, () is the minimum value function. The parameter noises transmitted by different receiving arrays are regarded as independently and identically distributed, that is , , then transform the above formula into:
[0046] Introduce a weight factor , and the above formula is further transformed into:
[0047] S5. Use least squares and eigenvalue decomposition to simplify the relevant part of the observed signal in the joint likelihood function; S6. Introduce normalization to process the joint likelihood function; S7. Search for the joint likelihood function. First, search with a wide grid of 1, use the obtained extreme value for normalization, establish a cost function to record the values of the joint likelihood function at different search positions. The cost function has four dimensions in total. The first dimension represents the coordinate of the searched source 1, the second dimension represents the coordinate of the searched source 1, the third dimension represents the coordinate of the searched source 2, the fourth dimension represents the coordinate of the searched source 2. Finally, obtain the source position matrix corresponding to the extreme point .
[0048] The test results of this embodiment are as shown in Figure 3a and Figure 3b . Figure 3a and Figure 3b show that the multi-array fusion positioning method can have good positioning accuracy in the case of multiple sources. In the simulation experiment, the weight factor is set to 0.6 and the signal-to-noise ratio is set to 0. Figure 3a represents the projection of the cost function of source 1, that is, at any search position of source 1, search for the maximum values of the third and fourth dimensions of the search cost function as its projection; Figure 3b represents the projection of the cost function of source 2, that is, at any search position of source 2, search for the maximum values of the first and second dimensions of the search cost function as its projection. From Figure 3a and Figure 3b , it can be seen that the multi-array fusion positioning method has good estimation accuracy and is applicable to the multi-source scenario.
[0049] The above embodiments are the preferred embodiments of the present invention, but the embodiments of the present invention are not limited by the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications made without departing from the spirit and principle of the present invention shall be equivalent replacement methods and shall all be included in the protection scope of the present invention.
Claims
1. A multi-array fusion positioning method based on maximum likelihood criterion, characterized in that: The multi-array fusion positioning method comprises the following steps: S1, initialization parameters, set the number of sources K, the signal center frequency of the kth source is , 1≤k≤K, the propagation speed is the speed of light c, and the wavelength corresponding to the signal center frequency of the kth source is , the position of the kth source is , are the x-axis and y-axis coordinate values of the k-th source position, respectively. The source position matrix is , is the signal waveform of the kth information source, is the signal waveform of the kth source at time t, the number of receiving arrays is L, and the position of the lth receiving array is , 1≤l≤L, are the x-axis and y-axis coordinate values of the lth receiving array respectively. The receiving array is a linear array with M array elements and d array element spacing. Among the L receiving arrays, there are L a The receiving array sends angle parameter information to the fusion center, and the remaining LL a The receiving array sends observation data information to the fusion center, and the receiving array sampling frequency is , the number of observed data snapshots is N s , the search area of interest; S2. Received observation data Build a model and assume that the observed data Noise is Gaussian noise, and Respectively represent the observation data and noise of the lth receiving array at time t, 1≤t≤N s , L a The receiving array uses the MUSIC method to estimate the positioning and obtain the result and transmit it to the fusion center, Represents the angle parameter vector estimated by the lth receiving array, and the expression is , represents the angle parameter estimated by the lth receiving array for the kth source; the remaining LL a The receiving array does not process the observation data directly. Transmitted to the fusion center, where represents the observation data transmitted by the lth receiving array; S3, Fusion Center to L a The angle parameters received by the receiving array Constructing the von Mises distribution, angle parameter The probability density function of , where represents the product of multiple terms, It represents the theoretical angle direction value from the kth signal source to the lth receiving array, and the expression is , represents the concentration parameter of the lth receiving array, is the 0th order modified Bessel function, expressed as ; Fusion center for the remaining LL a The observation data received by the receiving array Establish Gaussian distribution and observe data The probability density function of , where represents the standard deviation of the observation data transmitted by the lth receiving array, represents the theoretical observation data value of the lth receiving array; S4. According to the angle parameters received by the fusion center The probability distribution function and observation data The probability distribution function of The first likelihood function corresponding to the probability distribution function and observational data The second likelihood function corresponding to the probability distribution function , where c1 and c2 represent the first and second likelihood constants that are arbitrarily greater than zero. , ; S5. Establishing joint likelihood function , forming a maximum likelihood problem: . In the formula () is the maximum value function, () is the minimum value function, and the parameter noise transmitted by different receiving arrays is considered to be independent and identically distributed, that is, , , , then transform the above formula into: Introducing weight factors , the above formula is further transformed into: ； S5, using least squares and eigenvalue decomposition to simplify the relevant part of the observation signal in the joint likelihood function; S6, introduce normalization to process the joint likelihood function; S7. Search the joint likelihood function to obtain the source position matrix corresponding to the extreme point .
2. The multi-array fusion positioning method based on the maximum likelihood criterion according to claim 1, characterized in that: In step S2, the observation data model received by the lth receiving array is: In the formula, is the array manifold matrix from the kth source to the lth receiving array, 。 3. The multi-array fusion positioning method based on maximum likelihood criterion according to claim 1, characterized in that: The process of simplifying the relevant part of the observed signal in the objective function by using the least square method in step S5 is as follows: The cost function of the lth receiving array is established based on the least squares criterion: Assume that for the lth receiving array, there is The position estimation formula is derived: In the formula , , is the covariance matrix of the observed data, and the joint likelihood function is expressed as: 。 4. The multi-array fusion positioning method based on the maximum likelihood criterion according to claim 3 is characterized in that: The joint likelihood function in step S6 is expressed as: definition , , the joint likelihood function can be expressed as: The normalization process is: In the formula, , , and Respectively represent and The maximum value in the search area of interest, after normalization, the joint likelihood function is expressed as: 。 5. The multi-array fusion positioning method based on maximum likelihood criterion according to claim 1, characterized in that: The search process in step S6 is to first perform a coarse grid search on the search area of interest, use the maximum value of the coarse grid search as a basis for normalization, and perform a fine grid search near the minimum value of the coarse grid search.