A maximum likelihood node self-localization method based on DPMM clustering in multipath environment

Abstract

The present invention provides a maximum likelihood node self-positioning method for DPMM clustering in a multipath environment, drawing on the idea of ​​semi-supervised machine learning, and utilizing the characteristics of adaptive learning of actual data by the Dirichlet process mixture model in Bayesian non-parametric estimation, to carry out key method research based on the underwater acoustic sensor network positioning system, improve the positioning performance and adaptability of the positioning algorithm in a multipath environment, improve the accuracy of the underwater acoustic sensor network, and improve the overall performance of the underwater acoustic sensor network system in an actual ocean environment. The present invention introduces the Dirichlet process mixture model, replaces the measurement error caused by multipath from the original single zero-mean Gaussian model to the Gaussian mixture model, improves the positioning accuracy, improves the maximum likelihood positioning algorithm, and compares the performance with four other positioning algorithms through simulation. The results show that the positioning accuracy is significantly improved compared with other algorithms.

Description

Technical Field

[0001] The present invention relates to the field of underwater acoustic sensor network target tracking, and specifically to statistical signal processing, information fusion, and target tracking theory. It can track underwater targets with high precision in complex underwater environments and reduce the influence of measurement errors caused by multipath on target tracking accuracy. Background Art

[0002] The ocean occupies about 71% of the earth's surface and is rich in resources. With the scarcity of land resources, human beings are accelerating their pace of entering the ocean. Underwater acoustic sensor networks (UASNs) are different from wireless sensor networks (WSNs). The latter has been studied and developed more maturely in the air electromagnetic wave environment, while the former is limited by the complex ocean environment and the physical characteristics of sound wave propagation, and needs further in-depth research. The positioning problem in underwater acoustic sensor networks (UASN) can be roughly divided into two types: one is the self-positioning of sensor nodes inside the network by the underwater acoustic sensor network; the other is the positioning of target nodes outside the network by the underwater acoustic sensor network after detection. The former is the basis for realizing various functions of high-performance underwater acoustic sensor networks and an indispensable part of the initialization process of underwater acoustic sensor networks. It is also a very important link in target detection, positioning and tracking, seabed navigation, and the development and utilization of marine resources. Therefore, improving the self-positioning accuracy of nodes is of great significance to underwater acoustic sensor networks. Summary of the invention

[0003] In order to overcome the shortcomings of the prior art, the present invention provides a maximum likelihood node self-positioning method for DPMM clustering in a multipath environment. Aiming at the problems and difficulties existing in the underwater acoustic sensor network positioning system, the influence of multipath effect on the traditional positioning algorithm in the actual underwater acoustic environment is fully considered, the idea of ​​semi-supervised machine learning is borrowed, and the characteristics of adaptive learning of actual data by the Dirichlet process mixture model in Bayesian non-parametric estimation are used to carry out key method research based on the underwater acoustic sensor network positioning system, improve the positioning performance and adaptability of the positioning algorithm in a multipath environment, and improve the accuracy of the underwater acoustic sensor network, which can improve the overall performance of the underwater acoustic sensor network system in the actual marine environment.

[0004] The detailed steps of the technical solution adopted by the present invention to solve the technical problem are as follows:

[0005] Step 1: Establish the target measurement model of the underwater acoustic sensor network. The measurement equation is expressed as follows:

[0006] R it =ri +ε it (1)

[0007] In formula (1), R it is the distance measurement of the i-th anchor node at time t, r i =||A i -X||2 represents the actual distance from the i-th anchor node to the target node; the position of the i-th anchor node is A i =[x i ,y i ] T , the target node position is X = [x0, y0], the target node position is fixed, ε it Model the error vector of the i-th anchor node at time t, and establish a maximum likelihood positioning algorithm graph model based on DPMM clustering, such as Figure 1 As shown;

[0008] Step 2: Derivation of the posterior probability of each variable in the graph model structure of the maximum likelihood positioning algorithm based on DPMM clustering;

[0009] At this time, the coordinates of the target node are known to be X1, so the actual distance r is i is a constant term, without a posteriori derivation, and the error parameter indicator variable z for the i-th anchor node is it :

[0010] 2.1. When z it When the direction is k and k≤K, the posterior probability can be derived from the maximum likelihood positioning algorithm graph model based on DPMM clustering:

[0011]

[0012] Among them, K represents the total number of categories, k represents the current indicator variable z it The class pointed to;

[0013] Various parameter variables The posterior probability depends only on the hyperparameter λ and the number of observations R belonging to this class. k related:

[0014]

[0015] 2.2 When z it The direction is K+1. When a new class is generated, there are:

[0016]

[0017] If it To point to a new class, new parameters must be generated for the K+1th class from the given prior basic distribution. At this time, the new parameter μi,K+1 Independent of other parameters, the posterior probability is:

[0018]

[0019] Step 3: For the posterior probability obtained in step 2, Gibbs sampling is used, and the update formula for the jth iteration is as follows:

[0020] p(μ ik (j) |μ i,-k (j-1) R k ,r i ,λ)∝p(μ ik |λ)p(R k |μ ik (j-1) ,r i ) (7)

[0021] Step 4: After multiple Gibbs sampling iterations, the specific parameters of the error distribution corresponding to the distance measurement are obtained, and the likelihood function of the measurement at time t with respect to the coordinate variable is written as follows:

[0022]

[0023] in:

[0024]

[0025] Step 5: The n groups of observation data collected are processed iteratively through Gibbs sampling to cluster the n groups of measurements, and the parameters of each sub-model after clustering are substituted into the improved maximum likelihood self-localization algorithm for processing; Let:

[0026]

[0027] J is simultaneously related to x i ,y i Find the partial derivative and after sorting, we get:

[0028]

[0029] In the formula, let s = x 2 +y 2 ,K i =x i 2 +y i 2 ,and:

[0030]

[0031]

[0032] Formula (11) can be written in matrix form as follows:

[0033]

[0034] is equivalent to:

[0035] HX=β (15)

[0036] For formula (15), the least squares solution of the target position X is:

[0037] X=(H T H) -1 H T β (16)

[0038] make:

[0039]

[0040]

[0041] Then the least squares solution of the target position X is:

[0042]

[0043] Substituting equation (19) into s = x 2 +y 2 , we get the quadratic equation about s as:

[0044]

[0045] Step 6: Solve the quadratic equation of s in formula (20) using the root selection method (RSR) to obtain different J values. Substitute the s value corresponding to the smallest J value into formula (19) to obtain the target position coordinates.

[0046] In step 1, the maximum likelihood positioning algorithm graph model expression based on DPMM clustering is established as follows:

[0047]

[0048] Among them, π i is the mixing weight, α 0i , λ is a hyperparameter, z it is the indicator variable, μ zit is the category, G0 is the basic distribution, N(μ0,δ0 2 ) is a Gaussian distribution, μ0,δ0 2 refer to mean and variance respectively, GEM stands for broken stick model, μ k represents the k-th parameter variable, and K represents the total number of categories.

[0049] The root selection method (RSR) process is repeated 3-10 times.

[0050] The beneficial effects of the present invention are:

[0051] 1. The Dirichlet process mixture model is introduced to replace the measurement error caused by multipath from the original single zero-mean Gaussian model to the Gaussian mixture model, thereby improving the positioning accuracy;

[0052] 2. The maximum likelihood positioning algorithm was improved. The performance was compared with that of four other positioning algorithms through simulation. The results showed that the positioning accuracy was significantly improved compared with other algorithms. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 This is the maximum likelihood positioning algorithm graph model based on DPMM clustering of the present invention.

[0054] Figure 2 Schematic diagram of the coordinates of the anchor nodes of the present invention.

[0055] Figure 3 It is a statistical distribution diagram of the measurement error e1 of the present invention.

[0056] Figure 4 It is a statistical distribution diagram of the measurement error e2 of the present invention.

[0057] Figure 5 It is a statistical distribution diagram of the measurement error e3 of the present invention.

[0058] Figure 6 The RMSE histogram of the positioning results of the five algorithms.

[0059] Figure 7 This is the relationship between RMSE and error variance. DETAILED DESCRIPTION

[0060] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0061] The maximum likelihood positioning algorithm graph model based on DPMM clustering is as follows Figure 1 The positioning performance of the least squares method, Chan algorithm, Taylor algorithm, maximum likelihood estimation method and maximum likelihood node self-positioning algorithm based on DPMM clustering was investigated. A total of 1000 Monte Carlo independent experiments were conducted, and 1000 sets of propagation delay measurements were collected within a certain period of time, measured by the root mean square error RMSE:

[0062]

[0063] in, is the estimated result of the target node position at the i-th moment, X = [x, y] Tis the real position coordinate of the target node in the underwater acoustic sensor network.

[0064] The execution steps are as follows:

[0065] Step 1: Assuming the number of anchor nodes N = 3, randomly generate three anchor nodes in a 5000*5000 plane sea area with coordinates A1 = [4123.6, 2187.9] T , A2=[1287.8,4605.9] T Sum A3 = [3969.1, 3616.5] T The randomly generated target node position coordinates are X = [4822.4, 2707.0] T The coordinate diagram of each node is as follows: Figure 2 shown.

[0066] Calculate the real distance r1, r2, r3 from each anchor node to the target node, and establish the target measurement model of the underwater acoustic sensor network. The measurement equation is expressed as follows:

[0067] R it =r i +ε it (twenty two)

[0068] R it is the distance measurement of the i-th anchor node at time t, ε it To model the error vector of the i-th anchor node at time t, there is a maximum likelihood positioning algorithm graph model based on DPMM clustering as follows Figure 1 As shown, the model expression is:

[0069]

[0070] Among them, z it is the indicator variable, α 0i , λ is a hyperparameter, μ zit is the category, G0 is the basic distribution, π i is the mixing weight, R it is the measured value at time t, N(μ0,δ0 2 ) is a Gaussian distribution, μ0,δ0 2 refer to mean and variance respectively.

[0071] Step 2: Derivation of the posterior probability of each variable in the graph model structure of the maximum likelihood positioning algorithm based on DPMM clustering;

[0072] 2.1. When z it When the direction is k and k≤K, the posterior probability can be deduced from the graph model as follows:

[0073]

[0074]

[0075] 2.2 When z it The direction is K+1. When a new class is generated, there are:

[0076]

[0077]

[0078] Step 3: Perform Gibbs sampling; the update formula for the jth iteration after Gibbs sampling is as follows:

[0079] p(μ ik (j) |μ i,-k (j-1) R k ,r i ,λ)∝p(μ ik |λ)p(R k |μ ik (j-1) ,r i ) (28)

[0080] Step 4: After multiple Gibbs sampling iterations, the specific parameters of the error distribution corresponding to the distance measurement are obtained, and the likelihood function of the measurement at time t with respect to the coordinate variable is written as follows:

[0081]

[0082] in,

[0083]

[0084] The n groups of observation data collected are processed through multiple Gibbs sampling iterations to achieve clustering of the n groups of measurements.

[0085] Step 5: Substitute the parameters of each sub-model after clustering into the improved maximum likelihood self-localization algorithm for processing, and let:

[0086]

[0087] J is simultaneously related to x i ,y i Find the partial derivative and after sorting, we get:

[0088]

[0089] Where s = x 2 +y 2 ,K i =x i2 +y i 2

[0090]

[0091]

[0092] Write formula (31) in matrix form:

[0093]

[0094] is equivalent to:

[0095] HX=β (36)

[0096] For formula (35), the least squares solution of the target position X can be obtained:

[0097] X=(H T H) -1 H T β (37)

[0098] make:

[0099]

[0100]

[0101] Then the least squares solution of the target position X is:

[0102]

[0103] Substituting equation (40) into s = x 2 +y 2 , we get a quadratic equation about s:

[0104]

[0105] Step 6: Solve the quadratic equation of s using the root selection method (RSR) according to the root-finding formula. The steps of RSR are as follows:

[0106] 6.1. If only one root is positive, substitute that root into the least squares solution for X.

[0107] 6.2. If both roots are positive, choose the one that makes the value of J in equation (30) smaller.

[0108] 6.3. If both roots are negative or imaginary, take the absolute value of their real parts and choose the root that gives the smaller value of J in equation (30).

[0109] The RSR step is cycled 3-10 times, 5 times in this example, to obtain different J values. The s value corresponding to the smallest J value is substituted into formula (40) to obtain the positioning result.

[0110] Figure 3 is a statistical distribution diagram of the measurement error e1 of the present invention, Figure 4 is a statistical distribution diagram of the measurement error e2 of the present invention, Figure 5 is the statistical distribution diagram of the measurement error e3 of the present invention. In the simulation results, Figure 6 is the RMSE of the positioning results of the five algorithms, Figure 7 It is a relationship diagram between RMSE and error variance. According to the simulation results, it can be seen that the maximum likelihood positioning algorithm based on DPMM clustering proposed in the present invention has the highest positioning accuracy and the best positioning performance compared with the other four algorithms.

Claims

1. A maximum likelihood node self-localization method for DPMM clustering in a multipath environment, characterized in that The steps include: Step 1: Establish the target measurement model of the underwater acoustic sensor network. The measurement equation is expressed as follows: R it =r i +e it (1) In formula (1), R it is the distance measurement of the i-th anchor node at time t, r i =||A i -X||2 represents the actual distance from the i-th anchor node to the target node; The position of the i-th anchor node is A i =[x i ,y i ] T , the target node position is X = [x0, y0], the target node position is fixed, ε it Model the error vector of the i-th anchor node at time t and establish a maximum likelihood positioning algorithm graph model based on DPMM clustering; Step 2: Derivation of the posterior probability of each variable in the graph model structure of the maximum likelihood positioning algorithm based on DPMM clustering; At this time, the coordinates of the target node are known to be X1, so the actual distance r is i is a constant term, without a posteriori derivation, and the error parameter indicator variable z for the i-th anchor node is it : 2.

1. When z it When the direction is k and k≤K, the posterior probability can be derived from the maximum likelihood positioning algorithm graph model based on DPMM clustering: Among them, K represents the total number of categories, k represents the current indicator variable z it The class pointed to; Various parameter variables The posterior probability depends only on the hyperparameter λ and the number of observations R belonging to this class. k related: 2.2 When z it The direction is K+1. When a new class is generated, there are: If it To point to a new class, new parameters must be generated for the K+1th class from the given prior basic distribution. At this time, the new parameter μ i,K+1 Independent of other parameters, the posterior probability is: Step 3: For the posterior probability obtained in step 2, Gibbs sampling is used, and the update formula for the jth iteration is as follows: p(μ ik (j) |m i,-k (j-1) R k ,r i ,λ)∝p(μ ik |λ)p(R k |m ik (j-1) ,r i ) (7) Step 4: After multiple Gibbs sampling iterations, the specific parameters of the error distribution corresponding to the distance measurement are obtained, and the likelihood function of the measurement at time t with respect to the coordinate variable is written as follows: in: Step 5: The n groups of observation data collected are processed iteratively through Gibbs sampling to cluster the n groups of measurements, and the parameters of each sub-model after clustering are substituted into the improved maximum likelihood self-localization algorithm for processing; Let: J is simultaneously related to x i ,y i Find the partial derivative and after sorting, we get: In the formula, let s = x 2 +y 2 ,K i =x i 2 +y i 2 ,and: Formula (11) can be written in matrix form as follows: is equivalent to: HX=β (15) For formula (15), the least squares solution of the target position X is: X=(H T H) -1 H T β (16) make: Then the least squares solution of the target position X is: Substituting equation (19) into s = x 2 +y 2 , we get the quadratic equation about s as: Step 6: Solve the quadratic equation of s in formula (20) using the root selection method to obtain different J values. Take the s value corresponding to the smallest J value and substitute it into formula (19) to obtain the target position coordinates.

2. The maximum likelihood node self-positioning method of DPMM clustering in a multipath environment according to claim 1, characterized in that: In step 1, the maximum likelihood positioning algorithm graph model expression based on DPMM clustering is established as follows: p i |a 0i ~GEM(1,a 0i ) (2) z it |π i ～π i m zit |λ~G0(λ)=N(μ0,δ0 2 ) Among them, π i is the mixing weight, α 0i , λ is a hyperparameter, z it is the indicator variable, is the category, G0 is the basic distribution, N(μ0,δ0 2 ) is a Gaussian distribution, μ0,δ0 2 refer to mean and variance respectively, GEM stands for broken stick model, μ k represents the k-th parameter variable, and K represents the total number of categories.

3. The maximum likelihood node self-positioning method of DPMM clustering in a multipath environment according to claim 1, characterized in that: The root selection process is repeated 3-10 times.

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