A maximum-consensus-based underwater target cooperative positioning method and system

Abstract

This invention relates to a cooperative underwater target localization method and system based on maximum consistency, belonging to the field of underwater moving target localization. First, the centralized unscented Kalman filtering iterative process is rewritten into an information filtering form, namely, the unscented Kalman information filtering form, reducing the computational dimensionality of the sensors. Then, combined with the maximum consistency algorithm, a new distributed filtering method, the "maximum consistency unscented Kalman information filtering algorithm," is obtained. Finally, after each underwater sensor interacts with its neighboring underwater sensors to exchange current observations, the maximum consistency unscented Kalman information filtering algorithm is used to estimate the target's location, improving the localization accuracy of underwater acoustic sensor networks when locating underwater moving targets.

Description

Technical Field

[0001] This invention relates to the field of underwater moving target localization, and in particular to a method and system for cooperative underwater target localization based on maximum consistency. Background Technology

[0002] China has vast sea areas and a long coastline, creating an urgent need for advanced monitoring equipment and supporting computing methods. Underwater wireless sensing and measurement monitoring networks are systems that integrate environmental data acquisition, data processing, and data transmission. They can work with surface buoys to perform real-time positioning and tracking of underwater moving targets. Due to their low cost, self-configuration, and wireless transmission capabilities, they are widely used in data monitoring, target tracking, and environmental monitoring scenarios, which typically require collaborative work between nodes. Because of the unique characteristics of the underwater environment, nonlinear filtering algorithms are currently commonly used to estimate the target state.

[0003] Commonly used nonlinear filtering algorithms include the Unscented Kalman Filter (UKF) and the Extended Kalman Filter (EKF). Zhan et al. used the EKF method to recover the trajectory of underwater targets, but this method leads to a decrease in filter performance and even divergence. The Jacobian matrix computation is large, complex, and difficult to implement. Li et al. used the weighted average consensus UKF method to solve the problem of filter divergence in distributed estimation of underwater targets, but the average consensus strategy used in this method is an approximation technique and cannot achieve higher-precision positioning. In response, Liu et al. proposed a distributed Kalman filter algorithm based on finite-time maximum consensus. It is known that the maximum consensus in this algorithm can achieve precise consensus, but it is not applicable to nonlinear systems. Summary of the Invention

[0004] The purpose of this invention is to provide a method and system for cooperative underwater target localization based on maximum consistency, so as to improve the localization accuracy of underwater acoustic sensor networks when locating moving underwater targets.

[0005] To achieve the above objectives, the present invention provides the following solution:

[0006] A cooperative underwater target localization method based on maximum consistency includes:

[0007] The centralized unscented Kalman filter algorithm is rewritten into an information filtering form through equivalent transformation;

[0008] By combining the centralized unscented Kalman filter algorithm in the form of information filtering with the maximum consistency algorithm, the maximum consistency unscented Kalman information filtering algorithm is obtained.

[0009] Acquire current observations of targets measured by multiple underwater sensors;

[0010] Each underwater sensor interacts with its neighboring underwater sensors to exchange current observations.

[0011] Based on the current observations measured by each underwater sensor and the current observations measured by neighboring underwater sensors obtained through interaction, the target's position at the current moment is estimated using the maximum consistent unscented Kalman information filtering algorithm.

[0012] Optionally, the rewriting of the centralized unscented Kalman filter algorithm into an information filtering form through equivalent transformation specifically includes:

[0013] Using the statistical linear error propagation method, the error covariance matrix, self-covariance matrix, and cross-covariance matrix in the centralized unscented Kalman filter algorithm are rewritten as follows:

[0014]

[0015]

[0016]

[0017] In the formula, P(k|k-1) is the error covariance matrix, E{} is the covariance matrix, and X(k) is the target's state vector. P is the estimated state vector of the target at time k; ZZ (k|k-1) is the autocovariance matrix, and Z(k) is the observation value at time k. Let H(k) be the estimated observation at time k, and H(k) be the virtual measurement matrix, where H(k) = [P -1 (k|k-1)P ZX (k|k-1)] T =P ZX T (k|k-1)P -1 (k|k-1), where R(k) is the covariance matrix of additive noise; P ZX (k|k-1) is the cross-covariance matrix;

[0018] Based on the rewritten error covariance matrix, self-covariance matrix, and cross-covariance matrix, the information vector and information matrix are obtained using the information filter algorithm.

[0019] i k =H T (k)R -1 (k)[H(k)X(k)+ω(k)]

[0020] =P -1 (k|k-1)P ZX(k|k-1)R -1 (k)×[ω(k)+P ZX T (k|k-1)P -1 (k|k-1)X(k)]

[0021] I k =H T (k)R -1 (k)H(k)

[0022] =P -1 (k|k-1)P ZX (k|k-1)R -1 (k)×P ZX T (k|k-1)P -1 (k|k-1)

[0023] In the formula, i k Let I be the information vector, and ω(k) be the additive noise. k For information matrix;

[0024] Based on the information vector and information matrix, the update equations for the information state vector and information matrix are determined as follows: In the formula, Let be the updated information state vector at time k. Y(k|k) is the information state vector at time k, Y(k|k) is the updated information matrix at time k, and Y(k|k-1) is the information matrix at time k.

[0025] Optionally, the combination of the centralized unscented Kalman filter algorithm in the form of information filtering with the maximum consistency algorithm to obtain the maximum consistency unscented Kalman information filtering algorithm specifically includes:

[0026] Based on the observations of the target measured by each underwater sensor, the formula is used. and Y(k|k)=Y(k|k-1)+P -1 (k|k-1)P ZX (k|k-1)R -1 (k)P ZX T (k|k-1)P -1 (k|k-1), calculate the information state vector and information matrix;

[0027] Each underwater sensor communicates its observations with those of its neighboring underwater sensors, allowing them to obtain each other's observations.

[0028] Based on the observations measured by each underwater sensor and the observations measured by neighboring underwater sensors obtained through interaction, the maximum consensus algorithm is used to obtain the maximum value of the information vector and the maximum value of the information matrix.

[0029] Based on the maximum value of the information vector and the maximum value of the information matrix, using the formula... Update the state value; where, Y is the information state vector after N maximum consistency iterations. N (k) is the information state matrix after N maximum consistency iterations. This is the state update value at time k;

[0030] Based on the updated state value, use the formula Estimate the target's location; where n is the dimension of the random variable. This is the state estimate at time k+1. The weighting coefficients for the sigma sampling points. There are 2n+1 sigma sampling points; Let Y(k+1|k) be the information state vector at time k+1, and let Q be the information matrix at time k+1. k+1 Let be the covariance matrix of the process noise at time k+1.

[0031] Optionally, the step of using the maximum consensus algorithm to obtain the maximum value of the information vector and the maximum value of the information matrix based on the observations measured by each underwater sensor and the observations measured by neighboring underwater sensors obtained through interaction specifically includes:

[0032] Let variable ξ j =b j +δ j And when i≠j, b i =b j At that time, ξ i ≠ξ j Among them, b j =[(i k ) T ,col(I k ) T ] T The information vector i represents the information vector of the underwater sensor j. k and Information Matrix I k All elements in the array, col(·) represents column operations; δ j b represents a random vector; i The information vector i represents the information vector of the underwater sensor i. k and Information Matrix I k All elements in N, j∈N i N iRepresents the set of adjacent underwater sensors of underwater sensor i;

[0033] Based on the observations measured by each underwater sensor and the observations obtained interactively from adjacent underwater sensors, the formula is used... and Perform iterations; where ξ j (l), ξ j (l+1) represent the l-th and (l+1)-th dummy variables, respectively, j * b represents the sensor node with the maximum value. j (l+1) represents the information vector i of the sensor node with the maximum value. k and Information Matrix I k All elements are assigned to b j (l+1);

[0034] When the maximum number of iterations is reached, the iteration stops, and the maximum values ​​of the information vector and information matrix are obtained.

[0035] Optionally, acquiring the current observation values ​​of multiple underwater sensor measurement targets specifically includes:

[0036] The target is located using multiple underwater sensors, and the measurement information from each sensor is obtained. The measurement information includes the distance between the underwater sensor and the target, as well as the angle of the target relative to the underwater sensor.

[0037] Acquire the additive noise during each sensor measurement;

[0038] Based on the measurement information from each sensor and the additive noise, the measurement equations in the sensor-centered coordinate system are used. Obtain the current observation value of each underwater sensor measuring target;

[0039] Among them, Z j X(k) represents the observation value of the target measured by underwater sensor j at time k, X(k) is the target's state vector, and H... j (X(k)) is a nonlinear function, ω j (k) represents the additive noise of underwater sensor j at time k, and r(k) represents the distance between underwater sensor j and the target at time k. Let k be the angle of the target relative to the underwater sensor j. Let the additive noise of underwater sensor j at time k be the distance measurement. Let be the additive noise of underwater sensor j in angle measurement at time k.

[0040] A cooperative underwater target localization system based on maximum consensus includes:

[0041] The rewriting module is used to rewrite the centralized unscented Kalman filter algorithm into an information filtering form through equivalent transformation.

[0042] The algorithm reconstruction module is used to combine the centralized unscented Kalman filter algorithm in the form of information filtering with the maximum consistency algorithm to obtain the maximum consistency unscented Kalman information filtering algorithm.

[0043] The measurement module is used to acquire the current observation values ​​of multiple underwater sensor measurement targets;

[0044] The interaction module is used to enable each underwater sensor to exchange current observations with adjacent underwater sensors.

[0045] The position estimation module is used to estimate the target's position at the current moment based on the current observations measured by each underwater sensor and the current observations measured by neighboring underwater sensors obtained through interaction, using the maximum consistent unscented Kalman information filtering algorithm.

[0046] Optionally, the rewriting module specifically includes:

[0047] The covariance matrix rewriting submodule is used to rewrite the error covariance matrix, autocovariance matrix, and cross-covariance matrix in the centralized unscented Kalman filter algorithm using the statistical linear error propagation method.

[0048]

[0049]

[0050]

[0051] In the formula, P(k)k-1) is the error covariance matrix, E{} is the covariance matrix, and X(k) is the target's state vector. P is the estimated state vector of the target at time k; ZZ (k|k-1) is the autocovariance matrix, and Z(k) is the observation value at time k. Let H(k) be the estimated observation at time k, and H(k) be the virtual measurement matrix, where H(k) = [P -1 (k|k-1)P ZX (k|k-1)] T =P ZX T (k|k-1)P -1 (k|k-1), where R(k) is the covariance matrix of additive noise; P ZX (k|k-1) is the cross-covariance matrix;

[0052] The information vector and information matrix representation submodule is used to obtain the information vector and information matrix based on the rewritten error covariance matrix, autocovariance matrix, and cross-covariance matrix using an information filter algorithm.

[0053] i k =H T (k)R -1 (k)[H(k)X(k)+ω(k)]

[0054] =P -1 (k|k-1)P ZX (k|k-1)R -1 (k)×[ω(k)+P ZX T (k|k-1)P -1 (k|k-1)X(k)]

[0055] I k =H T (k)R -1 (k)H(k)

[0056] =P -1 (k|k-1)P ZX (k|k-1)R -1 (k)×P ZX T (k|k-1)P -1 (k|k-1)

[0057] In the formula, i k Let I be the information vector, and ω(k) be the additive noise. k For information matrix;

[0058] The update submodule is used to determine the update equations for the information state vector and the information matrix based on the information vector and the information matrix. In the formula, Let be the updated information state vector at time k. Y(k|k) is the information state vector at time k, Y(k|k) is the updated information matrix at time k, and Y(k|k-1) is the information matrix at time k.

[0059] Optionally, the algorithm reconstruction module specifically includes:

[0060] The node information calculation submodule is used to calculate the node information based on the observations of each underwater sensor's measured target, using a formula. Know that Y(k|k)=Y(k|k-1)+P -1 (k|k-1)P ZX (k|k-1)R -1 (k)P ZX T(k|k-1)P -1 (k|k-1), calculate the information state vector and information matrix;

[0061] The mutual communication submodule is used to communicate the observations of each underwater sensor with those of adjacent underwater sensors, so that each can obtain the observations of the other.

[0062] The maximum value acquisition submodule is used to obtain the maximum value of the information vector and the maximum value of the information matrix based on the observation values ​​measured by each underwater sensor and the observation values ​​measured by neighboring underwater sensors obtained through interaction, using the maximum consensus algorithm.

[0063] The state value update submodule is used to update the state value based on the maximum value of the information vector and the maximum value of the information matrix using the formula... Update the state value; where, Y is the information state vector after N maximum consistency iterations. N (k) is the information state matrix after N maximum consistency iterations. This is the state update value at time k;

[0064] The target location estimation submodule is used to estimate the target location based on the updated state value using a formula. Estimate the target's location; where n is the dimension of the random variable. This is the state estimate at time k+1. The weighting coefficients for the sigma sampling points. There are 2n+1 sigma sampling points; Let Y(k+1|k) be the information state vector at time k+1, and let Q be the information matrix at time k+1. k+1 Let be the covariance matrix of the process noise at time k+1.

[0065] Optionally, the maximum value acquisition submodule specifically includes:

[0066] Variable preset unit, used to set variable ξ j =b j +δ j And when i≠j, b i =b j At that time, ξ i ≠ξ j Among them, b j =[(i k ) T ,col(I k ) T ] T The information vector i represents the information vector of the underwater sensor j. k and Information Matrix I k All elements in the array, col(·) represents column operations; δj b represents a random vector; i The information vector i represents the information vector of the underwater sensor i. k and Information Matrix I k All elements in N, j∈N i N i Represents the set of adjacent underwater sensors of underwater sensor i;

[0067] An iterative unit is used to calculate the values ​​measured by each underwater sensor and the values ​​measured by adjacent underwater sensors obtained interactively, using the formula... and Perform iterations; where ξ j (l), ξ j (l+1) represent the l-th and (l+1)-th dummy variables, respectively, j * b represents the sensor node with the maximum value. j (l+1) represents the information vector i of the sensor node with the maximum value. k and Information Matrix I k All elements are assigned to b j (l+1);

[0068] The result output unit is used to stop iteration when the maximum number of iterations is reached, and to obtain the maximum value of the information vector and the maximum value of the information matrix.

[0069] Optionally, the measurement module specifically includes:

[0070] The positioning submodule is used to locate the target using multiple underwater sensors and obtain measurement information from each sensor; the measurement information includes the distance between the underwater sensor and the target and the angle of the target relative to the underwater sensor;

[0071] The additive noise acquisition submodule is used to acquire the additive noise during each sensor measurement.

[0072] The current observation acquisition submodule is used to obtain the measurement values ​​based on the measurement information from each sensor and the additive noise, using the measurement equations in the sensor-centered coordinate system. Obtain the current observation value of each underwater sensor measuring target;

[0073] Among them, Z j X(k) represents the observation value of the target measured by underwater sensor j at time k, X(k) is the target's state vector, and H... j (X(k)) is a nonlinear function, ω j (k) represents the additive noise of underwater sensor j at time k, and r(k) represents the distance between underwater sensor j and the target at time k. Let k be the angle of the target relative to the underwater sensor j. Let the additive noise of underwater sensor j at time k be the distance measurement. Let be the additive noise of underwater sensor j in angle measurement at time k.

[0074] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0075] This invention discloses an underwater target cooperative localization method and system based on maximum consistency. First, the centralized unscented Kalman filtering iterative process is rewritten into an information filtering form, namely the unscented Kalman information filtering form, reducing the computational dimensionality of the sensors. Then, combined with the maximum consistency algorithm, a new distributed filtering method, "maximum consistency unscented Kalman information filtering algorithm," is obtained. Finally, after each underwater sensor interacts with its neighboring underwater sensors to exchange current observations, the maximum consistency unscented Kalman information filtering algorithm is used to achieve target localization estimation, improving the localization accuracy of underwater acoustic sensor networks when locating moving underwater targets. Attached Figure Description

[0076] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0077] Figure 1 A flowchart of an underwater target cooperative localization method based on maximum consistency is provided in an embodiment of the present invention;

[0078] Figure 2 A schematic diagram of a cooperative underwater target localization method based on maximum consistency provided in an embodiment of the present invention;

[0079] Figure 3 This is a diagram of an underwater acoustic sensor network architecture provided in an embodiment of the present invention;

[0080] Figure 4 A simplified flowchart for rewriting traditional UKF into an information filtering form is provided for embodiments of the present invention. Detailed Implementation

[0081] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0082] The purpose of this invention is to provide a method and system for cooperative underwater target localization based on maximum consistency, so as to improve the localization accuracy of underwater acoustic sensor networks when locating moving underwater targets.

[0083] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0084] To address the low positioning accuracy of underwater acoustic sensor networks when locating moving underwater targets, this invention proposes a distributed maximum consistency unscented Kalman information filtering algorithm. This algorithm rewrites the centralized unscented Kalman filtering algorithm into an information filtering form through equivalent transformation, reducing the computational dimensionality of the sensor. Then, a maximum consistency processing strategy is applied to the rewritten information vector and information matrix, and virtual node technology is introduced to handle the problem of identical node values.

[0085] The basic idea of ​​underwater target cooperative localization is: assuming that the positions of each node in the sensor network are accurately known, after each node acquires the observation value, it extracts its relevant information according to a certain localization algorithm and communicates with its neighboring nodes. Each node can estimate the location of the sound source based on the information obtained.

[0086] An underwater acoustic sensor network consists of numerous sensor nodes equipped with acoustic modems. These nodes can be fixed to the seabed or at different depths via cables, and can communicate with each other underwater via acoustic means. Figure 3 The underwater acoustic sensor network architecture shown mainly includes surface buoys and sensor nodes, with the long dashed line representing the target's trajectory.

[0087] Surface buoys float on the water and are equipped with GPS to obtain their position and global time reference. They act as "satellite" nodes, whose main function is to provide self-positioning for underwater sensor nodes and to serve as hub nodes for transmitting underwater information to the surface, ensuring communication with sensor nodes in various underwater locations. They also need to have two communication modes: underwater acoustic communication and radio frequency communication. Underwater acoustic communication is used to receive the processed and integrated data from the underwater sensors, while radio frequency communication is used in the surface environment to transmit the received data to the crew on board.

[0088] The underwater sensor nodes are equipped with filters and are responsible for the overall network's communication, data acquisition, and computation. They are fixed and suspended underwater, using pressure sensors to determine depth. They are characterized by low complexity and low cost, and can determine their own position with the assistance of buoys. Each sensor node can interact with its neighboring nodes via underwater acoustic communication, fuse the data, and then transmit the fused information back to its neighbors.

[0089] Reference Figure 1 and Figure 2 The underwater target cooperative localization method based on maximum consistency provided by this invention includes the following steps:

[0090] Step S1: The centralized unscented Kalman filter algorithm is rewritten into an information filtering form through equivalent transformation.

[0091] Suppose that target s undergoes approximately uniformly accelerated linear motion in a two-dimensional plane xy, and its position, velocity, and acceleration at time k are represented by the state vector. The process noise is represented by v(k), and its covariance matrix is ​​represented by Q. k If we express this as an expression, then the kinematic model of the target in the coordinate system is:

[0092] X(k+1)=f(X(k))+u(k) (1)

[0093] in,

[0094]

[0095] Assume the coordinate position is (x j y j Sensor node j locates target s, and the distance r between the sensor and the target can be obtained. k and the angle of the target relative to the sensor node In actual measurements, there is additive noise ω j (k), whose covariance matrix is ​​denoted by R(k), the measurement equation in the coordinate system centered on the sensor in a wireless network consisting of N sensor nodes is:

[0096]

[0097] Where j∈{1,2,...,N}.

[0098] At current time k, based on the currently available observation value Z j (k), to estimate the state variable X(k). The estimated value of X(k) is used... Indicates, such as Figure 4 As shown, the main steps of the centralized UKF algorithm are as follows:

[0099] I. Prediction: After selecting Sigma points and performing weighted calculations, the prior state estimate can be calculated as follows:

[0100]

[0101] The covariance matrix is ​​calculated as follows:

[0102]

[0103] Among them W s =λ / (n+λ), if s=0, then W s = 1 / (2(n+λ)).

[0104] II. Update: Using the new information provided by the measurements, after point selection and weighting, we have the UKF gain K(k) and state estimate. The update of its covariance matrix P(k) is as follows:

[0105]

[0106]

[0107]

[0108] The remaining parts remain unchanged. The error covariance matrix P(k|k-1) and the autocovariance matrix Pk in the measurement update are redefined using the statistical linear error propagation method. ZZ (k|k-1), cross-covariance matrix P ZX (k|k-1) can be rewritten as follows:

[0109]

[0110]

[0111]

[0112] In the formula, H(k) = [P -1 (k|k-1)P ZX (k|k-1)] T =P ZX T (k|k-1)P -1 (k|k-1).

[0113] The information vector i of the unscented Kalman information filtering algorithm can be obtained from the information filter algorithm. k and Information Matrix I k It is expressed as follows:

[0114] i k =H T (k)R -1 (k)[H(k)X(k)+ω(k)]

[0115] =P -1 (k|k-1)P ZX (k|k-1)R -1 (k)×[ω(k)+P ZX T (k|k-1)P-1 [(k|k-1)X(k)] (12)

[0116] I k =H T (k)R -1 (k)H(k)

[0117] =P -1 (k|k-1)P ZX (k|k-1)R -1 (k)×P ZX T (k|k-1)P -1 (k|k-1) (13)

[0118] Known information state vector The definition of the information matrix Y is:

[0119]

[0120] Therefore, the update equations for the information state vector and the information matrix can be obtained as follows:

[0121]

[0122] Step S2: Combine the centralized unscented Kalman filter algorithm in the form of information filtering with the maximum consistency algorithm to obtain the maximum consistency unscented Kalman information filtering algorithm.

[0123] By fusing information obtained from sensor measurements using a maximum consistency processing strategy, accurate consistency is achieved. Furthermore, a novel distributed filtering method is proposed by combining the maximum consistency algorithm with the UKF information filtering approach, as shown in the table below:

[0124] (1) For each node j∈N, obtain the measurement value and calculate the information state vector and information matrix.

[0125]

[0126] Y(k|k)=Y(k|k-1)+P -1 (k|k-1)P ZX (k|k-1)R -1 (k)P ZX T (k|k-1)P -1 (k|k-1) (17)

[0127] (2) Maximum Consensus Process

[0128] 1) A single sensor i compares its measurement results with those of its neighboring nodes j∈N i Mutual communication allows each other to obtain information from the other.

[0129] 2) Let variable ξ j =b j +δ j Its initial value is ξ j (0)=b j (0)+δ j , where δ j It is a small random vector such that when b i =b j When i ≠ j, ξ i ≠ξ j To avoid the problem of nodes having the same value; use b j =[(i k ) T ,col(I k ) T ] T Represents information vector i k and Information Matrix I k All elements in; col(·) represents column operations, Let denot be a vector, and let its components represent the vector ∑ in N maximum consensus iterations. j N is from column s=1 to column s=n.

[0130] The loop continues when t = 0, 1, ..., N-1.

[0131] when Time loop (assuming each sensor knows the network diameter) )

[0132]

[0133]

[0134]

[0135] Finish

[0136]

[0137]

[0138] Finish

[0139]

[0140] (3) Status value update

[0141]

[0142] (4) State estimation and its covariance update

[0143]

[0144] The maximum consistent unscented Kalman information filtering algorithm selects the maximum value through a maximum consistency strategy, and then selects a second maximum value or another maximum value from different sensors, and so on.

[0145] Step S3: Obtain the current observation values ​​of the target measured by multiple underwater sensors.

[0146] Step S4: Each underwater sensor interacts with its neighboring underwater sensors to exchange current observations.

[0147] Step S5: Based on the current observation values ​​measured by each underwater sensor and the current observation values ​​measured by adjacent underwater sensors obtained through interaction, the position of the target at the current time is estimated using the maximum consistent unscented Kalman information filtering algorithm.

[0148] The target's position at the current moment is the position in formula (25).

[0149] The advantages of this invention are as follows:

[0150] 1. The centralized unscented Kalman filtering algorithm is rewritten into an information filtering form through equivalent transformation, which reduces the computational dimensionality of the sensor.

[0151] 2. The maximum consistency processing strategy is adopted for the rewritten information vector and information matrix, resulting in high positioning accuracy.

[0152] This invention also provides a maximum consensus-based underwater target cooperative localization system, comprising:

[0153] The rewriting module is used to rewrite the centralized unscented Kalman filter algorithm into an information filtering form through equivalent transformation.

[0154] The algorithm reconstruction module is used to combine the centralized unscented Kalman filter algorithm in the form of information filtering with the maximum consistency algorithm to obtain the maximum consistency unscented Kalman information filtering algorithm.

[0155] The measurement module is used to acquire the current observation values ​​of multiple underwater sensor measurement targets;

[0156] The interaction module is used to enable each underwater sensor to exchange current observations with adjacent underwater sensors.

[0157] The position estimation module is used to estimate the target's position at the current moment based on the current observations measured by each underwater sensor and the current observations measured by neighboring underwater sensors obtained through interaction, using the maximum consistent unscented Kalman information filtering algorithm.

[0158] The rewrite module specifically includes:

[0159] The covariance matrix rewriting submodule is used to rewrite the error covariance matrix, autocovariance matrix, and cross-covariance matrix in the centralized unscented Kalman filter algorithm using the statistical linear error propagation method.

[0160]

[0161]

[0162]

[0163] In the formula, P(k|k-1) is the error covariance matrix, E{} is the covariance matrix, and X(k) is the target's state vector. P is the estimated state vector of the target at time k; ZZ (k|k-1) is the autocovariance matrix, and Z(k) is the observation value at time k. Let H(k) be the estimated observation at time k, and H(k) be the virtual measurement matrix, where H(k) = [P -1 (K|k-1)P ZX (k|k-1)] T =P ZX T (k|k-1)P -1 (k|k-1), where R(k) is the covariance matrix of additive noise; P ZX (k|k-1) is the cross-covariance matrix;

[0164] The information vector and information matrix representation submodule is used to obtain the information vector and information matrix based on the rewritten error covariance matrix, autocovariance matrix, and cross-covariance matrix using an information filter algorithm.

[0165] i k =H T (k)R -1 (k)[H(k)X(k)+ω(k)]

[0166] =P -1 (k|k-1)P ZX (k|k-1)R -1 (k)×[ω(k)+P ZX T (k|k-1)P -1 (k|k-1)X(k)]

[0167] I k =H T (k)R -1 (k)H(k)

[0168] =P-1 (k|k-1)P ZX (k|k-1)R -1 (k)×P ZX T (k|k-1)P -1 (k|k-1)

[0169] In the formula, i k Let I be the information vector, and ω(k) be the additive noise. k For information matrix;

[0170] The update submodule is used to determine the update equations for the information state vector and the information matrix based on the information vector and the information matrix. In the formula, Let be the updated information state vector at time k. Y(k|k) is the information state vector at time k, Y(k|k) is the updated information matrix at time k, and Y(k|k-1) is the information matrix at time k.

[0171] The algorithm reconstruction module specifically includes:

[0172] The node information calculation submodule is used to calculate the node information based on the observations of each underwater sensor's measured target, using a formula. and Y(k|k)=Y(k|k-1)+P -1 (k|k-1)P ZX (k|k-1)R -1 (k)P ZX T (k|k-1)P -1 (k|k-1), calculate the information state vector and information matrix;

[0173] The mutual communication submodule is used to communicate the observations of each underwater sensor with those of adjacent underwater sensors, so that each can obtain the observations of the other.

[0174] The maximum value acquisition submodule is used to obtain the maximum value of the information vector and the maximum value of the information matrix based on the observation values ​​measured by each underwater sensor and the observation values ​​measured by neighboring underwater sensors obtained through interaction, using the maximum consensus algorithm.

[0175] The state value update submodule is used to update the state value based on the maximum value of the information vector and the maximum value of the information matrix using the formula... Update the state value; where, Y is the information state vector after N maximum consistency iterations. N (k) is the information state matrix after N maximum consistency iterations. This is the state update value at time k;

[0176] The target location estimation submodule is used to estimate the target location based on the updated state value using a formula. Estimate the target's location; where n is the dimension of the random variable. This is the state estimate at time k+1. The weighting coefficients for the sigma sampling points. There are 2n+1 sigma sampling points; Let Y(k+1|k) be the information state vector at time k+1, and let Q be the information matrix at time k+1. k+1 Let be the covariance matrix of the process noise at time k+1.

[0177] The maximum value retrieval submodule specifically includes:

[0178] Variable preset unit, used to set variable ξ j =b j +δ j And when i≠j, b i =b j At that time, ξ i ≠ξ j Among them, b j =[(i k ) T ,col(I k ) T ] T The information vector i represents the information vector of the underwater sensor j. k and Information Matrix I k All elements in the array, col(·) represents column operations; δ j b represents a random vector; i The information vector i represents the information vector of the underwater sensor i. k and Information Matrix I k All elements in N, j∈N i N i Represents the set of adjacent underwater sensors of underwater sensor i;

[0179] An iterative unit is used to calculate the values ​​measured by each underwater sensor and the values ​​measured by adjacent underwater sensors obtained interactively, using the formula... Know Perform iterations; where ξ j (l), ξ j (l+1) represent the l-th and (l+1)-th dummy variables, respectively, j * b represents the sensor node with the maximum value. j (l+1) represents the information vector i of the sensor node with the maximum value. k and Information Matrix I k All elements are assigned to b j (l+1);

[0180] The result output unit is used to stop iteration when the maximum number of iterations is reached, and to obtain the maximum value of the information vector and the maximum value of the information matrix.

[0181] The measurement module specifically includes:

[0182] The positioning submodule is used to locate the target using multiple underwater sensors and obtain measurement information from each sensor; the measurement information includes the distance between the underwater sensor and the target and the angle of the target relative to the underwater sensor;

[0183] The additive noise acquisition submodule is used to acquire the additive noise during each sensor measurement.

[0184] The current observation acquisition submodule is used to obtain the measurement values ​​based on the measurement information from each sensor and the additive noise, using the measurement equations in the sensor-centered coordinate system. Obtain the current observation value of each underwater sensor measuring target;

[0185] Among them, Z j X(k) represents the observation value of the target measured by underwater sensor j at time k, X(k) is the target's state vector, and H... j (X(k)) is a nonlinear function, ω j (k) represents the additive noise of underwater sensor j at time k, and r(k) represents the distance between underwater sensor j and the target at time k. Let k be the angle of the target relative to the underwater sensor j. Let the additive noise of underwater sensor j at time k be the distance measurement. Let be the additive noise of underwater sensor j in angle measurement at time k.

[0186] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0187] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for cooperative localization of underwater targets based on maximum consensus, characterized in that, include: The centralized unscented Kalman filter algorithm is rewritten into an information filtering form through equivalent transformation; By combining the centralized unscented Kalman filter algorithm in the form of information filtering with the maximum consistency algorithm, the maximum consistency unscented Kalman information filtering algorithm is obtained. Acquire current observations of targets measured by multiple underwater sensors; Each underwater sensor interacts with its neighboring underwater sensors to exchange current observations. Based on the current observations measured by each underwater sensor and the current observations measured by neighboring underwater sensors obtained through interaction, the position of the target at the current moment is estimated using the maximum consistent unscented Kalman information filtering algorithm. The method of combining the centralized unscented Kalman filter algorithm (information filtering form) with the maximum consistency algorithm to obtain the maximum consistency unscented Kalman information filter algorithm specifically includes: Based on the observations of the target measured by each underwater sensor, the formula is used. and Calculate the information state vector and information matrix; where, for k The updated information state vector at each time step. for k The information state vector at time step, Let be the error covariance matrix. The cross-covariance matrix; The covariance matrix of additive noise, Additive noise, The state vector of the target; for k The information matrix is ​​updated in real time. for k Information matrix at any given time; Each underwater sensor communicates its observations with those of its neighboring underwater sensors, allowing them to obtain each other's observations. Based on the observations measured by each underwater sensor and the observations measured by neighboring underwater sensors obtained through interaction, the maximum consensus algorithm is used to obtain the maximum value of the information vector and the maximum value of the information matrix. Based on the maximum value of the information vector and the maximum value of the information matrix, using the formula... Update the state value; where, For the process N The information state vector after the second maximum consistency iteration. For the process N The information state matrix after the second maximum consistency iteration for k The state update value at any given time; Based on the updated state value, use the formula Estimate the target's location; where, n Let be the dimension of the random variable. for k State estimate at time +1 The weighting coefficients for the sigma sampling points. 2 n +1 sigma sampling point; for k The information state vector at time +1 for k Information matrix at time +1 In order to be in k The covariance matrix of the process noise at time +1; The process involves using the maximum consensus algorithm to obtain the maximum value of the information vector and the maximum value of the information matrix based on the observations measured by each underwater sensor and the observations measured by neighboring underwater sensors obtained through interaction. Specifically, this includes: Let the variable , and when , hour, ;in, Indicates underwater sensor j Information vector and information matrix All elements in Indicates column operations; b represents a random vector; i Indicates underwater sensor i Information vector and information matrix All elements in , N i Indicates underwater sensor i The set of adjacent underwater sensors; Based on the observations measured by each underwater sensor and the observations obtained interactively from adjacent underwater sensors, the formula is used... , and Perform iterations; where, , They represent the first The, the +1 dummy variable, This represents the sensor node with the maximum value. The information vector representing the sensor node with the maximum value. and information matrix All elements are assigned to ; When the maximum number of iterations is reached, the iteration stops, and the maximum values ​​of the information vector and information matrix are obtained.

2. The underwater target cooperative localization method based on maximum consistency according to claim 1, characterized in that, The process of rewriting the centralized unscented Kalman filter algorithm into an information filtering form through equivalent transformation specifically includes: Using the statistical linear error propagation method, the error covariance matrix, self-covariance matrix, and cross-covariance matrix in the centralized unscented Kalman filter algorithm are rewritten as follows: In the formula, E{} is the covariance matrix. For the goal k The estimated state vector at time t; It is the autocovariance matrix. for k The observed value at time, for k Estimated observations at time, For virtual measurement matrix, ; Based on the rewritten error covariance matrix, self-covariance matrix, and cross-covariance matrix, the information vector and information matrix are obtained using the information filter algorithm. ； Based on the information vector and information matrix, the update equations for the information state vector and information matrix are determined as follows: .

3. The underwater target cooperative localization method based on maximum consistency according to claim 1, characterized in that, The acquisition of current observation values ​​of multiple underwater sensor measurement targets specifically includes: The target is located using multiple underwater sensors, and the measurement information from each sensor is obtained. The measurement information includes the distance between the underwater sensor and the target, as well as the angle of the target relative to the underwater sensor. Acquire the additive noise during each sensor measurement; Based on the measurement information from each sensor and the additive noise, the measurement equations in the sensor-centered coordinate system are used. = = This allows us to obtain the current observation value of each underwater sensor measuring target; in, underwater sensor j exist k Continuously measure the observed values ​​of the target. Let be the state vector of the target. It is a nonlinear function. for k underwater sensor j Additive noise during measurement for k underwater sensor j Distance to the target for k The target at any given time relative to the underwater sensor j Angle, for k underwater sensor j Additive noise in distance measurements, for k underwater sensor j Additive noise in angle measurements.

4. A cooperative underwater target localization system based on maximum consensus, characterized in that, include: The rewriting module is used to rewrite the centralized unscented Kalman filter algorithm into an information filtering form through equivalent transformation. The algorithm reconstruction module is used to combine the centralized unscented Kalman filter algorithm in the form of information filtering with the maximum consistency algorithm to obtain the maximum consistency unscented Kalman information filtering algorithm. The measurement module is used to acquire the current observation values ​​of multiple underwater sensor measurement targets; The interaction module is used to enable each underwater sensor to exchange current observations with adjacent underwater sensors. The position estimation module is used to estimate the target's position at the current moment based on the current observations measured by each underwater sensor and the current observations measured by neighboring underwater sensors obtained interactively; The algorithm reconstruction module specifically includes: The node information calculation submodule is used to calculate the node information based on the observations of each underwater sensor's measured target, using a formula. and Calculate the information state vector and information matrix; where, for k The updated information state vector at each time step. for k The information state vector at time step, Let be the error covariance matrix. The cross-covariance matrix; The covariance matrix of additive noise, Additive noise, The state vector of the target; for k The information matrix is ​​updated in real time. for k Information matrix at any given time; The mutual communication submodule is used to communicate the observations of each underwater sensor with those of adjacent underwater sensors, so that each can obtain the observations of the other. The maximum value acquisition submodule is used to obtain the maximum value of the information vector and the maximum value of the information matrix based on the observation values ​​measured by each underwater sensor and the observation values ​​measured by neighboring underwater sensors obtained through interaction, using the maximum consensus algorithm. The state value update submodule is used to update the state value based on the maximum value of the information vector and the maximum value of the information matrix using the formula... Update the state value; where, For the process N The information state vector after the second maximum consistency iteration. For the process N The information state matrix after the second maximum consistency iteration for k The state update value at any given time; The target location estimation submodule is used to estimate the target location based on the updated state value using a formula. Estimate the target's location; where, n Let be the dimension of the random variable. for k State estimate at time +1 The weighting coefficients for the sigma sampling points. 2 n +1 sigma sampling point; for k The information state vector at time +1 for k Information matrix at time +1 In order to be in k The covariance matrix of the process noise at time +1; The maximum value acquisition submodule specifically includes: Variable preset unit, used to set variables , and when , hour, ;in, Indicates underwater sensor j Information vector and information matrix All elements in Indicates column operations; b represents a random vector; i Indicates underwater sensor i Information vector and information matrix All elements in , N i Indicates underwater sensor i The set of adjacent underwater sensors; An iterative unit is used to calculate the values ​​measured by each underwater sensor and the values ​​measured by adjacent underwater sensors obtained interactively, using the formula... , and Perform iterations; where, , They represent the first The, the +1 dummy variable, This represents the sensor node with the maximum value. The information vector representing the sensor node with the maximum value. and information matrix All elements are assigned to ; The result output unit is used to stop iteration when the maximum number of iterations is reached, and to obtain the maximum value of the information vector and the maximum value of the information matrix.

5. The underwater target cooperative localization system based on maximum consistency according to claim 4, characterized in that, The rewriting module specifically includes: The covariance matrix rewriting submodule is used to rewrite the error covariance matrix, autocovariance matrix, and cross-covariance matrix in the centralized unscented Kalman filter algorithm using the statistical linear error propagation method. In the formula, E{} is the covariance matrix. For the goal k The estimated state vector at time t; It is the autocovariance matrix. for k The observed value at time, for k Estimated observations at time, For virtual measurement matrix, ; The information vector and information matrix representation submodule is used to obtain the information vector and information matrix based on the rewritten error covariance matrix, autocovariance matrix, and cross-covariance matrix using an information filter algorithm. ； The update submodule is used to determine the update equations for the information state vector and the information matrix based on the information vector and the information matrix. .

6. The underwater target cooperative localization system based on maximum consistency according to claim 4, characterized in that, The measurement module specifically includes: The positioning submodule is used to locate the target using multiple underwater sensors and obtain measurement information from each sensor; the measurement information includes the distance between the underwater sensor and the target and the angle of the target relative to the underwater sensor; The additive noise acquisition submodule is used to acquire the additive noise during each sensor measurement. The current observation acquisition submodule is used to obtain the measurement values ​​based on the measurement information from each sensor and the additive noise, using the measurement equations in the sensor-centered coordinate system. This allows us to obtain the current observation value of each underwater sensor measuring target; in, underwater sensor j exist k Continuously measure the observed values ​​of the target. Let be the state vector of the target. It is a nonlinear function. for k underwater sensor j Additive noise during measurement for k underwater sensor j Distance to the target for k The target at any given time relative to the underwater sensor j Angle, for k underwater sensor j Additive noise in distance measurements, for k underwater sensor j Additive noise in angle measurements.

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