A collaborative positioning method for AUV based on Mahalanobis distance and neural network assistance

Abstract

The present invention provides an AUV collaborative positioning method based on Mahalanobis distance and neural network assistance. The present invention uses adaptive volumetric Kalman filtering to process wild values, and uses dual-threshold Mahalanobis distance to detect whether an acoustic measurement is abnormal and what kind of abnormality has occurred. If the measurement is updated normally, the Kalman filter result is allowed to update the state. If the measurement is abnormal, different algorithms are used to assist the filter update according to the abnormality type, so as to achieve the purpose of improving the collaborative positioning accuracy.

Description

Technical Field

[0001] The invention belongs to the field of autonomous underwater robots, and in particular relates to an AUV collaborative positioning method based on Mahalanobis distance and neural network assistance. Background Art

[0002] As a new type of unmanned intelligent equipment at sea, autonomous underwater vehicles (AUVs) have been widely used in the fields of ocean observation, maritime rescue, mine countermeasures, intelligence reconnaissance, etc., especially in underwater search missions, where their advantages are more obvious. However, limited combat capabilities and complex mission environments are also difficulties faced by single AUVs. Therefore, the collaborative positioning technology of multiple AUVs based on hydroacoustic communication networks has received more attention. Different AUVs use hydroacoustic communication to share each other's information, use hydroacoustic ranging to measure relative distances as observation quantities, and then use data fusion technology to reduce positioning errors. This method is called "cooperative positioning". Since multi-vessel collaborative positioning can improve the overall positioning capability of the system, and has the advantages of low cost and good system robustness, it can greatly enhance the mission execution capability of the multi-AUV system and has important theoretical and application value. Therefore, the positioning algorithm that improves the accuracy of multi-vessel collaborative positioning is of great significance. Considering the complexity and uncertainty of the underwater environment faced by micro underwater vehicles during navigation, the errors of the collaborative navigation system can be roughly divided into two categories: one is the error caused by wild value noise, and the other is the error caused by the failure of the sensor to update the measurement. Summary of the invention

[0003] The purpose of the present invention is to use an adaptive volumetric Kalman filter to process outliers while using a double-threshold Mahalanobis distance to detect whether an abnormality occurs in acoustic measurement and what kind of abnormality occurs. A collaborative positioning method for AUVs based on Mahalanobis distance and neural network assistance is provided.

[0004] A collaborative positioning method for AUV based on Mahalanobis distance and neural network assistance includes the following steps:

[0005] Step 1: Establish a multi-AUV collaborative positioning state space model;

[0006] Step 2: Build a BP neural network;

[0007] Step 3: When the reference position is available, multi-AUV collaborative positioning estimation is performed through ACKF;

[0008] Step 4: Collect training data for the neural network;

[0009] Step 5: Use the data collected in step 4 to train the BP neural network;

[0010] Step 6: Construct a fault detection function and set a double threshold value according to the root mean square error σ of the neural network training result to perform fault detection on the measurement information;

[0011] Step 7: Save the fault detection results, classify the fault results, and use different algorithms for collaborative positioning;

[0012] Furthermore, the step 1 of establishing a multi-AUV collaborative positioning state space model is specifically as follows:

[0013] The state equation of the collaborative positioning system for relative position measurement is:

[0014]

[0015] In the formula, x k and k They are respectively following the AUV at t k The east and north positions at the moment; δt is the dead reckoning time; sensor input u k =[V k θ k ] T , V k For the following AUV at t k The forward velocity at time θ k For the following AUV at t k The heading angle at the moment; w x,k and w y,k It is a zero-mean and mutually independent Gauss white noise;

[0016] The coordinate position relationship between the pilot AUV and the follower AUV is:

[0017]

[0018] In the formula, the pilot AUV is at t k The location information at the moment is Z k is the relative distance measurement information between the leading AUV and the following AUV, v k is a Gauss white noise with zero mean and independent of each other;

[0019] Assume the known system noise covariance matrix and measurement noise covariance matrix:

[0020] Q k =E[w k w k T ]

[0021] R k =E[v k v kT ]

[0022] Define X k =[x k ,y k ] T To follow the AUV at t k The state quantity at the moment, w k =[w x,k ,w y,k ] T is the process noise vector, v k =[v k ] T is the measurement noise vector;

[0023] Establish a discrete time state space model of multi-AUV collaborative positioning system:

[0024]

[0025] In the formula, the state function Measurement function

[0026] Furthermore, the step 2 of building the BP neural network is specifically as follows:

[0027] The transfer function uses the Log-Sigmoid function:

[0028]

[0029] The range of x includes the entire real number domain, and the function value is between 0 and 1;

[0030] The BP neural network is constructed by the newff function, the number of iterations epochs is selected as 1000, the learning rate lr is selected as 0.0025, and the initial weight is Where F is the number of neurons connected to the weight input end;

[0031] Furthermore, when the reference position is available, the step 3 performs multi-AUV collaborative positioning estimation through ACKF as follows:

[0032] Step 3.1: Time Update

[0033] Step 3.1.1: Transform the state error covariance P through Cholesky k|k break down:

[0034]

[0035] Define variables:

[0036]

[0037] Where m = 2n is the number of volume points; n = 2 is the dimension of the state equation; ξ i is the generated volume point; [1] i is the i-th volume point in the point set, and the volume point set is: w i is the weight of each volume point;

[0038] Step 3.1.2: Calculate Cubature points:

[0039]

[0040] Step 3.1.3: Transfer the Cubature points through the transfer matrix function of the system state:

[0041] X i,k+1|k =f(X i,kk ,u k )

[0042] Step 3.1.4: k+1 The state prediction value at the moment is weighted summed:

[0043]

[0044] Step 3.1.5: Calculate t k+1 The predicted value of the state error covariance at time:

[0045]

[0046] Step 3.2: Measurement Update

[0047] Step 3.2.1: Use Cholesky to predict the state error covariance value P k+1|k break down:

[0048]

[0049] Step 3.2.2: Calculate Cubature points:

[0050]

[0051] Step 3.2.3: Transfer Cubature points through the system's measurement function:

[0052]

[0053] Step 3.2.4: k+1 Weighted sum of observed predicted values ​​at time:

[0054]

[0055] Step 3.2.5: Calculate t k+1 The predicted value of the measurement error covariance at time:

[0056]

[0057] Step 3.2.6: Cross-covariance matrix:

[0058]

[0059] Step 3.2.7: Estimate the Kalman filter gain:

[0060]

[0061] Step 3.2.8: Using the state update and covariance update process, obtain t k+1 Status of the moment and the state estimation error covariance matrix P k+1|k+1 :

[0062]

[0063]

[0064] Step 3.3: Construct an adaptive factor to perform line correction on the covariance matrix:

[0065]

[0066]

[0067] Define the innovation vector formula and the innovation vector matrix formula, and calculate Δe k and the autocovariance matrix P zz,k|k-1 The size of the trace is judged to construct an adaptive factor to achieve the purpose of online correction, specifically:

[0068]

[0069] Autocovariance matrix correction:

[0070]

[0071] Cross-covariance matrix correction:

[0072]

[0073] So far, the filtering correction process at time k+1 is completed;

[0074] Furthermore, the step 4 of collecting the training data of the neural network is specifically as follows:

[0075] When the datum reference position is available, and the main boat's -1 latitude and longitude x obtained by GPS a ,y a and step 3 and the main boat's -2 latitude and longitude x obtained by GPS c ,y c Two BP neural networks are introduced for training respectively, and finally two trained BP neural network-1 and BP neural network-2 are obtained;

[0076] Furthermore, the step 5 of training the neural network is specifically as follows:

[0077] Step 5.1: Forward Propagation

[0078] The input and output of the i-th hidden layer are:

[0079]

[0080]

[0081] The input and output of the jth hidden layer are:

[0082]

[0083]

[0084] Among them, x i is the input data, ω ij is the weight from the input layer to the hidden layer, is the weight from the hidden layer to the output layer, θ k is the threshold of the hidden layer, is the threshold of the output layer;

[0085] Step 5.2: Error calculation, network output and target signal y 0 The error is:

[0086]

[0087] Step 5.3: Error back propagation, adjust the connection coefficient according to the steepest gradient descent method:

[0088]

[0089]

[0090] Furthermore, the step 6 is specifically as follows:

[0091] The measurement residual of the Kalman filter is:

[0092]

[0093] in, is the measurement prediction value; is the recursive value of the system state; H k is the observation matrix; Z k is the actual measured value;

[0094] According to the orthogonality principle of Kalman filtering, the square of the residual Mahalanobis distance obeys the chi-square distribution, and the chi-square test statistic is constructed:

[0095]

[0096] Where M k Subject to the degree of freedom m z Chi-square distribution of m z Z k The dimension of

[0097] By setting the chi-square test significance level α, the confidence probability of the Mahalanobis distance under the significance level α can be obtained. The system fault detection process is:

[0098]

[0099] The chi-square detection degree of freedom is 1, and the false alarm rate is selected as 0.01, which corresponds to the upper threshold T 2 The value is 15.14. The selection of the lower threshold is related to the prediction accuracy of the neural network. The root mean square error σ of the network training is reflected in the test statistic level. According to the empirical formula, 3σ is selected as the basis. The lower threshold expression is:

[0100]

[0101] Furthermore, the step 7 is specifically as follows:

[0102] Normal data points are assigned a value of 0, faulty data points are assigned a value of 1, and disturbed data points are assigned a value of 2. When processing normal points, ACKF performs normal time and measurement updates; when processing faulty points, ACKF only performs time updates without status updates; when processing disturbed data points, if the measurement of the main boat-1 fails, the filter one-step prediction value at the current moment and the latitude and longitude information x provided by GPS are used. a ,y a The trained BP neural network-1 is then fed into the measurement prediction data output by the neural network into the ACKF measurement update; if the measurement of the main boat-2 fails, the filter one-step prediction value at the current moment and the latitude and longitude information x provided by GPS are used. c ,y cIt is brought into the trained BP neural network-2, and then the measurement prediction data output by the neural network is brought into the ACKF measurement update to improve the accuracy of the filtering algorithm.

[0103] The beneficial effects of the present invention are:

[0104] 1. In the case of multi-AUV collaborative positioning, the present invention takes into account the heading drift error of the following AUV, the influence of ocean current speed and the underwater acoustic noise related to the distance, and has higher practical value.

[0105] 2. The present invention utilizes the Mahalanobis distance and to determine sensor failures, and utilizes the BP neural network to predict measurements, thereby improving the ACKF algorithm when measurements are abnormal, and significantly improving collaborative positioning accuracy and stability.

[0106] 3. BP neural network has strong nonlinear mapping ability and flexible network structure. The number of intermediate layers and the number of neurons in each layer of the network can be set arbitrarily according to the specific situation. The algorithm is easy to implement and has good stability.

[0107] 4. Mahalanobis distance It is not affected by dimension. The Mahalanobis distance between two points has nothing to do with the measurement unit of the original data. The Mahalanobis distance between two points calculated by standardized data and centralized data (i.e., the difference between the original data and the mean) is the same. Mahalanobis distance can also eliminate the interference of correlation between variables. The ACKF algorithm can handle nonlinear systems and can reach the accuracy of third-order Taylor expansion. BRIEF DESCRIPTION OF THE DRAWINGS

[0108] Figure 1 is a flow chart of the present invention;

[0109] Figure 2 The present invention pilots the AUV and follows the real track of the AUV;

[0110] Figure 3 It is the measurement information between the master AUV-1 and the slave AUV of the present invention and the BP neural network prediction value;

[0111] Figure 4 It is the measurement information between the master AUV-2 and the slave AUV of the present invention and the BP neural network prediction value;

[0112] Figure 5 is the measurement error of the present invention;

[0113] Figure 6 The new information test statistic of the present invention is compared with the set threshold values ​​T1 and T2;

[0114] Figure 7 Measuring fault diagnosis results for the present invention;

[0115] Figure 8Comparison diagram of the GPS trajectory of the present invention, the trajectory calculated by this method and the trajectory calculated by other methods;

[0116] Fig. 9 This is a comparison chart of positioning errors between other methods of the present invention and this method. DETAILED DESCRIPTION

[0117] The present invention is further described below in conjunction with the accompanying drawings.

[0118] Step 1: Establish a multi-AUV collaborative positioning state space model;

[0119] Define pilot AUV at t k Time and t k+1 The position vectors at each moment are and Follow the AUV in t k Time and t k+1 The position vectors at each time (x k ,y k ,z k ) and (x k+1 ,y k+1 ,z k+1 ). The pilot AUV and the follower AUV are in t k The relative distance at time is Z k In actual underwater collaborative positioning, the depth and horizontal position of the AUV are independent of each other. Accurate depth information can be obtained through pressure sensors, so the three-dimensional collaborative positioning problem can be simplified to two-dimensional. In the discussion, the model is projected onto a two-dimensional horizontal plane for analysis. The state equation of the collaborative positioning system based on relative position measurement is specifically:

[0120]

[0121] In the formula, x k and k They are respectively following the AUV at t k The east and north positions at the moment; δt is the dead reckoning time; sensor input u k =[V k θ k ] T , V k For the following AUV at t k The forward velocity at time θ k For the following AUV at t k The heading angle at the moment; w x,k and w y,k is a zero-mean and mutually independent Gauss white noise.

[0122] Follow the AUV in t kThe relative observation information obtained by underwater acoustic communication at time t is the pilot AUV k Location information at the moment And the relative distance measurement information Z between the leading AUV and the following AUV k From the above information, the coordinate position relationship between the pilot AUV and the follower AUV can be obtained as follows:

[0123]

[0124] In the formula, v k is a Gauss white noise with zero mean and independent of each other.

[0125] Define X k =[x k ,y k ] T To follow the AUV at t k The state quantity at the moment, w k =[w x,k ,w y,k ] T is the process noise vector, v k =[v k ] T is the measurement noise vector, and

[0126] Q k =E[w k w k T ] (3)

[0127] R k =E[v k v k T ] (4)

[0128] are the system noise covariance matrix and measurement noise covariance matrix assumed to be known respectively.

[0129] Based on equations (1) and (2), the discrete time state space model (state equation and measurement equation) of the multi-AUV collaborative positioning system is established as follows:

[0130]

[0131] In the formula, the state function Measurement function

[0132] Step 2: Build a BP neural network

[0133] BP network design mainly includes several aspects such as the number of network layers, the number of input layer nodes, the number of hidden layer nodes, the number of output layer nodes and the transmission function.

[0134] The single hidden layer BP neural network can realize any nonlinear mapping by appropriately increasing the number of neuron nodes. Therefore, the designed neural network contains three layers: input layer, hidden layer and output layer. The number of input layer nodes is 4, the number of hidden layer nodes is 7, and the number of output layer nodes is 1. The transfer function uses the Log-Sigmoid function, which can be expressed as:

[0135]

[0136] The range of x includes the entire real number domain, and the function value is between 0 and 1.

[0137] The BP neural network is constructed by the newff function, and the number of iterations epochs is selected as 1000. If the learning rate is too small, the convergence speed is slow. If the learning rate is too large, it is easy to oscillate. Therefore, the learning rate lr is selected as 0.0025. The initial weight is Where F is the number of neurons connected to the weight input.

[0138] Step 3: When the reference position is available, multi-AUV collaborative positioning estimation is performed through ACKF;

[0139] The ACKF filtering algorithm is based on the Spherical-Radial criterion, uses a set of volume points with equal weights, and uses the statistical numerical integration principle to calculate the mean and covariance of random variables after nonlinear transformation, which can obtain state updates and state covariance matrix updates more accurately.

[0140] (1) Time update

[0141] Assume that the state vector X k =[x k ,y k ] T In t k The system posterior probability state at time And the posterior probability density function It is known that the state error covariance P is converted to k|k Decomposed into the following form:

[0142]

[0143] Define the following variables:

[0144]

[0145] Where m = 2n is the number of volume points; n = 2 is the dimension of the state equation; ξ i is the generated volume point; [1] i is the i-th volume point in the point set, and the volume point set is: w i is the weight of each volume point.

[0146] Calculate Cubature points (i = 1, 2…, m, m = 2n):

[0147]

[0148] Transfer Cubature points through the transfer matrix function of the system state:

[0149] X i,k+1|k =f(X i,k|k ,u k ) (10)

[0150] t k+1 The state prediction value at the moment is obtained by weighted summation:

[0151]

[0152] Calculate t k+1 The predicted value of the state error covariance at time:

[0153]

[0154] (2) Measurement update

[0155] The state error covariance prediction value P is converted into k+1|k Decomposed into the following form:

[0156]

[0157] Calculate Cubature points (i = 1, 2…, m, m = 2n):

[0158]

[0159] Transfer Cubature points through the system's measurement function:

[0160]

[0161] t k+1 The observed predicted value at the moment is obtained by weighted summation:

[0162]

[0163] Calculate t k+1 The predicted value of the measurement error covariance at time:

[0164]

[0165] Cross-covariance matrix:

[0166]

[0167] Estimate the Kalman filter gains:

[0168]

[0169] Using the state update and covariance update process, we can obtain t k+1 Status of the moment and the state estimation error covariance matrix P k+1|k+1 ,Right now:

[0170]

[0171]

[0172] In order to improve the adaptability and robustness of the CKF algorithm and further improve the filtering performance of the CKF algorithm, the CKF algorithm is improved to adapt to situations such as large system fluctuations and sudden load changes, and to improve the filtering accuracy. According to the CKF algorithm process, the Kalman gain K k+1 It has a great influence on the accuracy of filtering estimation, and the small value of Kalman gain is mainly due to the autocovariance matrix P zz,k|k-1 With the cross-covariance matrix P xz,k|k-1 Therefore, this paper constructs an adaptive factor to perform linear correction on the covariance matrix. The specific steps are as follows:

[0173]

[0174]

[0175] The volume point sampling method and the state quantity and quantity measurement prediction step remain unchanged. By defining the innovation vector formula (28) and the innovation vector matrix formula (29), and calculating Δe k and the autocovariance matrix P zz,k|k-1 The size of the trace is used to judge the adaptive factor to achieve the purpose of online correction. The specific implementation is as follows:

[0176]

[0177] According to formula (30), when there is a sudden load change in the system and there is no measured data, the real-time measurement value y of the system is k+1 Predicted value of the measurement The absolute error is large, that is, the trace of the innovation matrix Δe is larger than the autocovariance matrix P yy,k+1 The prediction error is large, so it is necessary to construct an adaptive factor η k+1The prediction error variance matrix is ​​corrected online to improve the estimation accuracy. On the contrary, if the new information vector error is within the allowable range, the adaptive factor value is taken as 1, and the original variance matrix is ​​not corrected, which not only ensures the accuracy of the state estimation result, but also ensures that the calculation time of the proposed algorithm is not extended.

[0178] Autocovariance matrix correction:

[0179]

[0180] Cross-covariance matrix correction:

[0181]

[0182] The filtering correction process at time k+1 is now completed.

[0183] Step 4: Collect training data for the neural network;

[0184] When the datum reference position is available, and the main boat's -1 latitude and longitude x obtained by GPS a ,y a and step 3 and the main boat's -2 latitude and longitude x obtained by GPS c ,y c Two BP neural networks are introduced for training respectively, and finally two trained BP neural network-1 and BP neural network-2 are obtained.

[0185] Step 5: Train the neural network;

[0186] Let the input data be x i , the weight from the input layer to the hidden layer is ω ij , the weight from the hidden layer to the output layer is The threshold of the hidden layer is θ k , the threshold of the output layer is The learning rate is η, the number of hidden layers is n, and the number of output layers is m.

[0187] (1) Forward Propagation

[0188] The input and output of the i-th hidden layer are:

[0189]

[0190]

[0191] The input and output of the jth hidden layer are:

[0192]

[0193]

[0194] where x i is the input data, ω ij is the weight from the input layer to the hidden layer, is the weight from the hidden layer to the output layer, θ k is the threshold of the hidden layer, is the threshold of the output layer,

[0195] (2) Error calculation, network output and target signal y 0 The error is expressed as:

[0196]

[0197] (3) Error back propagation, adjusting the connection coefficient according to the steepest gradient descent method:

[0198]

[0199]

[0200] Step 6: Construct a fault detection function and set a double threshold value according to the root mean square error σ of the neural network training result to perform fault detection on the measurement information;

[0201] In Kalman filter theory, when the system model is determined and there is no model error, the residual sequence output by the Kalman filter is Gaussian white noise with zero mean, so these residuals are orthogonal everywhere, which is the orthogonality of Kalman filtering.

[0202] The measurement residual of the Kalman filter can be expressed as:

[0203]

[0204] Where Z k —actual measured value;

[0205] —Measurement prediction value;

[0206] —Recursive value of system status;

[0207] H k — observation matrix;

[0208] According to the orthogonality principle of Kalman filtering, the square of the residual Mahalanobis distance obeys the chi-square distribution, and the following chi-square test statistic is obtained:

[0209]

[0210] Where M k Subject to the degree of freedom m z Chi-square distribution of mz Z k The dimension of .

[0211] Therefore, the system can be evaluated by calculating the square of the Mahalanobis distance of the residual sequence and then using the hypothesis testing principle. If the system state changes suddenly or there are observation anomalies, the square of the residual Mahalanobis distance will no longer be a chi-square distribution with n degrees of freedom.

[0212] Traditional 2 The detection method uses a fixed threshold to determine the occurrence of a fault, but the fixed threshold is bound to cause a contradiction between the missed alarm rate and the false alarm rate. If the threshold is too high, the missed alarm rate will increase; if the threshold is too low, the false alarm rate will increase. This paper uses a dual-threshold detection threshold. According to the distribution characteristics of the residual, a smaller false alarm rate is selected, and its χ2 distribution value is used as the upper threshold T2 of the fault alarm. The dynamic lower threshold T1 is determined according to the BP neural network training accuracy. The reliability and anti-interference ability of collaborative positioning are improved by using a dual-threshold detection threshold.

[0213] Based on this, the judgment process of the BP neural network-assisted slow-changing fault double threshold detection method is: By setting the chi-square test significance level α, the confidence probability of the Mahalanobis distance under the significance level α can be obtained as follows: At this time, the system fault detection process is:

[0214]

[0215] The chi-square detection degree of freedom is 1, and the false alarm rate is selected as 0.01, which corresponds to the upper threshold T 2 The value is 15.14. The selection of the lower threshold is related to the prediction accuracy of the neural network. The root mean square error σ of the network training is reflected in the test statistic level. According to the empirical formula, 3σ is selected as the basis. The lower threshold expression is:

[0216]

[0217] Step 7: Save the fault detection results, classify the fault results, and use different algorithms for collaborative positioning;

[0218] Normal data points are assigned a value of 0, faulty data points are assigned a value of 1, and disturbed data points are assigned a value of 2. When processing normal points, ACKF performs normal time and measurement updates; when processing faulty points, ACKF only performs time updates without status updates; when processing disturbed data points, if the measurement of the main boat-1 fails, the filter one-step prediction value at the current moment and the latitude and longitude information x provided by GPS are used. a ,y aThe trained BP neural network-1 is then fed into the measurement prediction data output by the neural network into the ACKF measurement update; if the measurement of the main boat-2 fails, the filter one-step prediction value at the current moment and the latitude and longitude information x provided by GPS are used. c ,y c It is brought into the trained BP neural network-2, and then the measurement prediction data output by the neural network is brought into the ACKF measurement update to improve the accuracy of the filtering algorithm.

[0219] The experiment of the present invention uses data collected from the lake test of the multi-AUV collaborative system, using three AUVs, two of which act as pilot AUVs and the other as a follower AUV. Both the pilot AUV and the follower AUV are equipped with an acoustic modem ATM-885 for one-way ranging and broadcasting information; a Doppler speedometer for obtaining speed information and a compass for providing heading information are also installed on the AUV; in addition, the follower AUV is also equipped with a global positioning system (GPS) to provide a reference position. The test time is 1700s, the sampling time is 1s, and the initial state of the system's state equation is provided by GPS. At each moment, the follower AUV communicates with only one of the two pilot AUVs, and the communication cycle of the follower boat is 5s. The heading information of the following AUV provided by the compass is used as the reference heading, and the input heading drift error is set to 15° / h to verify the effectiveness of the design method of the present invention.

[0220] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A collaborative positioning method for AUV based on Mahalanobis distance and neural network assistance, characterized in that: The following steps are involved: Step 1: Establish a multi-AUV collaborative positioning state space model; Step 2: Build a BP neural network; Step 3: When the reference position is available, multi-AUV collaborative positioning estimation is performed through ACKF; Step 4: Collect training data for the neural network; Step 5: Use the data collected in step 4 to train the BP neural network; Step 6: Construct a fault detection function and set a double threshold value according to the root mean square error σ of the neural network training result to perform fault detection on the measurement information; Step 7: Save the fault detection results, classify the fault results, and use different algorithms for collaborative positioning.

2. The AUV collaborative positioning method based on Mahalanobis distance and neural network assistance according to claim 1 is characterized in that: The step 1 of establishing a multi-AUV collaborative positioning state space model is specifically as follows: The state equation of the collaborative positioning system for relative position measurement is: In the formula, x k and k They are respectively following the AUV at t k The east and north positions at the moment; δt is the dead reckoning time; sensor input u k =[V k θ k ] T , V k For the following AUV at t k The forward velocity at time θ k For the following AUV at t k The heading angle at the moment; w x,k and w y,k It is zero-mean and mutually independent Gauss white noise; The coordinate position relationship between the pilot AUV and the follower AUV is: In the formula, the pilot AUV is at t k The location information at the moment is Z k is the relative distance measurement information between the leading AUV and the following AUV, v k is a Gauss white noise with zero mean and independent of each other; Assume the known system noise covariance matrix and measurement noise covariance matrix: Q k =E[w k w k T ] R k =E[v k v k T ] Define X k =[x k ,y k ] T To follow the AUV at t k The state quantity at the moment, w k =[w x,k ,w y,k ] T is the process noise vector, v k =[v k ] T is the measurement noise vector; Establish a discrete time state space model of multi-AUV collaborative positioning system: In the formula, the state function Measurement function .

3. The AUV collaborative positioning method based on Mahalanobis distance and neural network assistance according to claim 1 is characterized in that: The step 2 of building the BP neural network is specifically as follows: The transfer function uses the Log-Sigmoid function: The range of x includes the entire real number domain, and the function value is between 0 and 1; The BP neural network is constructed by the newff function, the number of iterations epochs is selected as 1000, the learning rate lr is selected as 0.0025, and the initial weight is Where F is the number of neurons connected to the weight input.

4. The AUV collaborative positioning method based on Mahalanobis distance and neural network assistance according to claim 1 is characterized in that: When the reference position is available, the step 3 of performing multi-AUV collaborative positioning estimation through ACKF is specifically as follows: Step 3.1: Time Update Step 3.1.1: Transform the state error covariance P through Cholesky kk break down: Define variables: Where m = 2n is the number of volume points; n = 2 is the dimension of the state equation; ξ i is the generated volume point; [1] i is the i-th volume point in the point set, and the volume point set is: w i is the weight of each volume point; Step 3.1.2: Calculate Cubature points: Step 3.1.3: Transfer the Cubature points through the transfer matrix function of the system state: X i,k+1|k =f(X i,k|k ,u k ) Step 3.1.4: k+1 The state prediction value at the moment is weighted summed: Step 3.1.5: Calculate t k+1 The predicted value of the state error covariance at time: Step 3.2: Measurement Update Step 3.2.1: Use Cholesky to predict the state error covariance value P k+1|k break down: Step 3.2.2: Calculate Cubature points: Step 3.2.3: Transfer Cubature points through the system's measurement function: Step 3.2.4: k+1 Weighted summation of observed predicted values ​​at time: Step 3.2.5: Calculate t k+1 The predicted value of the measurement error covariance at time: Step 3.2.6: Cross-covariance matrix: Step 3.2.7: Estimate the Kalman filter gain: Step 3.2.8: Using the state update and covariance update process, obtain t k+1 Status of the moment and the state estimation error covariance matrix P k+1|k+1 : Step 3.3: Construct an adaptive factor to perform line correction on the covariance matrix: Define the innovation vector formula and the innovation vector matrix formula, and calculate Δe k and the autocovariance matrix P zz,kk-1 The size of the trace is judged to construct an adaptive factor to achieve the purpose of online correction, specifically: Autocovariance matrix correction: Cross-covariance matrix correction: The filtering correction process at time k+1 is now completed.

5. The AUV collaborative positioning method based on Mahalanobis distance and neural network assistance according to claim 1 is characterized in that: The step 4 of collecting the training data of the neural network is specifically as follows: When the datum reference position is available, and the main boat's -1 latitude and longitude x obtained by GPS a ,y a and step 3 and the main boat's -2 latitude and longitude x obtained by GPS c ,y c Two BP neural networks are introduced for training respectively, and finally two trained BP neural network-1 and BP neural network-2 are obtained.

6. The AUV collaborative positioning method based on Mahalanobis distance and neural network assistance according to claim 1 is characterized in that: The step 5 of training the neural network is specifically as follows: Step 5.1: Forward Propagation The input and output of the i-th hidden layer are: The input and output of the jth hidden layer are: Among them, x i is the input data, ω ij is the weight from the input layer to the hidden layer, is the weight from the hidden layer to the output layer, θ k is the threshold of the hidden layer, is the threshold of the output layer; Step 5.2: Error calculation, the error between the network output and the target signal y0 is: Step 5.3: Error back propagation, adjust the connection coefficient according to the steepest gradient descent method: 。 7. The AUV collaborative positioning method based on Mahalanobis distance and neural network assistance according to claim 1 is characterized in that: The step 6 is specifically as follows: The measurement residual of the Kalman filter is: in, is the measurement prediction value; is the recursive value of the system state; H k is the observation matrix; Z k is the actual measured value; According to the orthogonality principle of Kalman filtering, the square of the residual Mahalanobis distance obeys the chi-square distribution, and the chi-square test statistic is constructed: Where M k Subject to the degree of freedom m z Chi-square distribution of m z Z k The dimension of By setting the chi-square test significance level α, the confidence probability of the Mahalanobis distance under the significance level α is obtained as; The system fault detection process is: The chi-square detection degree of freedom is 1, and the false alarm rate is selected as 0.01, then the corresponding upper threshold T2 is 15.

14. The selection of the lower threshold is related to the prediction accuracy of the neural network. The root mean square error σ of the network training is reflected in the test statistic level. According to the empirical formula, 3σ is selected as the basis, and the lower threshold expression is: 。 8. The AUV collaborative positioning method based on Mahalanobis distance and neural network assistance according to claim 1 is characterized in that: The step 7 is specifically as follows: Normal data points are assigned a value of 0, faulty data points are assigned a value of 1, and disturbed data points are assigned a value of 2. When processing normal points, ACKF performs normal time and measurement updates; when processing faulty points, ACKF only performs time updates without status updates; when processing disturbed data points, if the measurement of the main boat-1 fails, the filter one-step prediction value at the current moment and the latitude and longitude information x provided by GPS are used. a ,y a The trained BP neural network-1 is then fed into the measurement prediction data output by the neural network into the ACKF measurement update; if the measurement of the main boat-2 fails, the filter one-step prediction value at the current moment and the latitude and longitude information x provided by GPS are used. c ,y c It is brought into the trained BP neural network-2, and then the measurement prediction data output by the neural network is brought into the ACKF measurement update to improve the accuracy of the filtering algorithm.

Images