A method and system for robust underwater target azimuth tracking using uniform circular array

Abstract

The invention discloses a uniform circular array robust underwater target azimuth tracking method and system, which adopts a P-element uniform circular array with a radius of r to receive narrowband acoustic signals radiated by a target; each sensor on the uniform circular array converts the received underwater acoustic signal into an electrical signal, sets the time step k=0, initializes the target state estimation value, the root mean square error matrix, the degree of freedom estimation value, and the inverse scale matrix estimation value; calculates the target state estimation value of the kth time step according to the one-step predicted target state of the kth time step, the one-step predicted root mean square error matrix of the kth time step, the degree of freedom estimation value, and the inverse scale matrix estimation value; takes the first target azimuth estimation value of the target state estimation value of the kth time step as the underwater target azimuth tracking result of the kth time step, sets the time step k=k+1, continuously tracks the underwater target azimuth, and completes the uniform circular array robust underwater target azimuth tracking. High-precision, robust and efficient target azimuth tracking is achieved.

Description

Technical Field

[0001] The present invention belongs to the technical fields of sonar technology, array signal processing, extended Kalman filtering technology and variational Bayesian theory, and particularly relates to a method and system for robust underwater target azimuth tracking using a uniform circular array. Background Art

[0002] Underwater target position estimation based on passive sonar arrays is an important research topic in sonar signal processing. Existing target position estimation methods can be categorized based on their principles into two categories: traditional target position estimation methods and target position tracking methods. Target position tracking methods are primarily implemented within the framework of Bayesian filtering algorithms, treating the changing target position angle and the signal received by the sonar array as states and measurements perturbed by random noise, respectively. When estimating target position, target position tracking methods not only rely on the measurements obtained by the sonar array but also consider the target's kinematic characteristics, resulting in greater robustness and accuracy. Most current target position tracking methods assume that the measurement noise covariance matrix is ​​a fixed, known value. However, due to the influence of underwater environmental noise, the measurement noise covariance matrix often exhibits unknown, time-varying characteristics, severely degrading target position tracking performance.

[0003] To address the unknown, time-varying measurement noise covariance matrix in Bayesian filtering algorithms, some algorithmic research uses variational Bayesian iteration to adaptively and jointly estimate the measurement noise covariance matrix and state in real time during the Bayesian filtering process. However, in underwater target tracking applications, the measurement vectors of Bayesian filtering-based tracking systems are extremely high-dimensional due to the large number of sensors in the sonar array. This high-dimensional measurement significantly increases the computational complexity of the variational Bayesian iteration method, significantly impacting its application in real-world underwater target tracking scenarios. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a uniform circular array robust underwater target direction tracking method and system in response to the above-mentioned deficiencies in the existing technology, eliminate the influence of the unknown time-varying measurement noise covariance matrix caused by complex underwater environmental noise on the performance of the target direction tracking method, and at the same time solve the problem of high computational complexity of the variational Bayesian iterative method in the application of underwater target direction tracking.

[0005] The present invention adopts the following technical solutions:

[0006] A method for robust underwater target azimuth tracking using a uniform circular array comprises the following steps:

[0007] A uniform circular array is used to receive the narrowband acoustic signal radiated by the target. The collected signals are arranged in ascending order to form a vector, which is used as the measurement of the kth time step.

[0008] Determine the one-step prediction target state at the k-th time step, the one-step prediction root mean square error matrix at the k-th time step, the estimated value of the prediction degrees of freedom, and the estimated value of the prediction inverse scale matrix;

[0009] The target state estimate at the k-th time step is calculated based on the measurement at the k-th time step and the one-step predicted target state at the k-th time step, the one-step predicted root mean square error matrix at the k-th time step, the predicted degree of freedom estimate, and the predicted inverse scale matrix estimate. The first target orientation estimate of the target state estimate at the k-th time step is used as the underwater target orientation tracking result at the k-th time step. Let time step k = k + 1, repeat the above steps to continuously track the underwater target orientation until k equals the total number of tracking time steps, and stop the loop to complete the uniform circular array robust underwater target orientation tracking.

[0010] Specifically, one-step prediction of the target state for:

[0011]

[0012] Among them, F k|k-1 is the target state transfer matrix;

[0013] One-step prediction root mean square error matrix P k|k-1 for:

[0014]

[0015] Among them, F k|k-1 is the target state transfer matrix, F k|k-1 The transpose of G k-1 is the noise driving matrix, Q k-1 is the process noise covariance, G k-1 The transpose of

[0016] Estimate of the degrees of freedom for prediction and the predicted inverse scaling matrix estimate for:

[0017]

[0018]

[0019] Among them, ρ is the forgetting factor, and P is the number of array elements of the uniform circular array.

[0020] Specifically, the target state estimation value at the kth time step is calculated as follows:

[0021] S401, predicting the target state based on one step Calculation measurement function and its Jacobian matrix Hk|k-1 ;

[0022] S402, based on the known measurement z of step k k and the one obtained in step S401 Calculate the innovation root mean square error matrix

[0023] S403, let i = 0, estimate the value based on the predicted degrees of freedom and the predicted inverse scaling matrix estimate Initialize the iterative estimate of the measurement noise covariance matrix Predict the target state based on one step Initialize the iterative target state estimate

[0024] S404: When i≤1, execute steps S405 and S406; when i≥2, determine the deviation between the Jacobian matrices of the iterative measurement function of the i-1th and i-2th iterations. Is it greater than the set decision threshold δ, where ||·||2 represents the 2-norm? If so, execute steps S405 and S406 and skip step S407; otherwise, skip steps S405 and S406 and go directly to step S407.

[0025] S405, based on the estimated value of the iterative target state Calculate the Jacobian matrix of the iterative measurement function

[0026] S406: Jacobian matrix of the iterative measurement function obtained in step S405 The measurement function Jacobian matrix H obtained in step S401 k|k-1 , and the one-step prediction root mean square error matrix P k|k-1 Calculating deviation parameters

[0027] S407, set the deviation parameter Equal to the bias parameter in the i-1th iteration Let the iterative measurement function Jacobian matrix Equal to the Jacobian matrix of the iterative measurement function in the i-1th iteration

[0028] S408: Deviation parameter obtained according to step S407 The measurement function Jacobian matrix H obtained in step S401 k|k-1 And the innovation root mean square error matrix obtained in step S402 Update iterative measurement noise covariance matrix estimate

[0029] S409, let i = i + 1, and execute steps S404 to S408 in a loop until i = N-1, then stop the loop. Then the estimated value of the measurement noise covariance matrix at the kth time step is Degrees of freedom estimate Inverse scaling matrix estimate

[0030] S410, based on the estimated value of the measurement noise covariance matrix of the kth time step One-step prediction mean square error matrix P k|k-1 and the measurement function Jacobian matrix H obtained in step S401 k|k-1 Calculate the adaptive Kalman filter gain K k ;

[0031] S411, adaptive Kalman filter gain K obtained according to step S410 k , one-step prediction of the target state The measurement z at the kth time step is known k and the measurement function obtained in step S401 Calculate target state estimate

[0032] Furthermore, in step S401, the function is measured and its Jacobian matrix H k|k-1 Specifically:

[0033]

[0034]

[0035] Among them, real(·) represents the real part, is the array manifold vector of the uniform circular array, To predict the target azimuth, that is, to predict the target state in one step The first item, is the estimated value of the target radiated narrowband acoustic signal, [·] T represents transpose, h′ p is a matrix element.

[0036] Furthermore, in step S402, the innovation root mean square error matrix Specifically:

[0037]

[0038] where z k is the k-th step measurement, is the measurement function, (·) T Indicates transpose.

[0039] Furthermore, in step S406, the deviation parameter Specifically:

[0040]

[0041] in, is the Jacobian matrix of the iterative measurement function, H k|k-1 is the Jacobian matrix of the measurement function, P k|k-1 is the one-step prediction root mean square error matrix.

[0042] Furthermore, in step S408, the noise covariance matrix estimation value is iteratively measured for:

[0043]

[0044] in, is the iterative degrees of freedom estimate, is the iterative inverse scaling matrix estimate.

[0045] Furthermore, in step S410, the target state estimation value Specifically:

[0046]

[0047] Adaptive Kalman filter gain K k for:

[0048]

[0049] in, H k|k-1 The transpose of .

[0050] Furthermore, in step S411,

[0051] Target state estimate Specifically:

[0052]

[0053] In a second aspect, an embodiment of the present invention provides a uniform circular array robust underwater target azimuth tracking system, comprising:

[0054] The acquisition module uses a uniform circular array to receive the narrowband acoustic signal radiated by the target; the collected signals are arranged in ascending order to form a vector, which is used as the measurement of the kth time step;

[0055] a calculation module, which calculates an estimated value of the target state at the kth time step based on the measurement at the kth time step obtained by the acquisition module and the one-step predicted target state at the kth time step obtained by the update module, the one-step predicted root mean square error matrix at the kth time step, the estimated value of the predicted degrees of freedom, and the estimated value of the predicted inverse scale matrix;

[0056] The tracking module takes the first target azimuth estimation value of the target state estimation value of the kth time step as the underwater target azimuth tracking result of the kth time step, sets the time step k=k+1, and continuously tracks the underwater target azimuth until k equals the total number of tracking time steps, thus completing the uniform circular array robust underwater target azimuth tracking.

[0057] Compared with the prior art, the present invention has at least the following beneficial effects:

[0058] The present invention discloses a robust underwater target azimuth tracking method using a uniform circular array. This method uses a variational Bayesian method to adaptively estimate the measurement noise covariance matrix in real time during the target azimuth tracking process, targeting the unknown time-varying measurement noise covariance matrix caused by complex underwater environmental noise. This eliminates the impact of the unknown time-varying measurement noise covariance matrix on the performance of the target azimuth tracking method, achieving high-precision and robust target azimuth tracking under the condition of a time-varying measurement noise covariance matrix. A fast variational Bayesian iterative method is used to estimate the measurement noise covariance matrix for high-dimensional measurements in underwater target azimuth tracking applications, resolving the high computational complexity of the variational Bayesian iterative method in underwater target azimuth tracking applications and achieving highly efficient underwater target azimuth tracking.

[0059] Furthermore, the kinematic law of the target is used to obtain the one-step prediction of the target state. and the one-step prediction root mean square error matrix P k|k-1 , which is used to estimate the target state in the subsequent steps. The tracking accuracy and robustness of the method are improved by introducing the target kinematic prior information. The forgetting factor ρ is used to estimate the degree of freedom. and the inverse scaling matrix estimate Adjust to get the estimated degrees of freedom for prediction and the predicted inverse scale matrix The statistical characteristics of the estimated value of the measurement noise covariance matrix are changed, and the adaptability of the method to the time-varying measurement noise covariance matrix is ​​improved.

[0060] Furthermore, the measurement function is calculated based on the uniform circular array It is used in the subsequent steps to estimate the measurement noise covariance matrix and target state, which improves the tracking accuracy and robustness when the target position changes over a large range. The maximum likelihood estimation method is used to calculate the estimated value of the target radiated narrowband acoustic signal. This method has high estimation accuracy and ensures the measurement function The accurate calculation of , which can be used in the subsequent steps to accurately estimate the measurement noise covariance matrix and the target state, and calculate the measurement function Jacobian matrix H k|k-1 , which is used to accurately estimate the measurement noise covariance matrix and target state in subsequent steps.

[0061] Furthermore, the new information root mean square error matrix is ​​calculated It is used to accurately estimate the measurement noise covariance matrix and target state in subsequent steps.

[0062] Furthermore, the iterative innovation root mean square error matrix is ​​calculated To calculate the inverse scale matrix change and conversion parameters It is used to calculate the inverse scale matrix change, thereby accurately and efficiently estimating the measurement noise covariance matrix. Calculate the iterative degree of freedom estimate and iterative inverse scaling matrix estimates To calculate the iterative measurement noise covariance matrix estimate Used to update the measurement noise covariance matrix estimate until the estimate is accurate.

[0063] Furthermore, according to the estimated values ​​of the predicted degrees of freedom and the predicted inverse scaling matrix estimate Initialize the iterative estimate of the measurement noise covariance matrix Predict the target state based on one step Initialize the iterative target state estimate To improve the convergence speed of the algorithm and improve the computational efficiency, when i≤1, the estimated value of the iterative target state is Calculate the Jacobian matrix of the iterative measurement function Based on Jacobian matrix H of measurement function k|k-1 And the one-step prediction root mean square error matrix P k|k-1 Calculating deviation parameters When i ≥ 2, determine the deviation between the Jacobian matrix of the i-1th and i-2th iteration measurement functions Is it greater than the decision threshold δ set in step S2, ||·||2 represents the 2-norm, if so, then according to the iterative target state estimate value Calculate the Jacobian matrix of the iterative measurement function Based on Jacobian matrix H of measurement function k|k-1 And the one-step prediction root mean square error matrix P k|k-1 Calculating deviation parameters Otherwise, let the deviation parameter Equal to the bias parameter in the i-1th iteration Let the iterative measurement function Jacobian matrix Equal to the Jacobian matrix of the iterative measurement function in the i-1th iteration The deviation parameter This is used in subsequent steps to accurately and efficiently estimate the measurement noise covariance matrix and the target state.

[0064] Further, let i=i+1 and loop The loop stops when i=N-1, and the estimated value of the measurement noise covariance matrix at the kth time step is obtained. Degrees of freedom estimate Inverse scaling matrix estimate Used to accurately estimate the target state in subsequent steps, based on the measurement noise covariance matrix estimate One-step prediction mean square error matrix P k|k-1 and the measurement function Jacobian matrix H k|k-1 Calculate the adaptive Kalman filter gain K k , which is used to accurately estimate the target state.

[0065] Furthermore, the adaptive Kalman filter gain K k Predict the target state for one step Update to get an accurate target state estimate This allows accurate target azimuth estimation to be obtained, enabling high-precision and high-robust underwater target azimuth tracking, which can be used for robust underwater target azimuth tracking at the next moment.

[0066] Furthermore, the adaptive Kalman filter gain K k Update the one-step prediction mean square error matrix P k|k-1 , get the accurate mean square error matrix P k|k , in order to perform robust underwater target position tracking at the next moment.

[0067] It can be understood that the beneficial effects of the second aspect mentioned above can be found in the relevant description of the first aspect mentioned above, and will not be repeated here.

[0068] In summary, the present invention solves the problem of large computational complexity of the variational Bayesian iterative method in underwater target position tracking applications, and achieves highly efficient underwater target position tracking.

[0069] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 Schematic diagram of uniform circular array and target azimuth;

[0071] Figure 2Schematic diagram of the process of the present invention;

[0072] Figure 3 To simulate the target azimuth angle change trajectory;

[0073] Figure 4 Tracking trajectory for the target. DETAILED DESCRIPTION

[0074] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0075] In the description of the present invention, it is to be understood that the terms “include” and “comprise” indicate the presence of the described features, wholes, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or collections thereof.

[0076] It should also be understood that the terms used in the present specification are only for the purpose of describing particular embodiments and are not intended to limit the present invention. As used in the present specification and the appended claims, the singular forms "a", "an", and "the" are intended to include the plural forms unless the context clearly indicates otherwise.

[0077] It should be further understood that the term "and / or" as used in the present specification and the appended claims refers to and includes any and all possible combinations of one or more of the associated listed items. For example, A and / or B may represent: A alone, A and B simultaneously, or B alone. In addition, the character " / " herein generally indicates that the associated items are in an "or" relationship.

[0078] It should be understood that although the terms "first," "second," and "third" may be used to describe preset ranges in embodiments of the present invention, these preset ranges should not be limited to these terms. These terms are merely used to distinguish one preset range from another. For example, without departing from the scope of embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0079] The word "if," as used herein, may be interpreted as "at the time of" or "when" or "in response to determining" or "in response to detecting," depending on the context. Similarly, the phrases "if it is determined" or "if (stated condition or event) is detected" may be interpreted as "when it is determined" or "in response to the determination" or "when detecting (stated condition or event)" or "in response to detecting (stated condition or event)," depending on the context.

[0080] The accompanying drawings illustrate various schematic diagrams of structures according to embodiments disclosed herein. These figures are not drawn to scale; for clarity, some details are exaggerated and some details may be omitted. The shapes of the various regions and layers shown in the figures, as well as their relative sizes and positional relationships, are merely exemplary and may deviate in practice due to manufacturing tolerances or technical limitations. Those skilled in the art may design regions / layers with different shapes, sizes, and relative positions as needed.

[0081] The present invention provides a method for robust underwater target bearing tracking using a uniform circular array. Target bearing tracking is implemented within the framework of an extended Kalman filter. A variational Bayesian iteration method is used to adaptively estimate the unknown time-varying measurement noise covariance matrix in real time, thereby achieving high-precision and high-robust target bearing tracking. During the variational Bayesian iteration process, the number of iterations of a high-dimensional measurement function and its Jacobian matrix is ​​reduced, thereby avoiding a large number of trigonometric and exponential function operations, thereby achieving highly efficient target bearing tracking.

[0082] See also Figure 2 The present invention provides a method for robust underwater target azimuth tracking using a uniform circular array. The steps at the kth time step are as follows:

[0083] S1. Measurement

[0084] Set the total number of tracking time steps K to a positive integer, k is the time step, then k = 1, 2, ..., K, and the time interval between adjacent time steps is T. A P-element uniform circular array with a radius of r is used to receive the narrowband acoustic signal radiated by the target, such as Figure 1 As shown. Each sensor (element) on the uniform circular array converts the received underwater acoustic signal into an electrical signal, which is sampled once at each time step k using a data collector through an amplifying circuit. The P elements of the uniform circular array are numbered counterclockwise from 1 to P. The signals collected from the P elements are arranged in order from small to large to form a vector, which is the measurement z at the kth time step. k According to the above method, we can get K measurements {z1,z2,...,z K}.

[0085] S2. Set initial parameters

[0086] Set the process noise covariance Q k-1 , forgetting factor ρ, variational Bayes iteration number N, decision threshold δ and total tracking time step K. Let k = 0, initialize the target state estimate in To obtain the target position estimation result using conventional beamforming technology, initialize the root mean square error matrix P k-1|k-1 , initialize the degrees of freedom estimate (in ), inverse scaling matrix estimate Among them I P is the P-order unit matrix, and P is the number of elements in the uniform circular array.

[0087] S3. Prediction parameters

[0088] S301, based on the known target state estimation value of the k-1th time step Calculate one-step predicted target state

[0089]

[0090] Among them, F k|k-1 is the target state transfer matrix,

[0091]

[0092] Where T represents the time interval between adjacent time steps.

[0093] S302, based on the known root mean square error matrix P of the k-1th time step k-1|k-1 Calculate the one-step prediction root mean square error matrix P k|k-1 ;

[0094]

[0095] Among them, F k|k-1 is the target state transfer matrix, F k|k-1 The transpose of G k-1 is the noise driving matrix, Q k-1 is the process noise covariance, G k-1 The transpose of G. k-1 The expression is

[0096]

[0097] S303, based on the known estimated value of the degree of freedom of the k-1th time step and the inverse scaling matrix estimate Calculate the estimated degrees of freedom for prediction and the predicted inverse scaling matrix estimate

[0098]

[0099]

[0100] Among them, ρ is the forgetting factor, and P is the number of array elements of the uniform circular array.

[0101] S4. Update parameters

[0102] S401, one-step prediction target state obtained in step S3 Calculation measurement function and its Jacobian matrix H k|k-1 ;

[0103] Measurement Function is calculated as follows:

[0104]

[0105] Where real(·) represents the real part, is the array manifold vector of the uniform circular array, To predict the target azimuth, that is, to predict the target state in one step The first item, Estimated value of the target radiated narrowband acoustic signal. and is calculated as follows:

[0106]

[0107]

[0108]

[0109] in[·] T represents transpose, is the component of the array manifold vector on each array element, p is the array element number, p=1,2,...,P, P is the total number of array elements, exp(·) represents the exponential operation, f is the frequency of the narrowband signal radiated by the target, r is the radius of the uniform circular array, c is the speed of sound, for The conjugate transpose of , (·) -1 represents the inverse of the matrix, Hilbert(·) represents the Hilbert transform, z k is the known k-th step measurement.

[0110] Jacobian matrix H of measurement function k|k-1 The calculation method is as follows:

[0111]

[0112] in[·] T Represents transpose, matrix element h′ p The expression for (p=1,2,...,P) is as follows:

[0113]

[0114] Among them, the estimated value of the target radiated narrowband acoustic signal is It is given by formula (18).

[0115] S402, based on the known measurement z of step k k and the one obtained in step S401 Calculate the innovation root mean square error matrix

[0116]

[0117] in(·) T Indicates transpose.

[0118] S403, estimate the value based on the predicted degrees of freedom and the predicted inverse scaling matrix estimate Initialize the iterative estimate of the measurement noise covariance matrix According to the one-step prediction target state obtained in step S302 Initialize the iterative target state estimate

[0119] Let i = 0, then and Initialization value of and for

[0120]

[0121]

[0122] S404: When i≤1, execute steps S405 and S406; when i≥2, determine the deviation between the Jacobian matrices of the iterative measurement function of the i-1th and i-2th iterations. (where ||·||2 represents the 2-norm) is greater than the decision threshold δ set in step S2, if so, execute steps S405 and S406 and skip step S407, otherwise skip steps S405 and S406 and directly execute step S407;

[0123] S405, based on the estimated value of the iterative target state Calculate the Jacobian matrix of the iterative measurement function The calculation method is to use the iterative target state estimate The first item Substitute the following in formula (18)(19)(20):

[0124] S406: Jacobian matrix of the iterative measurement function obtained in step S405 The measurement function Jacobian matrix H obtained in step S401 k|k-1 , and the one-step prediction root mean square error matrix P obtained in step S302 k|k-1 Calculating deviation parameters

[0125]

[0126] S407, set the deviation parameter Equal to the bias parameter in the i-1th iteration Right now

[0127]

[0128] Let the iterative measurement function Jacobian matrix Equal to the Jacobian matrix of the iterative measurement function in the i-1th iteration

[0129]

[0130] S408: Based on the deviation parameter obtained in the previous step The measurement function Jacobian matrix H obtained in step S401 k|k-1 And the innovation root mean square error matrix obtained in step S402 Update iterative measurement noise covariance matrix estimate

[0131] Measurement noise covariance matrix estimate The update method is as follows:

[0132] Calculate the iterative innovation root mean square error matrix

[0133]

[0134] Calculating conversion parameters

[0135]

[0136] Calculate the inverse scale matrix change

[0137]

[0138] Update iterative degrees of freedom estimate

[0139]

[0140] Update iterative inverse scaling matrix estimate

[0141]

[0142] Update iterative measurement noise covariance matrix estimate

[0143]

[0144] S409, let i = i + 1, and execute steps S404 to S408 in a loop until i = N-1, then stop the loop. Then the estimated value of the measurement noise covariance matrix at the kth time step is Degrees of freedom estimate Inverse scaling matrix estimate

[0145] S410, based on the estimated value of the measurement noise covariance matrix of the kth time step The one-step prediction mean square error matrix P obtained in step S302 k|k-1 and the measurement function Jacobian matrix H obtained in step S401 k|k-1 Calculate the adaptive Kalman filter gain K k ;

[0146]

[0147] in, H k|k-1 The transpose of .

[0148] S411, based on the adaptive Kalman filter gain K obtained in the previous step k , the one-step predicted target state obtained in step S301 The measurement z at the kth time step is known k and the measurement function obtained in step S401 Calculate target state estimate

[0149]

[0150] According to the adaptive Kalman filter gain K k , the measurement function Jacobian matrix H obtained in step S401 k|k-1 and the one-step prediction mean square error matrix P obtained in step S302 k|k-1 Compute the mean squared error matrix.

[0151] P k|k =Pk|k-1 -K k H k|k-1 P k|k-1 (29)

[0152] The target state estimation value at the kth time step obtained from steps S3 to S4 The estimated value of the first target position is the angle between the target and array element 1 at the kth time step (positive direction is clockwise), i.e., the underwater target position tracking result at the kth time step. Let time step k = k + 1, and loop through steps S3 and S4 in sequence to continuously track the underwater target position, terminating the loop when k = K.

[0153] In another embodiment of the present invention, a uniform circular array robust underwater target azimuth tracking system is provided, which can be used to implement the above-mentioned uniform circular array robust underwater target azimuth tracking method. Specifically, the uniform circular array robust underwater target azimuth tracking system includes an acquisition module, a calculation module and a tracking module.

[0154] The acquisition module uses a uniform circular array to receive the narrowband acoustic signal radiated by the target. The collected signals are arranged in ascending order to form a vector, which is used as the measurement of the kth time step.

[0155] a calculation module, which calculates an estimated value of the target state at the kth time step based on the measurement at the kth time step obtained by the acquisition module and the one-step predicted target state at the kth time step obtained by the update module, the one-step predicted root mean square error matrix at the kth time step, the estimated value of the predicted degrees of freedom, and the estimated value of the predicted inverse scale matrix;

[0156] The tracking module takes the first target azimuth estimation value of the target state estimation value of the kth time step as the underwater target azimuth tracking result of the kth time step, sets the time step k=k+1, and continuously tracks the underwater target azimuth until k equals the total number of tracking time steps, thus completing the uniform circular array robust underwater target azimuth tracking.

[0157] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0158] In order to verify the effectiveness of the method provided by the present invention, a simulation experiment is designed as follows:

[0159] The initial azimuth angle relative to the uniform circular array underwater is 270°, the initial azimuth angle change rate is -0.02° / s, the target azimuth angle changes in a uniform speed model, and the process noise is 2×10- 4 ° / s 2 , the total tracking time steps are 5000, and the time interval between adjacent time steps is 1s, so the total tracking time is 5000s. Simulate the target azimuth angle change trajectory, such as Figure 3 shown.

[0160] The underwater sound speed is 1500m / s, and the target radiates a narrowband signal with a frequency of 170Hz. The signal amplitude is 1 when it reaches the uniform circular array. The measurement is obtained using a 12-element uniform circular array, and a zero-mean covariance matrix of 0.25I is added to the measurement. 12 Additive Gaussian white noise, where I 12 is a 12th-order unit matrix. In order to test the performance of the proposed method under the condition of time-varying measurement noise covariance matrix, strong Gaussian white noise is added to the measurement from 3600s to 4000s, so that the measurement noise covariance matrix from 3600s to 4000s is 2.5I 12 The measurement data is obtained by simulation based on the above conditions.

[0161] The proposed method is tested using the measurement data obtained by simulation. The parameters of the proposed method are set as follows:

[0162] Initialize the target state estimate: for

[0163] in, Initialize the mean square error matrix P for the target position estimation result obtained by conventional beamforming technology at time step k = 0 k|k for Process noise covariance Q k-1 Set to 2×10 -4 ° / s 2 , initialize the noise covariance matrix estimate to 0.25I 12 , initialize the degrees of freedom estimate and the inverse scaling matrix 16 and 16I respectively 12 , the forgetting factor ρ is set to 0.9995, the number of variational Bayesian iterations N is 5, and the decision threshold δ is 0.1.

[0164] See also Figure 4. The solid line is the simulated real target azimuth angle change trajectory, and the dotted line is the target azimuth tracking trajectory. It can be seen from the figure that the target azimuth tracking error of the present invention is extremely small, and the tracking trajectory is very accurate even when strong Gaussian white noise exists from 3600s to 4000s, achieving high-precision and robust target azimuth tracking. The average running time of one time step of the method of the present invention is 0.39ms, achieving high-efficiency target azimuth tracking, and achieving high-precision, robust and efficient target azimuth tracking.

[0165] In summary, the present invention provides a uniform circular array robust underwater target position tracking method and system, which uses the variational Bayesian method to adaptively estimate the measurement noise covariance matrix in real time during the target position tracking process, targeting the unknown time-varying measurement noise covariance matrix caused by complex underwater environmental noise, thereby eliminating the influence of the unknown time-varying measurement noise covariance matrix on the performance of the target position tracking method, and realizing high-precision and high-robust target position tracking in complex underwater environmental noise scenarios.

[0166] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0167] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the steps in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0168] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0169] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0170] The above content is only for explaining the technical idea of ​​the present invention and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical idea proposed by the present invention shall fall within the protection scope of the claims of the present invention.

Claims

1. A method for robust underwater target azimuth tracking using a uniform circular array, characterized in that: The following steps are involved: A uniform circular array is used to receive the narrowband acoustic signal radiated by the target; the collected signals are arranged in order from small to large to form a vector as the first k Measurement of time steps; According to k The measurement of time steps and k One-step prediction of the target state at time step, k The one-step forecast RMS error matrix, forecast degrees of freedom estimate, and forecast inverse scale matrix estimate are calculated for the time step k The target state estimate at the time step; One-step prediction of target state for: in, is the target state transfer matrix; One-step forecast root mean square error matrix for: in, for The transpose of is the noise driving matrix, is the process noise covariance, for The transpose of Prediction degrees of freedom estimate and the predicted inverse scaling matrix estimate for: in, For the forgetting factor, is the number of array elements of the uniform circular array; Calculate the k The estimated value of the target state at the time step is: S401, predicting the target state according to one step Calculate measurement function and its Jacobian matrix ; S402, according to the known k Step measurement and the value obtained in step S401 Calculate the innovation root mean square error matrix ; S403, Order , based on the estimated values ​​of the prediction degrees of freedom and the predicted inverse scaling matrix estimate Initialize the iterative estimate of the measurement noise covariance matrix ; Predict the target state based on the one-step prediction Initialize the iterative target state estimate ; S404, when When , execute step S405 and step S406; when When i -1st and i -2 iterations measure the deviation between the Jacobian matrices of the function Is it greater than the set judgment threshold? , represents the 2-norm, if yes, execute step S405 and step S406 and skip step S407, otherwise skip step S405 and step S406 and directly execute step S407; S405, based on the estimated value of the iterative target state Compute the Jacobian matrix of the iterative measurement function ; S406: Jacobian matrix of the iterative measurement function obtained in step S405 , the measurement function Jacobian matrix obtained in step S401 , and the one-step prediction root mean square error matrix Calculate the deviation parameter ; S407, set deviation parameter Equal to i -1 bias parameter in iteration , let the Jacobian matrix of the iterative measurement function Equal to i -1 iterations of the Jacobian matrix of the iterative measurement function ; S408: Deviation parameters obtained according to step S407 , the measurement function Jacobian matrix obtained in step S401 And the new information root mean square error matrix obtained in step S402 Update iterative measurement noise covariance matrix estimate ; S409, Order , loop through steps S404 to S408 until Then stop the cycle, is the number of variational Bayesian iterations, then k The estimated value of the measurement noise covariance matrix at time step , the estimated degrees of freedom , the inverse scaling matrix estimate ; S410, according to k The estimated value of the measurement noise covariance matrix at time step , the one-step prediction mean square error matrix is ​​obtained and the measurement function Jacobian matrix obtained in step S401 Calculate adaptive Kalman filter gains ; S411, adaptive Kalman filter gain obtained according to step S410 , the one-step predicted target state is obtained , known k Time step measurement and the measurement function obtained in step S401 Calculate target state estimate ; The first k The first target position estimate of the target state estimate at the time step is taken as the first k The underwater target position tracking result of time step is Repeat the above steps to continuously track the underwater target position until The loop is stopped when the number of tracking time steps is equal to the total time step, and the uniform circular array robust underwater target azimuth tracking is completed.

2. The method for robust underwater target position tracking using a uniform circular array according to claim 1, characterized in that: In step S401, the function is measured and its Jacobian matrix Specifically: in, represents the real part, is the array manifold vector of the uniform circular array, To predict the target azimuth, that is, to predict the target state in one step The first item, is the estimated value of the target radiated narrowband acoustic signal, represents transpose, is a matrix element.

3. The method for robust underwater target position tracking using a uniform circular array according to claim 1, characterized in that: In step S402, the new information root mean square error matrix Specifically: in For the k Step measurement, is the measurement function, Indicates transpose.

4. The method for robust underwater target position tracking using a uniform circular array according to claim 1, characterized in that: In step S406, the deviation parameter Specifically: in, is the Jacobian matrix of the iterative measurement function, is the Jacobian matrix of the measurement function, is the one-step prediction root mean square error matrix.

5. The method for robust underwater target position tracking using a uniform circular array according to claim 1, characterized in that: In step S408, the noise covariance matrix estimate is iteratively measured for: in, is the iterative degrees of freedom estimate, is the iterative inverse scaling matrix estimate.

6. The uniform circular array robust underwater target position tracking method according to claim 1, characterized in that: In step S410, the adaptive Kalman filter gain for: in, for The transpose of .

7. The method for robust underwater target position tracking using a uniform circular array according to claim 1, characterized in that: In step S411, the target state estimation value Specifically: 。 8. A uniform circular array robust underwater target azimuth tracking system, characterized in that: include: The acquisition module uses a uniform circular array to receive the narrowband acoustic signal radiated by the target; the collected signals are arranged in order from small to large to form a vector as the first k Measurement of time steps; The calculation module obtains the k The time step measurement and update module obtains the k One-step prediction of the target state at time step, k The one-step forecast RMS error matrix, forecast degrees of freedom estimate, and forecast inverse scale matrix estimate are calculated for the time step k The target state estimate at the time step; One-step prediction of target state for: in, is the target state transfer matrix; One-step forecast root mean square error matrix for: in, is the target state transfer matrix, for The transpose of is the noise driving matrix, is the process noise covariance, for The transpose of Prediction degrees of freedom estimate and the predicted inverse scaling matrix estimate for: in, For the forgetting factor, is the number of array elements of the uniform circular array; Calculate the k The estimated value of the target state at the time step is: S401, predicting the target state according to one step Calculate measurement function and its Jacobian matrix ; S402, according to the known k Step measurement and the value obtained in step S401 Calculate the innovation root mean square error matrix ; S403, Order , based on the estimated values ​​of the prediction degrees of freedom and the predicted inverse scaling matrix estimate Initialize the iterative estimate of the measurement noise covariance matrix ; Predict the target state based on the one-step prediction Initialize the iterative target state estimate ; S404, when When , execute step S405 and step S406; when When i -1st and i -2 iterations measure the deviation between the Jacobian matrices of the function Is it greater than the set judgment threshold? , represents the 2-norm, if yes, execute step S405 and step S406 and skip step S407, otherwise skip step S405 and step S406 and directly execute step S407; S405, based on the estimated value of the iterative target state Compute the Jacobian matrix of the iterative measurement function ; S406: Jacobian matrix of the iterative measurement function obtained in step S405 , the measurement function Jacobian matrix obtained in step S401 , and the one-step prediction root mean square error matrix Calculate the deviation parameter ; S407, set deviation parameter Equal to i -1 bias parameter in iteration , let the Jacobian matrix of the iterative measurement function Equal to i -1 iterations of the Jacobian matrix of the iterative measurement function ; S408: Deviation parameters obtained according to step S407 , the measurement function Jacobian matrix obtained in step S401 And the new information root mean square error matrix obtained in step S402 Update iterative measurement noise covariance matrix estimate ; S409, Order , loop through steps S404 to S408 until Then stop the cycle, is the number of variational Bayesian iterations, then k The estimated value of the measurement noise covariance matrix at time step , the estimated degrees of freedom , the inverse scaling matrix estimate ; S410, according to k The estimated value of the measurement noise covariance matrix at time step , the one-step prediction mean square error matrix is ​​obtained and the measurement function Jacobian matrix obtained in step S401 Calculate adaptive Kalman filter gains ; S411, adaptive Kalman filter gain obtained according to step S410 , the one-step predicted target state is obtained , known k Time step measurement and the measurement function obtained in step S401 Calculate target state estimate ; Tracking module, k The first target position estimate of the target state estimate at the time step is taken as the first k The underwater target position tracking result of time step is , continuously track the underwater target position until The loop is stopped when the number of tracking time steps is equal to the total time step, and the uniform circular array robust underwater target azimuth tracking is completed.

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