A method and apparatus for non-gaussian noise suppression with adaptive kernel width

Abstract

The application provides a non-Gaussian noise suppression method and device with adaptive kernel width, and belongs to the field of inertial base combined navigation algorithm and state estimation. The method solves the problems that the robust filtering method based on fixed kernel width is difficult to adapt to time-varying noise characteristics, and the scheme depending on an optimization algorithm has the problem of insufficient real-time performance. The method comprises the following steps: initializing filter parameters according to a SINS / DVL combined navigation system; performing time updating to obtain a predicted state vector and a predicted state covariance matrix at the current moment; updating a measurement noise covariance matrix through a variational Bayesian method, wherein the measurement noise covariance matrix is modeled as an inverse Wishart distribution; adaptively updating a kernel width parameter according to a filter innovation at the current moment and the measurement noise covariance matrix; and updating a state quantity estimation value and a state covariance matrix at the current moment through a fixed-point iteration algorithm by using the updated kernel width. The method is used in the field of underwater resource exploration.

Description

Technical Field

[0001] This invention belongs to the field of inertial basis integrated navigation algorithms and state estimation, and in particular relates to a non-Gaussian noise suppression method with adaptive kernel width. Background Technology

[0002] Autonomous underwater vehicles (AUVs) have significant applications in seabed topography surveying and underwater resource exploration. However, due to the rapid attenuation of electromagnetic waves underwater, Global Navigation Satellite Systems (GNSS) are not an effective navigation solution for AUVs. While strapdown inertial navigation systems (SINS) offer good autonomy and stealth, their positioning errors accumulate over time, requiring auxiliary correction from other sensors. Ultrasonic ranging beacons (USBLs) can provide positioning services using underwater acoustic ranging information, but require pre-deployment of underwater base stations, resulting in high costs. Database-based matching navigation methods (such as gravity matching and magnetic field matching) not only require pre-built databases but are also susceptible to environmental changes. Doppler velocities (DVLs) utilize the Doppler effect to measure the vehicle's velocity, requiring no external navigation information source and effectively improving navigation accuracy by correcting SINS velocity information. Therefore, SINS / DVL integrated navigation systems are widely used for underwater navigation of AUVs.

[0003] Despite the advantages of the SINS / DVL integrated navigation system, the complexity of the underwater environment poses a significant challenge to DVL measurements. DVL measurement results are susceptible to outliers, resulting in a heavy-tailed noise distribution that severely impacts the positioning accuracy of the navigation system. To suppress the influence of non-Gaussian noise, various robust filtering methods have been proposed. For example, Chinese patent document No. 201910186078.X, entitled "A Robust Kalman Filtering SINS / DVL Integrated Navigation Method Against Outliers," discloses a scheme that uses a Student's t-distribution to model the one-step prediction probability density function. This involves Gaussian layering of the SINS / DVL integrated system model and using a Beta-Bernoulli distribution to model outlier points when DVL outputs them. Finally, a variational Bayesian method is used to estimate the state vector and parameters. While this scheme can improve system robustness to some extent, the setting of the kernel function width still relies on experience and does not fully consider the time-varying nature of noise statistics, limiting its adaptability in dynamic underwater environments.

[0004] Another prior art, Chinese patent application number 202310069689.2, entitled "SINS / DVL Navigation Method Based on Particle Swarm Optimization Robust Filtering," discloses a robust filtering method based on particle swarm optimization. This method constructs a navigation model through state transformation, builds a fitness function, and performs adaptive particle swarm optimization to achieve filtered measurement updates. Although this method improves noise suppression, its optimization process has high computational complexity and poor real-time performance, making it difficult to meet the real-time response requirements of AUVs for navigation systems. Furthermore, this method does not effectively model the dynamic changes of the measurement noise covariance matrix, leading to a decrease in estimation accuracy under continuous repetitive noise interference.

[0005] In summary, existing robust filtering methods based on fixed kernel width struggle to adapt to time-varying noise characteristics, while optimization-based schemes suffer from insufficient real-time performance. More importantly, most methods fail to accurately estimate the time-varying characteristics of the noise covariance matrix, thus limiting navigation accuracy in complex underwater environments. Summary of the Invention

[0006] In view of this, the present invention aims to propose a non-Gaussian noise suppression method and apparatus with adaptive kernel width, so as to solve the problem that the robust filtering method based on fixed kernel width in the prior art is difficult to adapt to time-varying noise characteristics, while the scheme relying on optimization algorithm has insufficient real-time performance.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A non-Gaussian noise suppression method with adaptive kernel width, the method comprising: Step S1: Initialize the filter parameters according to the SINS / DVL integrated navigation system; Step S2: Perform time update to obtain the predicted state vector and predicted state covariance matrix at the current time. Step S3: Update the measurement noise covariance matrix using the variational Bayesian method, wherein the measurement noise covariance matrix is ​​modeled as an inverse Wissaud distribution; Step S4: Adaptively update the kernel width parameter based on the current filter information and measurement noise covariance matrix; Step S5: Using the updated kernel width, update the estimated state variables and state covariance matrix at the current time using a fixed-point iterative algorithm.

[0008] Furthermore, a preferred method is proposed, wherein the initialization in step S1 includes setting a state vector, a state covariance matrix, a system noise covariance matrix, and an initial measurement noise covariance matrix, wherein the state vector contains the error term of the inertial navigation system.

[0009] Furthermore, a preferred embodiment is proposed, wherein the time update in step S2 includes:

[0010] in, Let be the prior estimate of the state variable at time k. Let be the state transition matrix at time k. Let be the posterior estimate of the state variable at time k-1. Let be the prior estimate of the state covariance matrix at time k. Let be the posterior estimate of the state covariance matrix at time k-1. Let be the system noise covariance matrix at time k-1.

[0011] Furthermore, a preferred embodiment is proposed, wherein step S3 includes: The prior distribution of the measurement noise covariance matrix is ​​modeled as an inverse Wissaud distribution, with the following probability density function:

[0012] in, To measure the noise covariance matrix, Represents the degree of freedom parameter. Represents the dimension of the matrix. Represents the inverse scaling matrix. Represents determinant operations. This represents the trace operation. Represents the inverse Gamma distribution function; The measurement noise covariance matrix is ​​estimated by inferring the posterior distribution through variational Bayesian inference.

[0013] Furthermore, a preferred method is proposed, wherein the variational Bayesian inference includes calculating an auxiliary matrix:

[0014] in, As an intermediate variable, The measurement value at time k is... Let be the measurement transition matrix at time k; And update the parameters of the inverse Wissaud distribution: degrees of freedom parameter and inverse scaling matrix This allows us to obtain an estimate of the measurement noise covariance matrix. .

[0015] Furthermore, a preferred embodiment is proposed, wherein step S4 includes:

[0016] in, The confidence level factor, Let i be the value of the i-th message at time k. This is the estimated value of the i-th kernel width at time k. Let be the adaptive factor for the width of the i-th kernel at time k. This is the upper limit of the kernel width.

[0017] Furthermore, a preferred embodiment is proposed, wherein the convergence condition of the fixed-point iterative algorithm in step S5 is that the difference between the state estimates of two adjacent iterations is less than a preset threshold or the maximum number of iterations is reached.

[0018] Based on the same inventive concept, this invention also proposes an adaptive kernel width non-Gaussian noise suppression device, the device comprising: An initialization module is used to initialize filter parameters according to the SINS / DVL integrated navigation system. The time update module is used to perform time updates and obtain the predicted state vector and predicted state covariance matrix at the current moment. The variational Bayesian estimation module is used to update the measurement noise covariance matrix using the variational Bayesian method, wherein the measurement noise covariance matrix is ​​modeled as an inverse Wissaud distribution; The kernel width adaptive module is used to adaptively update the kernel width parameter based on the current filter information and the measurement noise covariance matrix. The state update module is used to update the estimated state variables and state covariance matrix at the current time using a fixed-point iterative algorithm with the updated kernel width.

[0019] Based on the same inventive concept, the present invention also proposes a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes an event-driven multi-unmanned vessel cooperative positioning and control method according to any of the preceding claims.

[0020] Based on the same inventive concept, the present invention also proposes a computer-readable storage medium storing a computer program that, when executed by a processor, performs the steps of an adaptive kernel width non-Gaussian noise suppression method as described in any of the above-mentioned embodiments.

[0021] Compared with the prior art, the beneficial effects of the present invention are: Existing robust filtering algorithms, such as certain maximum correlation entropy Kalman filters (MCKFs) based on a fixed kernel width, have inherent limitations when dealing with time-varying non-Gaussian heavy-tailed noise. These methods typically rely on an empirically preset kernel width parameter. Once set, this parameter remains constant throughout the filtering process, leading to insufficient adaptability: when noise suddenly increases, a fixed kernel width may not provide sufficient robustness; conversely, when noise is low, an excessively large kernel width reduces the filter's estimation accuracy, failing to achieve a dynamically optimal balance between robustness and accuracy. This invention fundamentally changes this static approach by proposing a dynamic adaptive kernel width strategy. By establishing a feedback mechanism, the adjustment of the kernel width is directly correlated with information reflecting the real-time state of the system and its covariance matrix. Specifically, this strategy employs a carefully designed mathematical relationship that allows the kernel width to automatically adjust based on the magnitude of the innovation: when the innovation significantly increases due to outliers, the algorithm automatically reduces the kernel width, decreasing its reliance on unreliable measurements and instead relying more on the predictions from the system model, thereby enhancing robustness; conversely, when the innovation is small, indicating high reliability of the measurements, the algorithm automatically increases the kernel width, bringing the filter performance close to the optimal Kalman filter to achieve higher estimation accuracy. This dynamic adaptive mechanism enables online tracking and response to changes in noise characteristics, representing a fundamental innovation that distinguishes it from all fixed-parameter methods.

[0022] Another key innovation lies in the real-time accurate estimation of the measurement noise covariance matrix (MNCM). Traditional filtering methods typically assume that MNCM is a known and invariant constant, but this is severely inconsistent with the reality that DVL measurement noise in complex underwater environments exhibits a time-varying, heavy-tailed distribution. Although some existing techniques, such as the Student's t-distribution method mentioned in the background, attempt to model the noise distribution more finely, they have failed to effectively solve the problem of online estimation of the time-varying characteristics of MNCM itself. Inaccurate MNCM directly leads to errors in gain calculation, thus affecting the accuracy of the entire state estimation. This invention introduces the variational Bayesian (VB) method, treating MNCM as a time-varying random matrix and assigning it an inverse Wieshardt (IW) prior distribution. Through variational inference, the algorithm can update the parameters of the IW distribution in real time during each filtering step, in parallel with state estimation, thereby obtaining the optimal estimate of MNCM at the current moment. This overcomes the MNCM estimation error caused by abnormal measurements, providing the filter with more accurate and reliable noise statistics. More importantly, this real-time estimated, more accurate MNCM serves as a key input and is further used in the calculation of the aforementioned adaptive kernel width. This allows the kernel width adjustment to be based not only on the new information but also on the latest assessment of the noise statistical characteristics, resulting in a dual adaptive optimization.

[0023] In this invention, the adaptive kernel width strategy and the variational Bayesian-based MNCM estimation method work together to form a powerful closed-loop system: accurate MNCM estimation provides a more reliable basis for adaptive adjustment of the kernel width; while dynamically optimized kernel width ensures more accurate state estimation, which in turn promotes better MNCM estimation by the VB method. This closed-loop collaborative working mechanism ensures that the algorithm maintains superior stability and accuracy even under continuous non-Gaussian heavy-tailed noise interference.

[0024] This invention is applied to the fields of seabed topographic surveying and underwater resource exploration. Attached Figure Description

[0025] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a flowchart of an adaptive kernel width non-Gaussian noise suppression method according to the present invention, where Gyroscope represents a gyroscope, Accelerometer represents an accelerometer, SINS represents a strapdown inertial navigation system, Proposed filter represents the filter proposed in this invention, MCKF represents a maximum correlation entropy Kalman filter, Adaptive Kernel width represents an adaptive kernel width, DVL represents a Doppler velocimeter, and VB estimation represents variational Bayesian estimation. Figure 2 The simulation trajectory diagram described in this invention, wherein Easting Coordinate represents the eastward coordinate and Northing Coordinate represents the northward coordinate; Figure 3 This is a schematic diagram showing the minimum mean square error results for different localization algorithms described in this invention. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other, and the described embodiments are only some embodiments of the present invention, not all embodiments.

[0027] Implementation Method 1: This implementation method addresses the shortcomings of existing robust filtering methods based on fixed kernel width, which struggle to adapt to time-varying noise characteristics, while optimization-based schemes suffer from insufficient real-time performance. It proposes an adaptive kernel width non-Gaussian noise suppression method, comprising: Step S1: Initialize the filter parameters according to the SINS / DVL integrated navigation system; Step S2: Perform time update to obtain the predicted state vector and predicted state covariance matrix at the current time. Step S3: Update the measurement noise covariance matrix using the variational Bayesian method, wherein the measurement noise covariance matrix is ​​modeled as an inverse Wissaud distribution; Step S4: Adaptively update the kernel width parameter based on the current filter information and measurement noise covariance matrix; Step S5: Using the updated kernel width, update the estimated state variables and state covariance matrix at the current time using a fixed-point iterative algorithm.

[0028] Implementation Method 2, see below Figures 1 to 3 This embodiment describes a preferred method for an adaptive kernel width non-Gaussian noise suppression method as described in Embodiment 1, the method comprising: Step S1: Initialize the filter parameters according to the SINS / DVL integrated navigation system; The state variables used in this embodiment are defined as follows:

[0029] in, This represents the three-dimensional positioning error in the navigation coordinate system (n-frame). This is the eastward position error. This is the northward position error. This is the celestial position error. This represents the three-dimensional velocity error in the navigation coordinate system (n-frame). For eastward velocity error, For northbound velocity error, For the upward velocity error, This represents the three-dimensional misalignment angle in the navigation coordinate system (n-frame). The angle of inaccuracy is eastward. The northward misalignment angle is... The angle of inaccuracy is due to the celestial orientation. and Let represent the zero bias of the three-axis gyroscope and the zero bias of the three-axis accelerometer, respectively. From this, the differential equations of the system state model can be written:

[0030] in, The derivative of the azimuth misalignment angle. This is the azimuth misalignment angle. Let n be the coordinate system from the n-frame to the geocentric inertial coordinate system (i-frame). Let be the attitude transition matrix from system b to system n. This is the measured value of the specific force in the b-system. Let be the derivative of the velocity in the n-frame. Let be the angular velocity from the geocentric Earth-fixed coordinate system (e-frame) to the geocentric inertial coordinate system (i-frame) in the n-frame. Let be the angular velocity from the n-system to the e-system in the n-system. For velocity error in the n-system, To achieve zero bias in the accelerometer, This represents the error in gravitational acceleration in the n-system. The derivative of the velocity error in the n-system is given. This represents the position error in the n-system. For velocity error in the n-system, This is the derivative of the position error in the n-system. To achieve zero bias in the gyroscope, This is gyroscope noise. The derivative of the gyroscope's zero bias is given by... The derivative of the accelerometer's zero bias. This is accelerometer noise.

[0031] Discretizing the differential equations yields the state transition matrix of the system's state model:

[0032] The elements in the matrix are represented as follows:

[0033]

[0034]

[0035]

[0036]

[0037]

[0038]

[0039]

[0040]

[0041]

[0042] in, The radius of curvature of the meridian (including height correction) is given. The radius of curvature of the y-axis circle (including height correction). It is the tangent of latitude. This is the Earth's rotational angular velocity. The sine value of the latitude. The cosine value of the latitude. For the northward velocity in the n-system, For the eastward velocity in the n-system, This is the theoretical value of the radius of curvature of the zonal loop. The specific force value in the n-system. The velocity in the n-system is The secant of latitude. The speed is eastward.

[0043] The simulation uses the difference between the 3D velocity output from the DVL coordinate system and the velocity output from the inertial navigation system as the measurement. First, the velocity in the DVL coordinate system (d-frame) needs to be transformed to the n-frame:

[0044] in, It is the attitude matrix from the d-frame to the carrier coordinate system (b-frame), which is generated by the attitude installation error between DVL and the carrier. The measurement values ​​are obtained from the attitude matrix from the b-system to the n-system. Because... Since it is a measurement value of n-series DVL, it can be decomposed into the sum of the true value and the error term:

[0045] in, This is the azimuth misalignment angle. The velocity is obtained by DVL measurement in the n-system. The velocity error is obtained from DVL measurements in the n-system.

[0046] Similarly, the velocity measurements of the IMU in the n-system can also be decomposed into the sum of the true value and the error term:

[0047] in, The velocity is obtained by IMU measurement in the n-system. The velocity error is obtained from IMU measurements in the n-system.

[0048] Therefore, the measured value The following definitions are possible:

[0049] Therefore, from the state variables Measurement The transformation matrix (denoted as) It can be defined as follows:

[0050] in, It is a three-dimensional identity matrix.

[0051] Step S2: Perform time update to obtain the predicted state vector and predicted state covariance matrix at the current time. The time update in this embodiment includes:

[0052] in, Let be the prior estimate of the state variable at time k. Let be the state transition matrix at time k. Let be the posterior estimate of the state variable at time k-1. Let be the prior estimate of the state covariance matrix at time k. Let be the posterior estimate of the state covariance matrix at time k-1. Let be the system noise covariance matrix at time k-1.

[0053] Step S3: Update the measurement noise covariance matrix using the variational Bayesian method, wherein the measurement noise covariance matrix is ​​modeled as an inverse Wissaud distribution; In step S3 of this embodiment, since the strapdown inertial navigation system (SINS) is almost unaffected by external interference, its noise characteristics are relatively stable. The covariance matrix of the system noise (PNCM) can be preset through system parameters and does not change over time. However, due to the interference of heavy-tailed noise, the covariance matrix of the measurement noise (MNCM) usually changes over time, leading to inaccurate estimation results. In this embodiment, the MNCM is modeled in the form of an inverse Weibull (IW) distribution. By using the variational Bayesian method, the parameters in the distribution are estimated, thereby achieving the effect of matrix adaptation over time.

[0054] The expression for the probability density function of the prior distribution It can be written as:

[0055] In the above formula, To measure the noise covariance matrix, Represents the degree of freedom parameter. Represents the dimension of the matrix. Represents the inverse scaling matrix. Represents determinant operations. This represents the trace operation. This represents the inverse Gamma distribution function; in the IW distribution, we have:

[0056] in, for The expectation at time k.

[0057] Next, we need to estimate and The joint probability density function is denoted as , This is the posterior estimate of the state variables at time k.

[0058] Due to the complexity of the joint posterior probability density, its closed-form solution cannot be obtained. Therefore, this implementation uses the variational Bayesian (VB) method and mean-field theory to decompose the posterior density into a product of several probability density functions with known distribution forms, as shown below:

[0059] in, Follows a Gaussian distribution. It follows the IW distribution. Since the forms of these two distributions are known, we only need to adjust the parameters to make them as close as possible. In this implementation, KL divergence (KLD) is used to measure the difference between the two distributions, thus the task becomes... and Find the optimal parameters to minimize the KL divergence on both sides of the probability density function of the distribution, i.e.:

[0060] in, express and The optimal solution of the above equation satisfies the following equation: (The equation is missing from the provided text.)

[0061]

[0062] in, To remove The joint expectation of all external random variables to be estimated. Let be the joint probability density function of all random variables to be estimated and all quantities measured. It is a constant. Let be the set of all random variables to be estimated.

[0063] Based on the conditional independence assumption of Kalman filtering, it can be Decomposed into the following formula:

[0064] Since the purpose of using the variational Bayesian VB method in this implementation is to achieve adaptation of the MNCN, rather than estimation... Therefore, you only need to set You can then obtain:

[0065] in, For the dimension of measurement, It is a constant. The measurement value at time k is... Let be the measurement transition matrix at time k. , As an intermediate variable; At this point, we have obtained The probability density function is then used, and the parameters of the inverse Wissaud distribution are updated based on the results of the previous iteration: , , , , in, For the degree of freedom parameter, It is the inverse scaling matrix; Finally, using the expectation formula of the IW distribution, the estimated value of the measurement noise covariance matrix can be obtained: .

[0066] Step S4: Adaptively update the kernel width parameter based on the current filter information and measurement noise covariance matrix; In this embodiment, step S4, adaptively updating the kernel width parameter, includes:

[0067] in, The confidence level factor, Let i be the value of the i-th message at time k. This is the estimated value of the i-th kernel width at time k. Let be the adaptive factor for the width of the i-th kernel at time k. This is the upper limit of the kernel width.

[0068] Step S5: Using the updated kernel width, update the estimated state variables and state covariance matrix at the current time using a fixed-point iterative algorithm.

[0069] The parameters of the inertial measurement unit (IMU) components in the strapdown inertial navigation system are as follows:

[0070] Figure 2 The simulation trajectory settings are shown, and the simulation time is set to half an hour.Figure 3 The results of 1000 Monte Carlo simulations are presented. As can be seen from the figures, the method proposed in this invention is significantly better than the traditional method in terms of positioning accuracy. The mean square error (RMSE) and average mean square error (ARMSE) are shown below:

[0071] Implementation Method 3: This implementation method proposes a computer device, including a memory and a processor. The memory stores a computer program. When the processor runs the computer program stored in the memory, the processor executes an event-driven multi-unmanned vessel cooperative positioning and control method according to any one of Implementation Methods 1 to 2.

[0072] Implementation Method 4: This implementation method proposes a computer-readable storage medium storing a computer program that, when executed by a processor, performs the steps of an adaptive kernel width non-Gaussian noise suppression method as described in any one of Implementation Methods 1 to 2.

[0073] Those skilled in the art will understand that embodiments of this disclosure can be provided as methods, systems, or computer program products. Therefore, this disclosure can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this disclosure can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0074] This disclosure is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create a machine for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0075] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this disclosure and not to limit its protection scope. Although this disclosure has been described in detail with reference to the above embodiments, those skilled in the art should understand that after reading this disclosure, they can still make various changes, modifications or equivalent substitutions to the specific implementation of the invention, but these changes, modifications or equivalent substitutions are all within the protection scope of the published pending claims.

Claims

1. A non-Gaussian noise suppression method with adaptive kernel width, characterized in that, The method includes: Step S1: Initialize the filter parameters according to the SINS / DVL integrated navigation system; Step S2: Perform time update to obtain the predicted state vector and predicted state covariance matrix at the current time. Step S3: Update the measurement noise covariance matrix using the variational Bayesian method, wherein the measurement noise covariance matrix is ​​modeled as an inverse Wissaud distribution; Step S4: Adaptively update the kernel width parameter based on the current filter information and measurement noise covariance matrix; Step S5: Using the updated kernel width, update the estimated state variables and state covariance matrix at the current time using a fixed-point iterative algorithm.

2. The non-Gaussian noise suppression method with adaptive kernel width according to claim 1, characterized in that, The initialization in step S1 includes setting the state vector, the state covariance matrix, the system noise covariance matrix, and the initial measurement noise covariance matrix. The state vector contains the error term of the inertial navigation system.

3. The non-Gaussian noise suppression method with adaptive kernel width according to claim 1, characterized in that, The time update in step S2 includes: in, Let be the prior estimate of the state variable at time k. Let be the state transition matrix at time k. Let be the posterior estimate of the state variable at time k-1. Let be the prior estimate of the state covariance matrix at time k. Let be the posterior estimate of the state covariance matrix at time k-1. Let be the system noise covariance matrix at time k-1.

4. The non-Gaussian noise suppression method with adaptive kernel width according to claim 3, characterized in that, Step S3 includes: The prior distribution of the measurement noise covariance matrix is ​​modeled as an inverse Wissaud distribution, with the following probability density function: in, To measure the noise covariance matrix, Represents the degree of freedom parameter. Represents the dimension of the matrix. Represents the inverse scaling matrix. Represents determinant operations. This represents the trace operation. Represents the inverse Gamma distribution function; The measurement noise covariance matrix is ​​estimated by inferring the posterior distribution through variational Bayesian inference.

5. The non-Gaussian noise suppression method with adaptive kernel width according to claim 4, characterized in that, The variational Bayesian inference includes calculating the auxiliary matrix: in, As an intermediate variable, The measurement value at time k is... Let be the measurement transition matrix at time k; And update the parameters of the inverse Wissaud distribution: degrees of freedom parameter and inverse scaling matrix This allows us to obtain an estimate of the measurement noise covariance matrix. .

6. The non-Gaussian noise suppression method with adaptive kernel width according to claim 5, characterized in that, Step S4 includes: in, The confidence level factor, Let i be the value of the i-th message at time k. This is the estimated value of the i-th kernel width at time k. Let be the adaptive factor for the width of the i-th kernel at time k. This is the upper limit of the kernel width.

7. The non-Gaussian noise suppression method with adaptive kernel width according to claim 1, characterized in that, The convergence condition of the fixed-point iterative algorithm in step S5 is that the difference between the state estimates of two adjacent iterations is less than a preset threshold or the maximum number of iterations is reached.

8. A non-Gaussian noise suppression device with adaptive kernel width, characterized in that, The device includes: An initialization module is used to initialize filter parameters according to the SINS / DVL integrated navigation system. The time update module is used to perform time updates and obtain the predicted state vector and predicted state covariance matrix at the current moment. The variational Bayesian estimation module is used to update the measurement noise covariance matrix using the variational Bayesian method, wherein the measurement noise covariance matrix is ​​modeled as an inverse Wissaud distribution; The kernel width adaptive module is used to adaptively update the kernel width parameter based on the current filter information and the measurement noise covariance matrix. The state update module is used to update the estimated state variables and state covariance matrix at the current time using a fixed-point iterative algorithm with the updated kernel width.

9. A computer device, characterized in that: It includes a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes an event-driven multi-unmanned vessel cooperative positioning and control method according to any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, performs the steps of an adaptive kernel width non-Gaussian noise suppression method as described in any one of claims 1-7.

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