NHC noise adaptive estimation method and variational Bayesian filtering method

Abstract

The invention provides an NHC noise adaptive estimation method and a variational Bayesian filtering method, and the method comprises the steps: firstly, detecting whether a vehicle is in a turning state or not through a vehicle turning detection algorithm, and carrying out the adaptive estimation of an NHC lateral speed noise initial value; secondly, according to the motion state of the vehicle, a variational Bayesian method is adopted, and on the basis that lateral speed noise is modeled into Gaussian white noise or student T distribution thick tail noise, statistical characteristics of the measured noise are estimated in a real-time and self-adaptive mode; a complete combined filtering method is formed through the two methods, positioning errors caused by NHC failure are greatly reduced, and the method can be used independently and is high in applicability.

Description

Technical Field

[0001] The present invention relates to the field of navigation technology, and in particular to an NHC noise adaptive estimation method and a variational Bayesian filtering method. Background Art

[0002] The combination navigation of Global Navigation Satellite System (GNSS) / Inertial Navigation System (INS) is a commonly used method for vehicle navigation at present. This method uses the high-precision positioning information of GNSS to assist INS to realize autonomous continuous combined recursion to obtain positioning results, and has been widely used to reduce the error accumulation of strapdown inertial navigation systems. However, when the vehicle passes through complex scenarios such as tree-lined roads, tunnels, viaducts, etc., the GNSS signal is frequently blocked or even interrupted, resulting in insufficient credibility of the observation information, and thus the combined navigation result diverges. To solve the above problems, nonholonomic constraints are generally adopted. That is, according to the kinematic principle, when the carrier moves close to the ground, if there is no lateral sliding or up-and-down bumping, it can be considered that its lateral and vertical speeds are close to 0. Therefore, based on this principle, combined with odometer information, the observable quantity can be determined to construct a filtering equation to suppress the divergence of positioning errors.

[0003] However, in the GNSS / NHC / INS / ODO combined navigation system, most road conditions do not meet the conditions of nonholonomic constraints. When the vehicle encounters road conditions such as turning, potholes on the road surface, up-and-down bumps, muddy sections, etc., the lateral and vertical speeds are not 0. At this time, the observation information constructed by nonholonomic constraints (NHC) is not credible. Based on the above problems, some scholars have proposed an observation noise covariance matrix adaptive adjustment method. However, the NHC lateral noise is closely related to the changes in forward vehicle speed and heading angle. Since vehicle speed is affected by human factors and is not absolutely controllable, how to control these two variables so that the adaptive factor can be controllable within a certain range; in addition, the nonlinearity of the combined navigation system is enhanced in a strong vehicle-mounted environment, and there are some defects in the nonlinear estimation based on the error Kalman filter with Gaussian distribution, and with the increase of the number of iterations, the problem of filtering error divergence is inevitable.

[0004] Therefore, a new method is needed to comprehensively solve the above problems. Summary of the Invention

[0005] The present invention provides an NHC noise adaptive estimation method and a variational Bayesian filtering method to solve the defects of the pseudo velocity measurement noise of nonholonomic constraints in the combined navigation of vehicle-mounted global satellite navigation system / inertial navigation system, such as time-varying, heavy-tailed, and inability to accurately predict in complex road conditions (turning, side-sliding, etc.).

[0006] In a first aspect, the present invention provides a method for adaptively estimating NHC noise, including: Obtaining vehicle experiment reference data, GNSS data, INS data, and ODO data; Using the vehicle experiment reference data, the GNSS data, the INS data, and the ODO data to establish a binary regression analysis model for NHC lateral velocity noise; Based on the binary regression analysis model, establishing an NHC / ODO / INS Kalman filter model; Determining an adjustment value for the initial value of NHC lateral velocity noise by a preset turning detection algorithm, and outputting an NHC observation noise covariance matrix.

[0007] According to the method for adaptively estimating NHC noise provided by the present invention, obtaining vehicle experiment reference data, GNSS data, INS data, and ODO data includes: The vehicle experiment reference data includes the position, speed, and attitude reference values of the vehicle at each epoch, and post-processing the vehicle experiment reference data to obtain the vehicle lateral velocity in the b coordinate system and the heading angle difference between epochs; The GNSS data includes position, satellite signal strength, and timestamp; The INS data includes angular velocity and acceleration; The ODO data includes the forward position increment and speed information of the vehicle.

[0008] According to the method for adaptively estimating NHC noise provided by the present invention, using the vehicle experiment reference data, the GNSS data, the INS data, and the ODO data to establish a binary regression analysis model for NHC lateral velocity noise includes:

[0009] Wherein, is the NHC lateral velocity noise, is the weighting factor of the forward speed and heading angle error, is a constant coefficient, is the compensation adaptive factor; Evaluating the performance of the binary regression analysis model through regression model evaluation indexes, and the regression model evaluation indexes include mean square error, fitting residual normality test index, and goodness of fit.

[0010] According to the method for adaptively estimating NHC noise provided by the present invention, based on the binary regression analysis model, establishing an NHC / ODO / INS Kalman filter model includes: Constructing a system state equation and an observation equation:

[0011] Among them, and are the state vectors of the system at time k and time k-1 respectively, represents the one-step state transition matrix from time k-1 to time k, is a matrix related to noise, is the observation value at time k, is the observation matrix at time k, is the system noise, is the observation noise, where and are white noises and are uncorrelated with each other; Construct the observation noise covariance matrix:

[0012] Among them, represents the odometer speed measurement noise term, respectively represent the NHC noise terms, where the former is the adaptive estimation term.

[0013] Second, the present invention also provides a variational Bayesian filtering method, including: Obtain filtering parameters and initialize the filtering parameters; Perform standard Kalman filter time update and variational Bayesian filtering Ga-StVBAKF measurement update of Gaussian-Student T distribution; Adopt the variational Bayesian method for posterior approximation of parameters; Update the NHC observation noise covariance matrix; If it is determined that the preset number of iterations has been reached, wait for the next filtering moment, otherwise perform Ga-St VBAKF measurement update again.

[0014] According to a variational Bayesian filtering method provided by the present invention, obtaining filtering parameters and initializing the filtering parameters includes: Initialize the state vector, one-step state transition matrix, error covariance matrix, system state noise variance matrix, system noise driving matrix, and NHC observation noise covariance matrix.

[0015] According to a variational Bayesian filtering method provided by the present invention, performing standard Kalman filter time update and Ga-St VBAKF measurement update includes: The standard Kalman filter time update includes:

[0016]

[0017] In the formula, is the state value for one-step prediction, is the optimal state estimate value at time k-1, is the state covariance matrix for one-step prediction, is the optimal state covariance estimate value at time k-1, is the system noise covariance matrix at time k-1; The measurement update of Ga-St VBAKF includes:

[0018] where, is the iterative value of the th Kalman filter gain, are respectively the iterative value of the th optimal estimate covariance matrix and the one-step prediction covariance matrix, is the observation matrix, is the th optimal iterative value of the noise covariance matrix, is the observation value at time k.

[0019] According to a variational Bayesian filtering method provided by the present invention, parameter posterior approximation is performed by using the variational Bayesian method, including:

[0020] where, is the expectation of the Bernoulli random variable proposed to quantitatively distinguish between good NHC observations and NHC failures, and is defined as follows:

[0021] The mixing probability is set according to the NHC failure degree, and the expectation of the auxiliary random variable at the th time is determined according to the Gamma prior distribution as follows:

[0022] where, represents the trace of the matrix, and thus is updated as follows:

[0023] Similarly, is updated as follows: .

[0024] In a third aspect, the present invention further provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, the NHC noise adaptive estimation method or the variational Bayesian filtering method as described in any one of the above is implemented.

[0025] In a fourth aspect, the present invention further provides a non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the NHC noise adaptive estimation method or the variational Bayesian filtering method as described in any one of the above is implemented.

[0026] The NHC noise adaptive estimation method and the variational Bayesian filtering method provided by the present invention first detect whether the vehicle is in a turning state through a vehicle turning detection algorithm, so as to adaptively estimate the initial value of the NHC lateral velocity noise. Secondly, according to the vehicle motion state, the variational Bayesian method is used to model the lateral velocity noise as Gaussian white noise or student T-distribution thick-tailed noise, and then the statistical characteristics of the measurement noise are adaptively estimated in real time. The two form a complete combined filtering method, which greatly reduces the positioning error caused by NHC failure and can also be used alone, with strong applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0028] Figure 1 is a schematic flow chart of the NHC noise adaptive estimation method provided by the present invention; Figure 2 is a flow chart of the NHC lateral velocity noise regression analysis provided by the present invention; Figure 3 is a schematic flow chart of the variational Bayesian filtering method provided by the present invention; Figure 4 is a flow chart of the Ga-St VBAKF algorithm provided by the present invention; Figure 5 is a schematic structural diagram of the electronic device provided by the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0029] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions in the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of them. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present invention without creative efforts belong to the scope of protection of the present invention.

[0030] In view of the limitations of the existing technology, the present invention proposes a method for adaptively estimating the initial value of the NHC lateral velocity noise based on multiple linear regression and a variational Bayesian filtering algorithm (Ga-St VBAKF) of Gaussian-student T distribution based on NHC pseudo-velocity measurement noise modeling. Among them, the former is an auxiliary method for the latter Ga-St VBAKF algorithm.

[0031] Figure 1 It is a schematic flowchart of the NHC noise adaptive estimation method provided by the embodiments of the present invention, as Figure 1 shown, including: Step 101: Obtain vehicle experiment reference data, GNSS data, INS data, and ODO data; Step 102: Use the vehicle experiment reference data, the GNSS data, the INS data, and the ODO data to establish a binary regression analysis model for the NHC lateral velocity noise; Step 103: Based on the binary regression analysis model, establish an NHC / ODO / INS Kalman filter model; Step 104: Determine the adjustment value of the initial value of the NHC lateral velocity noise by a preset turning detection algorithm, and output the NHC observation noise covariance matrix.

[0032] Specifically, the method for adaptively estimating the initial value of the NHC lateral velocity noise based on multiple linear regression proposed by the embodiments of the present invention is implemented as follows: Step 1: Obtain the experimental reference data and perform post-processing to obtain the vehicle lateral velocity in the b system y and the heading angle difference between epochs , and obtain GNSS, INS, and OD data. The experimental equipment uses a high-precision navigation and positioning device Novatel SPAN-CPT and a low-cost integrated multi-sensor module. The experimental reference data includes the position, speed, and attitude reference values of the vehicle at each epoch. The GNSS data includes information such as position, satellite signal strength, and timestamp; the INS data includes information such as angular velocity and acceleration; the ODO data includes the forward position increment and speed information of the vehicle.

[0033] Step 2: Establish a binary regression analysis model based on experimental data. Based on the existing problem model, this step requires obtaining the weighting factors and constant coefficients of the regression model for this section of data, and conducting a credibility demonstration of the regression model to determine the adjustment range of the error adaptive factor.

[0034] Step 3: Establish a Kalman filter model, namely the NHC / OD / INS combined model.

[0035] Step 4: Determine whether to adjust the initial value of the NHC lateral velocity noise through the existing turning detection algorithm.

[0036] Among them, in Step 1, the microprocessor is connected to the GNSS receiver, inertial navigation unit, and odometer through the serial port, serial peripheral interface, and timer respectively to obtain GNSS, INS, and ODO data. The experimental reference data includes the position, speed, and attitude reference values of the vehicle at each epoch. The GNSS data includes information such as position, satellite signal strength, and timestamp; the INS data includes information such as angular velocity and acceleration; the ODO data includes the forward position increment and speed information of the vehicle.

[0037] The binary regression analysis model in Step 2 is established as follows: (1) Among them, is the NHC lateral velocity noise, is the weighting factor of the forward speed and heading angle error, is the constant coefficient, is the compensation adaptive factor. The evaluation indexes of the regression model include the mean square error, the goodness-of-fit test index of the fitting residuals, and the goodness of fit. As shown in Figure 2 , among them, the mean square error should be less than 0.01, the goodness-of-fit test index of the fitting residuals should be greater than 0.05, that is, there is a 95% significant level that it conforms to the normal distribution. The closer the goodness of fit is to 1, the better the regression fitting effect. The error adaptive factor should be adjusted within the range of [-0.15, 0.2].

[0038] In Step 3, first construct the system state equation and observation equation as follows, (2) In the formula, , are the state vectors of the system at time k and time k-1 respectively, represents the state one-step transition matrix from time k-1 to time k, is the matrix related to the noise, is the observed value at time k, is the observation matrix at time k, is the system noise, is the observation noise. Among them and are white noise and are uncorrelated with each other. Secondly, construct the observation noise covariance matrix as follows, (3) wherein, represents the speed measurement noise term of the odometer, respectively represent the NHC noise terms, where the former is the adaptive estimation term.

[0039] Figure 3 is a schematic flow chart of the variational Bayesian filtering method provided by the embodiment of the present invention. As Figure 3 shown, it includes: Step 201: Obtain filtering parameters and initialize the filtering parameters; Step 202: Perform standard Kalman filter time update and measurement update of variational Bayesian filtering Ga-St VBAKF of Gaussian-student T distribution; Step 203: Adopt a variational Bayesian method to perform parameter posterior approximation; Step 204: Update the NHC observation noise covariance matrix; Step 205: If it is determined that the preset number of iterations has been reached, wait for the next filtering moment; otherwise, perform the Ga-StVBAKF measurement update again.

[0040] Specifically, as Figure 4 shown, the variational Bayesian filtering algorithm of Gaussian-student T distribution based on NHC pseudo velocity measurement noise modeling proposed by the embodiment of the present invention specifically includes the following implementation steps: Step 1: Filtering parameter initialization, including the state vector, the state one-step transition matrix, the error covariance matrix, and the NHC observation noise covariance matrix. The detailed content is as follows: Select a suitable system state vector. For a low-cost MEMS IMU, due to large random errors, the modeling of the scale factor error not only has limited improvement on the filtering performance, but also increases the calculation amount. Therefore, the vector selected for the GNSS / INS integrated navigation filtering model is 15-dimensional, including the position error, speed error, attitude error, zero bias errors of the gyroscope and accelerometer of the integrated navigation. Specifically: (4) wherein, respectively represent the position error, speed error, and attitude error of the integrated navigation, respectively represent the zero bias errors of the gyroscope and accelerometer.

[0041] Construct the system state equation: (5) In the formula, , are the state vectors of the system at time k and k-1 respectively, represents the state one-step transition matrix from k-1 to k, is a matrix related to noise, is the system noise.

[0042] At the same time, estimate the time transition matrix Constructed as (6) where, is a three-dimensional identity matrix, is the specific force in the n system, and are the correlation times of the gyroscope and accelerometer biases respectively, and are the scale factors of the gyroscope and accelerometer respectively.

[0043] Construct the system observation equation: (7) In the formula, is the observed value at time k, is the observation matrix at time k, is the predicted value of the state vector, is the observation noise. Among them, the observation matrices of the three Kalman filter models are respectively expressed as: Observation matrix when estimating simultaneously Constructed as (8) where, is an identity matrix of dimension 3, is a zero matrix of dimension 3, is the transition matrix from the body frame to the navigation frame, the angular velocity of the body frame relative to the navigation frame.

[0044] Step 2: Standard Kalman filter time update and Ga-St VBAKF measurement update.

[0045] The standard Kalman filter time update includes: (9) (10) In the formula, is the state value of the one-step prediction, is the optimal estimated value of the state at time k-1, is the state covariance matrix of the one-step prediction, is the optimal estimated value of the state covariance at time k-1, is the system noise covariance matrix at time k-1.

[0046] The measurement update content of the Ga-St VBAKF includes the following: (11) Where is the iterative value of the -th Kalman filter gain, are the iterative value of the -th optimal estimation covariance matrix and the one-step prediction covariance matrix respectively, is the observation matrix, is the -th optimal iterative value of the noise covariance matrix, is the observation value at time k.

[0047] Step 3: Posterior approximation of parameters based on the variational Bayesian method.

[0048] The expectation of the auxiliary random variable at the -th time is determined according to the Gamma prior distribution as follows: (12) Where represents the trace of the matrix, and thus is updated as follows: (13) Similarly, is updated as follows, (14) Step 4: The NHC noise covariance matrix adaptive estimation should be adjusted and estimated at each epoch according to Step 4 of the NHC noise adaptive estimation method.

[0049] Figure 5 Illustrates a schematic diagram of the physical structure of an electronic device, such as Figure 5As shown in the figure, the electronic device may include: a processor 510, a communications interface 520, a memory 530, and a communication bus 540. Among them, the processor 510, the communications interface 520, and the memory 530 communicate with each other through the communication bus 540. The processor 510 may call logic instructions in the memory 530 to execute the NHC noise adaptive estimation method, which includes: obtaining vehicle experiment reference data, GNSS data, INS data, and ODO data; using the vehicle experiment reference data, the GNSS data, the INS data, and the ODO data to establish a binary regression analysis model for NHC lateral velocity noise; based on the binary regression analysis model, establishing an NHC / ODO / INS Kalman filter model; determining an adjustment value for the initial value of the NHC lateral velocity noise by a preset turning detection algorithm, and outputting an NHC observation noise covariance matrix.

[0050] Or execute the variational Bayesian filtering method, which includes: obtaining filtering parameters and initializing the filtering parameters; performing standard Kalman filter time update and measurement update of variational Bayesian filtering Ga-St VBAKF of Gaussian-student T distribution; using the variational Bayesian method for posterior approximation of parameters; updating the NHC observation noise covariance matrix; if it is determined that the preset number of iterations has been reached, waiting for the next filtering moment, otherwise performing the Ga-St VBAKF measurement update again.

[0051] In addition, when the logic instructions in the above-mentioned memory 530 are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The foregoing storage medium includes: various media such as USB flash drives, mobile hard disks, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), magnetic disks, or optical discs that can store program codes.

[0052] On the other hand, the present invention also provides a non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements the NHC noise adaptive estimation method provided by the above-mentioned various methods. The method includes: acquiring vehicle experiment reference data, GNSS data, INS data, and ODO data; using the vehicle experiment reference data, the GNSS data, the INS data, and the ODO data to establish a binary regression analysis model for NHC lateral velocity noise; based on the binary regression analysis model, establishing an NHC / ODO / INS Kalman filter model; determining an adjustment value for the initial value of the NHC lateral velocity noise by a preset turning detection algorithm, and outputting an NHC observation noise covariance matrix.

[0053] Or execute the variational Bayesian filtering method, which includes: acquiring filtering parameters and initializing the filtering parameters; performing standard Kalman filter time update and measurement update of variational Bayesian filtering Ga-St VBAKF of Gaussian-student T distribution; adopting the variational Bayesian method to perform parameter posterior approximation; updating the NHC observation noise covariance matrix; if it is determined that a preset number of iterations has been reached, wait for the next filtering moment, otherwise perform the Ga-St VBAKF measurement update again.

[0054] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed to multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art can understand and implement it without creative labor.

[0055] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, and of course also by hardware. Based on this understanding, the above technical solution, in essence, or the part that contributes to the prior art can be embodied in the form of a software product. The computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0056] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An NHC noise adaptive estimation method, characterized in that Including: Obtain vehicle experiment reference data, GNSS data, INS data, and ODO data; Utilize the vehicle experiment reference data, the GNSS data, the INS data, and the ODO data to establish a binary regression analysis model for NHC lateral velocity noise; Based on the binary regression analysis model, establish an NHC / ODO / INS Kalman filter model; Determine the adjustment value of the initial value of the NHC lateral velocity noise by a preset turning detection algorithm, and output the NHC observation noise covariance matrix.

2. The NHC noise adaptive estimation method according to claim 1, characterized in that Obtain vehicle experiment reference data, GNSS data, INS data, and ODO data, including: The vehicle experiment reference data includes the position, speed, and attitude reference values of the vehicle at each epoch, and post-process the vehicle experiment reference data to obtain the vehicle lateral velocity in the b coordinate system and the heading angle difference between epochs; The GNSS data includes position, satellite signal strength, and timestamp; The INS data includes angular velocity and acceleration; The ODO data includes the forward position increment and speed information of the vehicle.

3. The NHC noise adaptive estimation method according to claim 1, wherein Utilize the vehicle experiment reference data, the GNSS data, the INS data, and the ODO data to establish a binary regression analysis model for NHC lateral velocity noise, including: Among them, is the NHC lateral velocity noise, is the weighting factor of the forward velocity and the heading angle error, is a constant coefficient, is the compensation adaptive factor; Evaluate the performance of the binary regression analysis model through regression model evaluation indicators, and the regression model evaluation indicators include mean square error, goodness-of-fit residual normality test indicator, and coefficient of determination.

4. The NHC noise adaptive estimation method according to claim 1, characterized in that Based on the binary regression analysis model, establish an NHC / ODO / INS Kalman filter model, including: Construct a system state equation and an observation equation: Among them, and are the state vectors of the system at time k and time k - 1 respectively, represents the one-step state transition matrix from time k - 1 to time k, is a matrix related to noise, is the observation value at time k, is the observation matrix at time k, is the system noise, is the observation noise, where and are white noises and are uncorrelated with each other; Construct an observation noise covariance matrix: Among them, represents the odometer speed measurement noise term, respectively represent the NHC noise terms, where the former is the adaptive estimation term.

5. A variational Bayesian filtering method, based on the NHC noise adaptive estimation method according to any one of claims 1 to 4, characterized in that, Including: Obtain filtering parameters and initialize the filtering parameters; Perform standard Kalman filter time update and Gaussian-Student's T distribution variational Bayesian filter Ga-St VBAKF measurement update; Adopt the variational Bayesian method for parameter posterior approximation; Update the NHC observation noise covariance matrix; If it is determined that the preset number of iterations has been reached, wait for the next filtering moment, otherwise perform the Ga-St VBAKF measurement update again.

6. The NHC noise adaptive estimation method according to claim 5, characterized in that Obtain filtering parameters and initialize the filtering parameters, including: Initialize the state vector, state one-step transition matrix, error covariance matrix, system state noise variance matrix, system noise driving matrix, and NHC observation noise covariance matrix.

7. The NHC noise adaptive estimation method according to claim 5, characterized in that Perform standard Kalman filter time update and Ga-St VBAKF measurement update, including: The standard Kalman filter time update includes: Wherein, is the state value of one-step prediction, is the optimal state estimation value at time k-1, is the state covariance matrix of one-step prediction, is the optimal state covariance estimation value at time k-1, is the system noise covariance matrix at time k-1; The Ga-St VBAKF measurement update includes: Among them, is the iterative value of the th Kalman filter gain, are respectively the iterative value of the th optimal estimation covariance matrix and the one-step prediction covariance matrix, is the observation matrix, is the th optimal iterative value of the noise covariance matrix, is the observed value at time k.

8. The NHC noise adaptive estimation method according to claim 5, characterized in that Adopt the variational Bayesian method for parameter posterior approximation, including: wherein, is the expectation of a Bernoulli random variable proposed for quantitatively distinguishing between good NHC observations and NHC failures, and is defined as follows: Mixed probability Set according to the NHC failure degree, the expectation of the auxiliary random variable at the th time Determined according to the Gamma prior distribution as follows: Among them, represents the trace of the matrix, and thus is updated as follows: Similarly, The update is as follows: 。 9. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the NHC noise adaptive estimation method according to any one of claims 1 to 4 or the variational Bayesian filtering method according to any one of claims 5 to 8.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the NHC noise adaptive estimation method according to any one of claims 1 to 4 or the variational Bayesian filtering method according to any one of claims 5 to 8.

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