Gravity matching secondary filter method and device based on noise distribution assumption

Abstract

The application relates to a gravity matching secondary filtering method and device based on noise distribution assumption. The method comprises the following steps: constructing a measurement model of secondary filtering by combining inertial navigation results and taking an estimated value of a position after primary filtering matching and an estimated value of a position error as measurements; approximating the measurement model of secondary filtering to a student distribution based on noise distribution assumption; rewriting a posterior probability density function of the student distribution and a one-step prediction posterior probability density function based on a theory that the posterior probability density function of the student distribution can be regarded as a mixture of multiple Gaussian distribution posterior probability density functions; approximately decomposing a to-be-estimated state space model in a layered Gaussian distribution form after rewriting; solving an approximate posterior probability density function obtained according to a variational Bayesian method, and obtaining a position result after secondary filtering. The method can improve the robustness of a gravity matching result.

Description

Technical Field

[0001] This application relates to the field of gravity matching technology for inertial navigation, and in particular to a gravity matching two-stage filtering method and apparatus based on noise distribution assumptions. Background Technology

[0002] Inertial / gravity matching integrated navigation primarily aims to improve navigation accuracy by combining gravity matching results with inertial navigation. A marine inertial / gravity matching integrated navigation system comprises the following components: an inertial navigation system, a gravity anomaly map, a gravity measurement system, a gravity matching algorithm, and an integrated navigation algorithm. For a marine vehicle, the complete workflow of inertial / gravity matching integrated navigation is as follows: First, a gravity matching map is prepared. Gravity anomaly information within the matching area is collected using mapping satellites, survey vessels, high-order spherical harmonic models of the global gravity field, and survey aircraft. The gravity anomaly map is prepared at a mapping center and assembled onto the vehicle. When the vehicle enters the matching area, it queries the gravity anomaly map based on its own position information to obtain the query value. Simultaneously, the gravity measurement system acquires gravity anomaly information, and both sets of information are input into the gravity anomaly matching algorithm to obtain the matched position estimate. The matching result is then used as an observation value and input into the integrated navigation algorithm to update the navigation parameters of the inertial navigation system, resulting in a corrected navigation result. In addition to position information, velocity and attitude are also updated, thus achieving passive autonomous navigation. As can be seen from the above workflow, the positional accuracy of inertial / gravity matching integrated navigation is related to the following four factors: the initial positional accuracy of the vehicle itself, the resolution and accuracy of the gravity anomaly map, the accuracy of the gravity measurement system, and the performance of the inertial / gravity matching integrated navigation algorithm.

[0003] However, traditional gravity matching methods each have their limitations. For example, batch processing algorithms cannot meet the requirements of marine inertial / gravity matching integrated navigation applications in terms of data output frequency and real-time performance. Traditional sequential filtering algorithms have high requirements for noise distribution, and the thick-tailed distribution of measurement noise that may exist in the marine gravity measurement environment will lead to a decrease in the performance of traditional sequential filtering algorithms designed for Gaussian noise distribution. Conventional robust filtering algorithms, including the advanced robust filtering algorithm RSTKF, have made adaptive improvements to the case of non-Gaussian thick-tailed noise by describing noise with a Student's distribution. However, since they do not take into account the specific situation of the transformation from gravity measurement results to matching position results and then to integrated navigation results in gravity matching applications, they are prone to poor matching results. Summary of the Invention

[0004] Therefore, it is necessary to provide a gravity matching two-stage filtering method and apparatus based on noise distribution assumptions that can improve the robustness of gravity matching results in addressing the above-mentioned technical problems.

[0005] A gravity-matched two-stage filtering method based on noise distribution assumptions, the method comprising:

[0006] The gravity information measured by the gravimeter and the gravity extracted from the gravity anomaly map are matched by a first-level filter using a point group filtering algorithm to obtain the estimated value of the position and the estimated value of the position error.

[0007] The estimated position and the estimated position error are used as measurements, and a measurement model for two-stage filtering is constructed by combining the inertial navigation results. Based on the noise distribution assumption, the measurement model for two-stage filtering is approximated as a Student's distribution, and the likelihood posterior probability density function and the one-step prediction posterior probability density function of the Student's distribution are calculated.

[0008] The theory that the posterior probability density function based on the Student's distribution can be regarded as a mixture of the posterior probability density functions of multiple Gaussian distributions can be used to rewrite the apparent posterior probability density function and the one-step prediction posterior probability density function to obtain the state space model to be estimated in the form of a hierarchical Gaussian distribution.

[0009] The state-space model to be estimated, in the form of a hierarchical Gaussian distribution, is approximated by decomposition to obtain an approximate posterior probability density function. The approximate posterior probability density function is then solved using the variational Bayesian method to obtain the position result after secondary filtering.

[0010] In one embodiment, the estimated position and the estimated position error are used as measurements, and a two-stage filtering measurement model is constructed by combining the inertial navigation results, including:

[0011] Using the estimated position and position error as measurements, and combining them with the inertial navigation results, a two-stage filtering measurement model is constructed.

[0012]

[0013] in, This is the state estimation result of the first-level filter; X = [φ E φ N φ U δv E δv N δλ δL] T , φ E , φ N and φ U These are the attitude error angles in the east, north, and sky directions, respectively, δV E and δV N These represent the eastward velocity error and the northward velocity error, respectively; δλ and δL represent the eastward position error and the northward position error, respectively; n k It is an estimate of the position error of the first-stage filter; This is the measurement matrix.

[0014] In one embodiment, the measurement model for the second-level filter is approximated as a Student's distribution based on noise distribution assumptions, including:

[0015] Based on the noise distribution assumption, the measurement model of the second-level filter is approximated by a Student's distribution.

[0016] P(u k )=ST(u k ;0,r k ,v)

[0017] Among them, ST(u k ;0,r k Let v) represent the posterior probability density function of the measurement noise distribution with a mean of 0, a nominal covariance matrix of rk, and a degree of freedom parameter v.

[0018] In one embodiment, calculating the likelihood posterior probability density function and the one-step prediction posterior probability density function of the Student's distribution includes:

[0019] The likelihood a posteriori probability density function of the Student's distribution is calculated as follows:

[0020]

[0021] in, The mean is H k X k The nominal covariance matrix of the measured noise is r k The measured value of the measurement noise with degree of freedom parameter v is Time state value The posterior probability density function of the student's distribution;

[0022] The one-step prediction posterior probability density function of the Student's distribution is calculated as follows:

[0023]

[0024] in, This indicates that the mean is μ. k The scale matrix is ​​Σ k The measured value of the degree of freedom parameter ω Time state value The posterior probability density function of the student's distribution.

[0025] In one embodiment, the theory that the posterior probability density function based on the Student's distribution can be viewed as a mixture of multiple Gaussian posterior probability density functions rewrites the apparent posterior probability density function and the one-step prediction posterior probability density function to obtain a hierarchical Gaussian distribution form of the state space model to be estimated, including:

[0026] The theory that the posterior probability density function based on the Student's distribution can be viewed as a mixture of posterior probability density functions of multiple Gaussian distributions rewrites the apparent posterior probability density function and the one-step prediction posterior probability density function, resulting in a hierarchical Gaussian distribution form of the state-space model to be estimated.

[0027]

[0028]

[0029]

[0030]

[0031] in, and P(ξ) k () represents the expansion of the posterior probability density function for one-step prediction. This represents the measurements from the initial time up to time k-1. Let k represent the position estimate at time k. Σ represents the prediction result at time k-1. k Let ξ represent the scaling matrix. k and λ k Describe the different auxiliary random variables at time k. Indicates having shape parameters and rate parameters ξ k The gamma posterior probability density function, where v and ω represent different degrees of freedom parameters. and P(λ) k () represents the expansion of the similar a posteriori probability density function. This represents the measurement at time k. Indicates having shape parameters and rate parameters λ k The gamma posterior probability density function.

[0032] In one embodiment, the state-space model to be estimated, in the form of a hierarchical Gaussian distribution, is approximated by decomposition to obtain an approximate posterior probability density function, including:

[0033] An approximate decomposition of the state-space model to be estimated, in the form of a hierarchical Gaussian distribution, yields the approximate posterior probability density function as follows:

[0034]

[0035] Here, q() is the approximate posterior probability density function.

[0036] In one embodiment, the approximate posterior probability density function is solved using the variational Bayesian method to obtain the second-level filtered position result, including:

[0037] The approximate posterior probability density function is solved using the variational Bayesian method. The approximate posterior probability density function is obtained by minimizing the KLD between the approximate posterior probability density function and the true posterior probability density function. The transformed approximate posterior probability density function is then obtained. After a pre-set number of iterations at the fixed point, the transformed approximate posterior probability density function is updated to obtain the approximate posterior probability density function of the position estimate.

[0038] The approximate posterior probability density function of the location estimate is solved to obtain the location result after secondary filtering.

[0039] In one embodiment, the approximate posterior probability density function is solved using the variational Bayesian method. The approximate posterior probability density function is obtained by minimizing the KLD between the approximate and true posterior probability density functions, resulting in the transformed approximate posterior probability density function, including:

[0040]

[0041] Where q() is the approximate posterior probability density function. Let ξ represent the position estimate at time k. k and λ k Let Σ represent the different auxiliary random variables at time k. k Represents the scale matrix. KLD represents the KLD loss function, which is an approximate posterior probability density function.

[0042] In one embodiment, after N iterations at a fixed point, the transformed approximate posterior probability density function is updated to obtain the approximate posterior probability density function of the location estimate, including:

[0043] After N iterations at a fixed point, the transformed approximate posterior probability density function is updated to obtain the approximate posterior probability density function of the position estimate.

[0044]

[0045] in, This represents the prediction result obtained at time k after N fixed-point iterations. This represents the prediction error covariance matrix obtained after N fixed-point iterations. P represents the prediction result at time k. k|k Let represent the prediction error covariance matrix, and q() be the approximate posterior probability density function.

[0046] A gravity-matched two-stage filter device based on noise distribution assumptions, the device comprising:

[0047] The first-level filtering and matching module is used to perform first-level filtering and matching on the gravity information measured by the gravimeter and the gravity extracted from the gravity anomaly map according to the point group filtering algorithm, so as to obtain the estimated value of the position and the estimated value of the position error.

[0048] The measurement model approximation module is used to construct a two-stage filtered measurement model by taking the estimated position and the estimated position error as measurements and combining them with the inertial navigation results. Based on the noise distribution assumption, the two-stage filtered measurement model is approximated as a Student's distribution, and the likelihood posterior probability density function and the one-step prediction posterior probability density function of the Student's distribution are calculated.

[0049] The function rewriting module is used to rewrite the apparent posterior probability density function and the one-step prediction posterior probability density function based on the theory that the posterior probability density function of the Student's distribution can be regarded as a mixture of multiple Gaussian distribution posterior probability density functions, so as to obtain the state space model to be estimated in the form of a hierarchical Gaussian distribution.

[0050] The second-level filtering module is used to approximate the decomposition of the state space model to be estimated in the form of a hierarchical Gaussian distribution, and obtain the approximate posterior probability density function. The approximate posterior probability density function is then solved using the variational Bayesian method to obtain the position result after the second-level filtering.

[0051] The aforementioned gravity-matched two-stage filtering method and apparatus based on noise distribution assumptions, in this application, first constructs a measurement model for the two-stage filtering, and then uses a robust Student's distribution Kalman filter, assuming a Student's distribution, to handle the case of heavy-tailed noise distribution. Adjusting the two-stage filtering based on the noise distribution assumptions improves the robustness of the point-group filtering algorithm, thereby increasing the accuracy of the two-stage filtering. The theory that the posterior probability density function based on the Student's distribution can be considered as a mixture of multiple Gaussian posterior probability density functions rewrites the apparent posterior probability density function and the one-step prediction posterior probability density function into a hierarchical Gaussian distribution form of the state-space model to be estimated. By transforming the state estimation problem of a linear state-space model with heavy-tailed processes and measurement noise into a state estimation problem of a hierarchical Gaussian state-space model based on Student's distribution, and solving the hierarchical Gaussian state-space model state estimation problem, accurate filtering results can be obtained. When estimating the position results... First, the hierarchical Gaussian distribution of the state space model to be estimated is approximated to obtain an approximate posterior probability density function. Then, the variational Bayesian method is used to obtain the transformed approximate posterior probability density function by minimizing the KLD between the approximate posterior probability density function and the true posterior probability density function. After a pre-set number of iterations at a fixed point, the transformed approximate posterior probability density function is updated to obtain the approximate posterior probability density function of the position estimate. The approximate posterior probability density function of the position estimate is solved to obtain the position result after secondary filtering. By continuously updating the approximate posterior probability density function, the accuracy of the solved position result after secondary filtering is greatly improved. Attached Figure Description

[0052] Figure 1 This is a flowchart illustrating a gravity-matched two-stage filtering method based on noise distribution assumptions in one embodiment.

[0053] Figure 2 This is a structural block diagram of a gravity-matched two-stage filter device based on noise distribution assumptions in one embodiment. Detailed Implementation

[0054] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0055] In one embodiment, such as Figure 1 As shown, a gravity-matched two-stage filtering method based on noise distribution assumptions is provided, including the following steps:

[0056] Step 102: Perform a first-level filtering match between the gravity information measured by the gravimeter and the gravity extracted from the gravity anomaly map according to the point group filtering algorithm to obtain the estimated value of the position and the estimated value of the position error.

[0057] In gravity matching, point group filtering algorithm is usually used for first-level filtering matching. However, due to the complexity of the marine environment and the nonlinear relationship between gravity maps and measured gravity, the noise statistics of the first-level filtering result may not meet the Gaussian normal distribution based on the characteristics of the point group filtering algorithm. In this case, the second-level filtering result may be affected, or even cause the filter to diverge.

[0058] Step 104: Using the estimated position and the estimated position error as measurements, and combining them with the inertial navigation results, construct a measurement model for the second-level filtering. Based on the noise distribution assumption, approximate the measurement model of the second-level filtering as a Student's distribution, and calculate the likelihood posterior probability density function and the one-step prediction posterior probability density function of the Student's distribution.

[0059] This application constructs a measurement model for a two-stage filter by using estimated position and position error as measurements, combined with pre-acquired inertial navigation results. Then, a robust Student's distribution Kalman filter, assuming a Student's distribution for noise distribution, is used to handle the case of heavy-tailed noise. The two-stage filter is adjusted based on the noise distribution assumption to improve the robustness of the point-group filtering algorithm, thereby increasing the accuracy of the two-stage filter.

[0060] Step 106: Based on the theory that the posterior probability density function of the Student's distribution can be regarded as a mixture of the posterior probability density functions of multiple Gaussian distributions, the apparent posterior probability density function and the one-step prediction posterior probability density function are rewritten to obtain the state space model to be estimated in the form of a hierarchical Gaussian distribution.

[0061] The theory that the posterior probability density function based on the Student's distribution can be regarded as a mixture of posterior probability density functions of multiple Gaussian distributions rewrites the apparent posterior probability density function and the one-step prediction posterior probability density function into a hierarchical Gaussian distribution form of the state space model to be estimated. By transforming the state estimation problem of the linear state space model with heavy-tailed processes and measurement noise into the state estimation problem of the hierarchical Gaussian state space model based on the Student's distribution, accurate filtering results can be obtained by solving the state estimation problem of the hierarchical Gaussian state space model.

[0062] Step 108: Approximately decompose the state space model to be estimated in the form of a hierarchical Gaussian distribution to obtain the approximate posterior probability density function; solve the approximate posterior probability density function according to the variational Bayesian method to obtain the position result after secondary filtering.

[0063] To estimate the location, the state-space model to be estimated, in the form of a hierarchical Gaussian distribution, needs to be approximated to obtain an approximate posterior probability density function. Then, the variational Bayesian method is used to obtain the transformed approximate posterior probability density function by minimizing the KLD between the approximate and true posterior probability density functions. After a pre-set number of iterations at a fixed point, the transformed approximate posterior probability density function is updated to obtain the approximate posterior probability density function of the location estimate. Solving the approximate posterior probability density function of the location estimate yields the second-level filtered location result. By continuously updating the approximate posterior probability density function, the accuracy of the solved second-level filtered location result is significantly improved. The process of solving the approximate posterior probability density function of the location estimate is existing technology and will not be elaborated upon in this application.

[0064] In the aforementioned gravity-matched two-stage filtering method based on noise distribution assumptions, this application first constructs a measurement model for the two-stage filtering, and then uses a robust Student's distribution Kalman filter, which assumes a Student's distribution, to handle the case of heavy-tailed noise distribution. Adjusting the two-stage filtering based on the noise distribution assumption improves the robustness of the point-group filtering algorithm, thereby increasing the accuracy of the two-stage filtering. The theory that the posterior probability density function based on the Student's distribution can be considered as a mixture of multiple Gaussian posterior probability density functions rewrites the apparent posterior probability density function and the one-step prediction posterior probability density function into a hierarchical Gaussian distribution form of the state-space model to be estimated. By transforming the state estimation problem of a linear state-space model with heavy-tailed processes and measurement noise into a state estimation problem of a hierarchical Gaussian state-space model based on the Student's distribution, and solving the hierarchical Gaussian state-space model state estimation problem, accurate filtering results can be obtained. When estimating the position results... First, the hierarchical Gaussian distribution of the state space model to be estimated is approximated to obtain an approximate posterior probability density function. Then, the variational Bayesian method is used to obtain the transformed approximate posterior probability density function by minimizing the KLD between the approximate posterior probability density function and the true posterior probability density function. After a pre-set number of iterations at a fixed point, the transformed approximate posterior probability density function is updated to obtain the approximate posterior probability density function of the position estimate. The approximate posterior probability density function of the position estimate is solved to obtain the position result after secondary filtering. By continuously updating the approximate posterior probability density function, the accuracy of the solved position result after secondary filtering is greatly improved.

[0065] In one embodiment,

[0066] Using the estimated position and position error as measurements, and combining them with the inertial navigation results, a two-stage filtering measurement model is constructed, including:

[0067] Using the estimated position and position error as measurements, and combining them with the inertial navigation results, a two-stage filtering measurement model is constructed.

[0068]

[0069] in, This is the state estimation result of the first-level filter; X = [φ E φ N φ U δv E δv N δλ δL] T , φ E , φ N and φ U These are the attitude error angles in the east, north, and sky directions, respectively, δV E and δV N These represent the eastward velocity error and the northward velocity error, respectively; δλ and δL represent the eastward position error and the northward position error, respectively; n k It is an estimate of the position error of the first-stage filter; This is the measurement matrix.

[0070] In one embodiment, the measurement model for the second-level filter is approximated as a Student's distribution based on noise distribution assumptions, including:

[0071] Based on the noise distribution assumption, the measurement model of the second-level filter is approximated by a Student's distribution.

[0072] P(u k )=ST(u k ;0,r k ,v)

[0073] Among them, ST(u k ;0,r k (v) represents the nominal covariance matrix of the measurement noise with a mean of 0, and r. k The posterior probability density function of the measurement noise with degree of freedom parameter v is the Student's distribution.

[0074] In one embodiment, calculating the likelihood posterior probability density function and the one-step prediction posterior probability density function of the Student's distribution includes:

[0075] The likelihood a posteriori probability density function of the Student's distribution is calculated as follows:

[0076]

[0077] in, The mean is H k X k The nominal covariance matrix of the measured noise is rk The measured value of the measurement noise with degree of freedom parameter v is Time state value The posterior probability density function of the student's distribution;

[0078] The one-step prediction posterior probability density function of the Student's distribution is calculated as follows:

[0079]

[0080] in, This indicates that the mean is μ. k The scale matrix is ​​Σ k The measured value of the degree of freedom parameter ω Time state value The posterior probability density function of the student's distribution.

[0081] In one embodiment, the theory that the posterior probability density function based on the Student's distribution can be viewed as a mixture of multiple Gaussian posterior probability density functions rewrites the apparent posterior probability density function and the one-step prediction posterior probability density function to obtain a hierarchical Gaussian distribution form of the state space model to be estimated, including:

[0082] The theory that the posterior probability density function based on the Student's distribution can be viewed as a mixture of posterior probability density functions of multiple Gaussian distributions rewrites the apparent posterior probability density function and the one-step prediction posterior probability density function, resulting in a hierarchical Gaussian distribution form of the state-space model to be estimated.

[0083]

[0084]

[0085]

[0086]

[0087] in, and P(ξ) k () represents the expansion of the posterior probability density function for one-step prediction. This represents the measurements from the initial time up to time k-1. Let k represent the position estimate at time k. Σ represents the prediction result at time k-1. k Let ξ represent the scaling matrix. k and λ k Describe the different auxiliary random variables at time k. Indicates having shape parameters and rate parameters ξ kThe gamma posterior probability density function, where v and ω represent different degrees of freedom parameters. and P(λ) k () represents the expansion of the similar a posteriori probability density function. This represents the measurement at time k. Indicates having shape parameters and rate parameters λ k The gamma posterior probability density function.

[0088] In a specific embodiment, since the Student's distribution posterior probability density function (PDF) can be viewed as a mixture of multiple Gaussian distribution PDFs, one-step prediction... and likelihood It can be represented as:

[0089]

[0090]

[0091] Where N(x; μ, Σ) represents a Gaussian PDF with mean μ and covariance matrix Σ; G(.; α, β) represents a gamma PDF with shape parameter α and rate parameter β; ξ k and λ k It is an auxiliary random variable.

[0092] Equations (1) and (2) can be rewritten as a hierarchical Gaussian distribution form of the state space model to be estimated. By transforming the state estimation problem of the linear state space model with thick tails and measurement noise into the state estimation problem of the hierarchical Gaussian state space model based on Student's method, the position result after the second-level filtering can be solved according to the variational Bayesian method.

[0093] In one embodiment, the state-space model to be estimated, in the form of a hierarchical Gaussian distribution, is approximated by decomposition to obtain an approximate posterior probability density function, including:

[0094] An approximate decomposition of the state-space model to be estimated, in the form of a hierarchical Gaussian distribution, yields the approximate posterior probability density function as follows:

[0095]

[0096] Here, q() is the approximate posterior probability density function.

[0097] In one embodiment, the approximate posterior probability density function is solved using the variational Bayesian method to obtain the second-level filtered position result, including:

[0098] The approximate posterior probability density function is solved using the variational Bayesian method. The approximate posterior probability density function is obtained by minimizing the KLD between the approximate posterior probability density function and the true posterior probability density function. The transformed approximate posterior probability density function is then obtained. After a pre-set number of iterations at the fixed point, the transformed approximate posterior probability density function is updated to obtain the approximate posterior probability density function of the position estimate.

[0099] The approximate posterior probability density function of the location estimate is solved to obtain the location result after secondary filtering.

[0100] In one embodiment, the approximate posterior probability density function is solved using the variational Bayesian method. The approximate posterior probability density function is obtained by minimizing the KLD between the approximate and true posterior probability density functions, resulting in the transformed approximate posterior probability density function, including:

[0101]

[0102] Where q() is the approximate posterior probability density function. Let ξ represent the position estimate at time k. k and λ k Let Σ represent the different auxiliary random variables at time k. k Represents the scale matrix. KLD represents the KLD loss function, which is an approximate posterior probability density function.

[0103] In one embodiment, after N iterations at a fixed point, the transformed approximate posterior probability density function is updated to obtain the approximate posterior probability density function of the location estimate, including:

[0104] After N iterations at a fixed point, the transformed approximate posterior probability density function is updated to obtain the approximate posterior probability density function of the position estimate.

[0105]

[0106] in, This represents the prediction result obtained at time k after N fixed-point iterations. This represents the prediction error covariance matrix obtained after N fixed-point iterations. P represents the prediction result at time k. k|k Let represent the prediction error covariance matrix, and q() be the approximate posterior probability density function.

[0107] In a specific embodiment, after N iterations at the fixed point, q(ξ k ), q(Σ k) and q(λ k The approximate posterior PDF of ) can be updated to:

[0108]

[0109]

[0110]

[0111]

[0112] For equation (3), the mean and covariance matrix of the Gaussian PDF are respectively:

[0113]

[0114]

[0115] The corrected Kalman filter gain is:

[0116]

[0117] For equation (9), the corrected measurement noise covariance matrix and the corrected prediction error covariance matrix are respectively:

[0118]

[0119]

[0120] in,

[0121] For equation (4), the shape parameter and rate parameter of the gamma distribution PDF are respectively:

[0122]

[0123]

[0124] For equation (5), the degree-of-freedom parameters and the inverse scaling matrix are as follows:

[0125]

[0126]

[0127] in,

[0128] For equation (6), the shape parameter and rate parameter of the gamma distribution PDF are respectively:

[0129]

[0130]

[0131] in,

[0132] In summary, the corrected prediction error covariance matrix in equation (11) can be rewritten as:

[0133]

[0134] The tuning parameter τ∈[2,6].

[0135] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0136] In one embodiment, such as Figure 2 As shown, a gravity-matched two-stage filtering device based on noise distribution assumptions is provided, comprising: a first-stage filtering matching module 202, a measurement model approximation module 204, a function rewriting module 206, and a second-stage filtering module, wherein:

[0137] The first-level filtering and matching module 202 is used to perform first-level filtering and matching on the gravity information measured by the gravimeter and the gravity extracted from the gravity anomaly map according to the point group filtering algorithm, so as to obtain the estimated value of the position and the estimated value of the position error.

[0138] The measurement model approximation module 204 is used to construct a two-stage filtered measurement model by taking the estimated position and the estimated position error as measurements and combining them with the inertial navigation results. Based on the noise distribution assumption, the two-stage filtered measurement model is approximated as a Student's distribution, and the likelihood posterior probability density function and the one-step prediction posterior probability density function of the Student's distribution are calculated.

[0139] The function rewriting module 206 is used to rewrite the apparent posterior probability density function and the one-step prediction posterior probability density function based on the theory that the posterior probability density function of the Student's distribution can be regarded as a mixture of multiple Gaussian distribution posterior probability density functions, so as to obtain the state space model to be estimated in the form of a hierarchical Gaussian distribution.

[0140] The second-level filtering module 208 is used to approximate the decomposition of the state space model to be estimated in the form of a hierarchical Gaussian distribution to obtain an approximate posterior probability density function; the approximate posterior probability density function is solved according to the variational Bayesian method to obtain the position result after second-level filtering.

[0141] Specific limitations regarding the gravity-matched two-stage filtering device based on the noise distribution assumption can be found in the limitations of the gravity-matched two-stage filtering method based on the noise distribution assumption above, and will not be repeated here. Each module in the aforementioned gravity-matched two-stage filtering device based on the noise distribution assumption can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in hardware or independently of the processor in a computer device, or stored in software in the memory of a computer device, so that the processor can call and execute the operations corresponding to each module.

[0142] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0143] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A gravity-matched two-stage filtering method based on noise distribution assumptions, characterized in that, The method includes: The gravity information measured by the gravimeter and the gravity extracted from the gravity anomaly map are matched by a first-level filter using a point group filtering algorithm to obtain the estimated value of the position and the estimated value of the position error. The estimated position and the estimated position error are used as measurements, and a two-stage filtering measurement model is constructed by combining the inertial navigation results. Based on the noise distribution assumption, the two-stage filtering measurement model is approximated as a Student's distribution, and the likelihood posterior probability density function and the one-step prediction posterior probability density function of the Student's distribution are calculated. The theory that the posterior probability density function based on the Student's distribution can be regarded as a mixture of multiple Gaussian distribution posterior probability density functions is used to rewrite the apparent posterior probability density function and the one-step prediction posterior probability density function to obtain the state space model to be estimated in the form of a hierarchical Gaussian distribution. The state space model to be estimated in the form of a hierarchical Gaussian distribution is approximated by decomposition to obtain an approximate posterior probability density function; the approximate posterior probability density function is then solved using the variational Bayesian method to obtain the position result after secondary filtering. The estimated position and the estimated position error are used as measurements, and a two-stage filtering measurement model is constructed by combining the inertial navigation results, including: The estimated position and the estimated position error are used as measurements, and a two-stage filtering measurement model is constructed by combining the inertial navigation results. in, This is the state estimation result of the first-level filter; , express time, , and These are the attitude error angles in the east, north, and sky directions, respectively. and These are the eastward velocity error and the northward velocity error, respectively. and These are the eastward position error and the northward position error, respectively. It is an estimate of the position error of the first-stage filter; For measurement matrix; Based on the noise distribution assumption, the measurement model of the second-level filter is approximated as a Student's distribution, including: Based on the noise distribution assumption, the measurement model of the second-level filter is approximated by a Student's distribution. in, The nominal covariance matrix of the measurement noise, with a mean of 0, is: The degree of freedom parameters are The posterior probability density function of the Student's distribution of measurement noise; Calculating the likelihood posterior probability density function and the one-step prediction posterior probability density function of the Student's distribution includes: Calculate the likelihood a posteriori probability density function of the Student's distribution as follows: in, The mean is The nominal covariance matrix of the measured noise is The degree of freedom parameters are The measured value of the noise is Time state value The posterior probability density function of the student's distribution; The one-step prediction posterior probability density function of the Student's distribution is calculated as follows: in, This indicates that the mean is provided. The scale matrix is The degree of freedom parameters are Measurement values Time state value The posterior probability density function of the student's distribution.

2. The method according to claim 1, characterized in that, The theory that the posterior probability density function based on the Student's distribution can be viewed as a mixture of posterior probability density functions of multiple Gaussian distributions rewrites the apparent posterior probability density function and the one-step prediction posterior probability density function, resulting in a hierarchical Gaussian distribution form of the state-space model to be estimated, including: The theory that the posterior probability density function based on the Student's distribution can be viewed as a mixture of posterior probability density functions of multiple Gaussian distributions can be used to rewrite the apparent posterior probability density function and the one-step prediction posterior probability density function, resulting in a hierarchical Gaussian distribution form of the state-space model to be estimated. in, and To expand the posterior probability density function for one-step prediction, Indicates initial until Measurement of time, express Position estimate at time. express The prediction results for the time period, Represents the scale matrix, and express Auxiliary random variables that are different at different times, Indicates having shape parameters and rate parameters of The gamma posterior probability density function, and Representing different degrees of freedom parameters, and For the expansion of the similar a posteriori probability density function, express Measurement of time, Indicates having shape parameters and rate parameters of The gamma posterior probability density function.

3. The method according to claim 2, characterized in that, The estimated state-space model in the form of a hierarchical Gaussian distribution is approximated by decomposition to obtain an approximate posterior probability density function, including: The estimated state-space model in the form of a hierarchical Gaussian distribution is approximated by decomposition, yielding the approximate posterior probability density function as follows: in, It is an approximate posterior probability density function.

4. The method according to claim 1, characterized in that, The approximate posterior probability density function is solved using the variational Bayes method to obtain the position result after secondary filtering, including: The approximate posterior probability density function is solved using the variational Bayesian method. The approximate posterior probability density function is obtained by minimizing the KLD between the approximate posterior probability density function and the true posterior probability density function. The transformed approximate posterior probability density function is then obtained. After a pre-set number of iterations at the fixed point, the transformed approximate posterior probability density function is updated to obtain the approximate posterior probability density function of the position estimate. The approximate posterior probability density function of the location estimate is solved to obtain the location result after secondary filtering.

5. The method according to claim 4, characterized in that, The approximate posterior probability density function is solved using the variational Bayesian method. The approximate posterior probability density function is obtained by minimizing the KLD between the approximate and true posterior probability density functions, resulting in the transformed approximate posterior probability density function, including: in, It is an approximate posterior probability density function. express Position estimate at time. and express Auxiliary random variables that are different at different times, Represents the scale matrix, This is an approximate posterior probability density function. express Loss function.

6. The method according to claim 4, characterized in that, Iteration at fixed points Then, the transformed approximate posterior probability density function is updated to obtain the approximate posterior probability density function of the location estimate, including: Iteration at fixed points Then, the transformed approximate posterior probability density function is updated to obtain the approximate posterior probability density function of the location estimate. in, Represents the result after N fixed-point iterations The predicted results obtained at each time point, This represents the prediction error covariance matrix obtained after N fixed-point iterations. express The prediction results for the time period, This represents the prediction error covariance matrix. It is an approximate posterior probability density function.

7. A gravity-matched two-stage filter device based on noise distribution assumptions, characterized in that, The apparatus for performing the gravity-matched two-stage filtering method based on noise distribution assumptions as described in claim 1, the apparatus comprising: The first-level filtering and matching module is used to perform first-level filtering and matching on the gravity information measured by the gravimeter and the gravity extracted from the gravity anomaly map according to the point group filtering algorithm, so as to obtain the estimated value of the position and the estimated value of the position error. The measurement model approximation module is used to construct a two-stage filtered measurement model by taking the estimated value of the position and the estimated value of the position error as measurements and combining them with the inertial navigation results; based on the noise distribution assumption, the two-stage filtered measurement model is approximated as a Student's distribution, and the likelihood posterior probability density function and the one-step prediction posterior probability density function of the Student's distribution are calculated. The function rewriting module is used to rewrite the apparent posterior probability density function and the one-step prediction posterior probability density function based on the theory that the posterior probability density function of the Student's distribution can be regarded as a mixture of multiple Gaussian distribution posterior probability density functions, so as to obtain the state space model to be estimated in the form of a hierarchical Gaussian distribution. The second-level filtering module is used to approximate the decomposition of the hierarchical Gaussian distribution form of the state space model to be estimated, and obtain an approximate posterior probability density function; the approximate posterior probability density function is solved according to the variational Bayesian method to obtain the position result after second-level filtering.

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