Improved AEKF algorithm for integrated navigation under GNSS imperfect conditions

Abstract

This application belongs to the field of navigation technology, specifically disclosing an integrated navigation method for improving the AEKF algorithm under GNSS incomplete conditions. The method includes performing the following operations in each filtering cycle of the AEKF algorithm: determining the prior state estimate for the current filtering cycle based on the state transition matrix and the state vector from the previous filtering cycle (the state vector is constructed based on the receiver's position, velocity, and clock error); determining the prior error covariance estimate for the current filtering cycle based on the state noise variance matrix and the error covariance matrix from the previous filtering cycle; correcting the observation matrix and measurement noise variance matrix based on the dynamic weighting coefficients of GNSS and Loran C; and obtaining the Kalman gain for the current filtering cycle based on the corrected observation matrix and measurement noise variance matrix, and updating the prior estimate. This application can improve the overall performance of the integrated navigation system under GNSS incomplete conditions.

Description

Technical Field

[0001] This application belongs to the field of navigation technology, and more specifically, relates to a combined navigation method for improving the AEKF algorithm under the condition of incomplete GNSS. Background Technology

[0002] Global Navigation Satellite Systems (GNSS) are widely used in the field of navigation. For GNSS, receivers typically need to effectively acquire satellite signals from four or more satellites in order to perform positioning.

[0003] However, GNSS is susceptible to obstruction or interference in complex scenarios such as urban canyons, tunnels, and areas with strong electromagnetic interference. For example, in scenarios like urban canyons, forest canopy obstruction, shallow tunnel entrances and exits, and mountain valleys, the receiver's line of sight to satellites is blocked, leading to the loss of some satellite signals. For example, portable jammers and localized industrial electromagnetic radiation can suppress some satellite signals, making them unretrievable by the receiver. For example, in high-latitude regions and remote mountainous areas with weak satellite coverage, satellite signal strength is low, and some satellites are easily judged as "lost" due to insufficient signal-to-noise ratio. For example, in scenarios like urban building complexes and water surfaces, direct satellite signals are obstructed, with only weak reflected signals remaining, making it impossible for the receiver to effectively lock onto some satellites, resulting in signal loss. For GNSS, if the receiver can effectively acquire satellite signals from N satellites, and 3. In this case, the situation is called GNSS incompleteness.

[0004] How to achieve effective navigation under incomplete GNSS conditions is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0005] In view of the shortcomings of the prior art, the purpose of this application is to achieve effective navigation under the condition of incomplete GNSS.

[0006] To achieve the above objectives, in a first aspect, this application provides an integrated navigation method for improving the AEKF algorithm under GNSS incomplete conditions, including performing the following operations in each filtering cycle of the AEKF algorithm:

[0007] Based on the state transition matrix and the state vector of the previous filtering cycle, the prior state estimate for the current filtering cycle is determined. The state vector is constructed based on the receiver's position, receiver speed, and GNSS receiver clock error.

[0008] Based on the state noise variance matrix and the error covariance matrix of the previous filtering cycle, the prior estimate of the error covariance in the current filtering cycle is determined.

[0009] Based on the dynamic weighting coefficients of the GNSS observation matrix and the Loran C observation matrix, the observation matrix and the measurement noise variance matrix are corrected to obtain the corrected observation matrix and the corrected measurement noise variance matrix. The dynamic weighting coefficients are determined based on the GNSS pseudorange observation information entropy and the Loran C time difference observation information entropy.

[0010] Based on the prior estimation of error covariance, the corrected observation matrix, and the corrected measurement noise variance matrix, the Kalman gain for the current filtering period is obtained.

[0011] Based on the Kalman gain under the current filtering cycle, update the state prior estimate and the error covariance prior estimate, and obtain the state vector and error covariance matrix under the current filtering cycle.

[0012] In one possible implementation, the dynamic weighting coefficients are obtained using the following formula:

[0013] ;

[0014] ;

[0015] ;

[0016] ;

[0017] in, This represents the entropy of GNSS pseudorange observation information. This represents the entropy of Loran C time difference observation information. and for and The normalization result, Represents the dynamic weighting coefficients of the GNSS observation matrix. This represents the dynamic weighting coefficients of the Loran C observation matrix.

[0018] In one possible implementation, the prior state estimate for the current filtering cycle is determined based on the state transition matrix and the state vector from the previous filtering cycle. This includes determining the prior state estimate for the current filtering cycle using the following formula:

[0019] ;

[0020] in, Indicates the first State prior estimation over one filtering cycle Represents the state transition matrix. Indicates the first The state vector under each filtering cycle.

[0021] In one possible implementation, the prior estimate of the error covariance for the current filtering cycle is determined based on the state noise variance matrix and the error covariance matrix of the previous filtering cycle. This includes determining the prior estimate of the error covariance for the current filtering cycle using the following formula:

[0022] ;

[0023] in, Indicates the first Prior estimation of error covariance over one filtering cycle Represents the state transition matrix. Indicates the first Error covariance matrix under each filtering period Represents the process noise driving matrix. This represents the state noise variance matrix.

[0024] In one possible implementation, the formula used to correct the observation matrix is ​​as follows:

[0025] ;

[0026] in, This represents the corrected observation matrix. Represents the dynamic weighting coefficients of the GNSS observation matrix. This represents the dynamic weighting coefficients of the Loran C observation matrix. This represents the original observation matrix.

[0027] In one possible implementation, the formula used to correct the measurement noise variance matrix is ​​as follows:

[0028] ;

[0029] in, This represents the corrected measurement noise variance matrix. Represents the dynamic weighting coefficients of the GNSS observation matrix. This represents the dynamic weighting coefficients of the Loran C observation matrix. This represents the original GNSS measurement noise variance matrix. This represents the original measurement noise variance matrix of Loran C.

[0030] In one possible implementation, the Kalman gain for the current filtering period is obtained based on the prior estimate of the error covariance, the corrected observation matrix, and the corrected measurement noise variance matrix. This includes obtaining the Kalman gain for the current filtering period using the following formula:

[0031] ;

[0032] in, Indicates the first Kalman gain over one filtering cycle Indicates the first Prior estimation of error covariance over one filtering cycle This represents the corrected observation matrix. This represents the corrected measurement noise variance matrix.

[0033] In one possible implementation, based on the Kalman gain under the current filtering cycle, the state prior estimate and the error covariance prior estimate are updated to obtain the state vector and error covariance matrix under the current filtering cycle, including obtaining the state vector and error covariance matrix under the current filtering cycle through the following formulas:

[0034] ;

[0035] ;

[0036] in, Indicates the first The state vector under each filtering cycle Indicates the first State prior estimation over one filtering cycle Indicates the first Kalman gain over one filtering cycle For the first Combined observation vector under each filtering period It is a nonlinear observation function;

[0037] Indicates the first Error covariance matrix under each filtering period Represents the identity matrix. Indicates the first The observed Jacobian matrix under each filtering period Indicates the first Prior estimation of error covariance over one filtering cycle Indicates the first Kalman gain over one filtering cycle This represents the corrected observation matrix. This represents the corrected measurement noise variance matrix.

[0038] In a second aspect, this application provides an electronic device, including: a memory and one or more processors; the memory is coupled to the one or more processors, the memory is used to store computer program code, the computer program code including computer instructions; the one or more processors invoke the computer instructions to cause the electronic device to perform the method described in the first aspect or any possible implementation of the first aspect.

[0039] Thirdly, this application provides a computer-readable storage medium including instructions that, when executed on an electronic device, cause the electronic device to perform the method described in the first aspect or any possible implementation thereof.

[0040] Overall, the technical solutions conceived in this application have the following beneficial effects compared with the prior art:

[0041] (1) Under the AEKF framework, the combined navigation of GNSS and Loran C can improve navigation accuracy and stability under the condition of incomplete GNSS, and achieve effective navigation in complex scenarios.

[0042] (2) Based on the information entropy weighted improvement AEKF model to achieve information fusion in integrated navigation, the information entropy weight is introduced into the AEKF framework. By dynamically quantifying the observation quality of each data source, the weight is adaptively allocated, ensuring fault tolerance and fusion accuracy, and improving the overall performance of the integrated navigation system under the condition of incomplete GNSS. Attached Figure Description

[0043] Figure 1 This is a schematic diagram of the static experimental northward position error provided in an embodiment of this application;

[0044] Figure 2 This is a schematic diagram of the static experimental eastward position error provided in the embodiments of this application;

[0045] Figure 3 This is a schematic diagram illustrating the changing trends of signal weights and information entropy based on the improved AEKF algorithm in a static experiment provided in this application embodiment;

[0046] Figure 4 This is a dynamic test trajectory diagram provided in the embodiments of this application;

[0047] Figure 5 This is a schematic diagram of the dynamic test northward position error provided in an embodiment of this application;

[0048] Figure 6 This is a schematic diagram of the eastward position error of the dynamic test provided in the embodiments of this application;

[0049] Figure 7This is a schematic diagram illustrating the changing trends of signal weights and information entropy based on the improved AEKF algorithm in the dynamic experiment provided in this application embodiment;

[0050] Figure 8 This is a schematic diagram illustrating the changing trends of signal weights and information entropy when signals are blocked, as provided in an embodiment of this application.

[0051] Figure 9 This is a flowchart illustrating the integrated navigation method of the improved AEKF algorithm under incomplete GNSS conditions provided in the embodiments of this application.

[0052] Figure 10 This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0053] To facilitate a clearer understanding of the various embodiments of this application, some relevant background knowledge will be introduced as follows.

[0054] The Loran C long-range hyperbolic radio navigation system possesses strong anti-interference capabilities, no single point of failure, and wide coverage, complementing the characteristics of GNSS technology. Combined GNSS and Loran C navigation has become an important means of improving navigation accuracy and stability in complex scenarios.

[0055] Information fusion algorithms are the core of integrated navigation systems, with Kalman filtering and its improved versions being the main technical paths for achieving integrated navigation information fusion. The standard Kalman filter was initially applied to high-precision navigation scenarios in aerospace and aviation, achieving high-precision state estimation under error-free conditions by constructing linear state equations for receiver position, velocity, and other states. However, in actual GNSS and Loran C integrated navigation, processes such as GNSS pseudorange observation and Loran C time delay measurement exhibit nonlinear characteristics, making the standard Kalman filter difficult to adapt to these real-world features. The Extended Kalman Filter (EKF) was subsequently applied to navigation fusion. EKF linearizes the nonlinear system through a first-order Taylor series expansion. However, during the conversion of GNSS and Loran C from nonlinear to linear, linearization errors tend to accumulate in scenarios with low data source redundancy and abrupt changes in observation noise, ultimately leading to decreased filtering accuracy or even divergence.

[0056] To compensate for the insufficient robustness of the Unscented Kalman Filter (EKF), nonlinear filtering algorithms such as the Unscented Kalman Filter (UKF) and the Cumulative Kalman Filter (CKF) have been proposed and applied in the field of navigation fusion. Among them, the UKF avoids the linearization error of the EKF by selecting the probability density distribution of the approximate state at the sigma point. The CKF improves the accuracy of numerical integration based on the third-order spherical radial volume criterion and is widely used in combined navigation fusion after the nonlinear correction of the time delay error of the Loran C Additional Quadratic Phase Factor (ASF), further reducing the estimation bias of the nonlinear system. Both the UKF and CKF suffer from high computational complexity, making them difficult to adapt to low-computing-power navigation scenarios such as vehicle-mounted and portable terminals, and they still do not overcome the limitations of unknown and time-varying noise characteristics in the navigation environment.

[0057] To address the time-varying noise statistics caused by GNSS multipath and Loran C ASF disturbances, the Adaptive Extended Kalman Filter (AEKF) adjusts the process noise or observation noise covariance matrix in real time through information covariance matching, residual weighting, and variance component estimation. This adapts to the dynamic changes in data source reliability and effectively suppresses filter divergence in occlusion scenarios. While AEKF addresses the robustness issues of traditional EKF models to some extent by adjusting the filter noise covariance in real time, the observation quality of GNSS and Loran C information dynamically changes with the environment. Furthermore, under incomplete observation conditions (such as GNSS signal interruptions or abrupt changes in Loran C propagation delay errors), traditional AEKF lacks differentiated weight allocation for different data sources, resulting in significant deficiencies in its fault tolerance and fusion accuracy.

[0058] To overcome the above-mentioned shortcomings, this application provides an integrated navigation method with an improved AEKF algorithm under GNSS incomplete conditions, which can achieve effective navigation in complex scenarios, ensure fault tolerance and fusion accuracy, and improve the overall performance of the integrated navigation system under GNSS incomplete conditions.

[0059] 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.

[0060] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0061] In the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more, for example, multiple processing units means two or more processing units, multiple elements means two or more elements, etc.

[0062] The embodiments of this application are described below with reference to the accompanying drawings.

[0063] Figure 9 This is a flowchart illustrating the integrated navigation method for the improved AEKF algorithm under incomplete GNSS conditions provided in this application. Figure 9 As shown, the method includes performing the following operations in each filtering cycle of the AEKF algorithm: steps S101 to S105.

[0064] Step S101, based on the state transition matrix (denoted as...) ) and the state vector of the previous filtering cycle (denoted as ) ), determine the prior state estimate under the current filtering period (denoted as ). ), state vector (denoted as ) is based on the receiver's location (denoted as ), receiver speed (denoted as ) and GNSS receiver clock bias (denoted as It was constructed by ).

[0065] When the current filtering cycle is the first filtering cycle, the state vector of the previous filtering cycle is the preset initial state vector.

[0066] In one possible implementation, the prior state estimate for the current filtering period is determined by the following formula:

[0067] ;

[0068] in, Indicates the first The state prior estimate under each filtering cycle (as the current filtering cycle) Represents the state transition matrix. Indicates the first The state vector under each filtering cycle (as the previous filtering cycle).

[0069] Step S102, based on the state noise variance matrix (denoted as...) , It is constructed based on the standard deviation of position state noise, the standard deviation of velocity state noise, and the standard deviation of receiver clock noise, and the error covariance matrix of the previous filtering cycle (denoted as...). ), determine the prior estimate of the error covariance under the current filtering period ( ).

[0070] When the current filtering cycle is the first filtering cycle, the error covariance matrix of the previous filtering cycle is the preset initial error covariance matrix.

[0071] In one possible implementation, the prior estimate of the error covariance for the current filtering period is determined by the following formula:

[0072] ;

[0073] in, Indicates the first Prior estimation of error covariance over 1 filter cycle (as the current filter cycle), Represents the state transition matrix. Indicates the first The error covariance matrix over each filtering cycle (as the previous filtering cycle) Represents the process noise driving matrix. This represents the state noise variance matrix.

[0074] Step S103, based on the dynamic weighting coefficients of the GNSS observation matrix (denoted as...) The dynamic weighting coefficients of the Loran C observation matrix (denoted as ) and the Loran C observation matrix. ), corrected observation matrix (GNSS observation matrix denoted as The observation matrix of Loran C is denoted as ) and measurement noise variance matrix (denoted as ), to obtain the corrected observation matrix (denoted as ) and the corrected measurement noise variance matrix (denoted as ) The dynamic weighting coefficient is based on the GNSS pseudorange observation information entropy (denoted as...). ) and Loran C time difference observation information entropy (denoted as It is certain.

[0075] In one possible implementation, the dynamic weighting coefficients are obtained using the following formula:

[0076] ;

[0077] ;

[0078] ;

[0079] ;

[0080] in, This represents the entropy of GNSS pseudorange observation information. This represents the entropy of Loran C time difference observation information. and for and The normalization result, Represents the dynamic weighting coefficients of the GNSS observation matrix. This represents the dynamic weighting coefficients of the Loran C observation matrix.

[0081] In one possible implementation, the formula used to correct the observation matrix is ​​as follows:

[0082] ;

[0083] in, This represents the corrected observation matrix. Represents the dynamic weighting coefficients of the GNSS observation matrix. This represents the dynamic weighting coefficients of the Loran C observation matrix. This represents the original observation matrix.

[0084] In one possible implementation, the formula used to correct the measurement noise variance matrix is ​​as follows:

[0085] ;

[0086] in, This represents the corrected measurement noise variance matrix. Represents the dynamic weighting coefficients of the GNSS observation matrix. This represents the dynamic weighting coefficients of the Loran C observation matrix. This represents the original GNSS measurement noise variance matrix. This represents the original measurement noise variance matrix of Loran C.

[0087] Step S104: Based on the prior estimation of error covariance, the corrected observation matrix, and the corrected measurement noise variance matrix, obtain the Kalman gain (denoted as ) for the current filtering period. ).

[0088] In one possible implementation, the Kalman gain for the current filtering period is obtained using the following formula:

[0089] ;

[0090] in, Indicates the first Kalman gain over 1 filter cycle (as the current filter cycle), Indicates the first Prior estimation of error covariance over one filtering cycle This represents the corrected observation matrix. This represents the corrected measurement noise variance matrix.

[0091] Step S105: Based on the Kalman gain in the current filtering period, update the state prior estimate and the error covariance prior estimate to obtain the state vector (i.e., the state posterior estimate, denoted as ) in the current filtering period. ) and the error covariance matrix (i.e., the posterior estimate of the error covariance, denoted as ) ).

[0092] In one possible implementation, the state vector and error covariance matrix for the current filtering cycle are obtained using the following formula:

[0093] ;

[0094] ;

[0095] in, Indicates the first The state vector under each filtering cycle (as the current filtering cycle), Indicates the first State prior estimation over one filtering cycle Indicates the first Kalman gain over one filtering cycle For the first Combined observation vector under each filtering period It is a nonlinear observation function;

[0096] Indicates the first The error covariance matrix under each filtering cycle (as the current filtering cycle), Represents the identity matrix. Indicates the first The observed Jacobian matrix under each filtering period Indicates the first Prior estimation of error covariance over one filtering cycle Indicates the first Kalman gain over one filtering cycle This represents the corrected observation matrix. This represents the corrected measurement noise variance matrix.

[0097] Understandably, within the AEKF framework, combining GNSS and Loran C navigation can improve navigation accuracy and stability even with incomplete GNSS coverage, enabling effective navigation in complex scenarios.

[0098] In information fusion based on the information entropy weighted improved AEKF model for integrated navigation, information entropy weighting is introduced into the AEKF framework. By dynamically quantifying the observation quality of each data source, the weights are adaptively allocated, ensuring fault tolerance and fusion accuracy, and improving the overall performance of the integrated navigation system under incomplete GNSS conditions.

[0099] Example 1.

[0100] The following example, using a Loran C system with 3 satellites (the receiver can effectively acquire the satellite signals of the 3 satellites) and 1 master station and 2 slave stations under incomplete GNSS conditions, as Example 1, illustrates the combined navigation method of the improved AEKF algorithm under incomplete GNSS conditions provided in this application.

[0101] Example 1 includes the following parts: (1) constructing the system state equation, (2) constructing the observation equation, (3) constructing the noise variance matrix, (4) obtaining the observation information entropy, (5) dynamic weight allocation based on information entropy, and (6) information fusion based on the information entropy weighted improvement AEKF model to achieve integrated navigation.

[0102] (1) Construct the system state equations.

[0103] For a Loran C integrated navigation scenario with 3 satellites (the receiver can effectively acquire satellite signals from all 3 satellites), 1 master station and 2 slave stations, the receiver's position, velocity, and clock bias are selected as the core state variables, and the discretized system state equations are constructed as follows:

[0104] ;

[0105] Where: state vector subscript Indicates the first Each filter cycle, subscript Indicates the first One filter cycle. This represents the three-dimensional position of the receiver in the Earth-centered Earth-fixed (ECEF) coordinate system. For three-dimensional velocity, For GNSS receiver clock bias; The state transition matrix is ​​constructed using a constant-rate model (CV) that satisfies:

[0106] ;

[0107] in, For the filter update period, for The identity matrix, for The identity matrix, for The zero matrix, for The zero matrix, for The zero matrix; The process noise driving matrix is ​​matched with the dimension of the state transition matrix; The state noise vector follows a zero-mean Gaussian distribution, and its statistical properties are characterized by the state noise variance matrix.

[0108] (2) Construct the observation equation.

[0109] (2-1) The GNSS pseudorange observation equation is as follows:

[0110] For the 3 satellites in GNSS (numbered) Its pseudorange observation equation is:

[0111] ;

[0112] in, Represents pseudorange observations. This represents the three-dimensional position of the receiver in the Earth-centered Earth-fixed (ECEF) coordinate system. For the first The position of each satellite in the ECEF coordinate system (calculated from ephemeris data). The speed of electromagnetic wave propagation in a vacuum (speed of light) , The first in GNSS The clock bias of each satellite (corrected by broadcast ephemeris); The first in GNSS The pseudorange observation noise of the satellite includes multipath error, ionospheric / tropospheric delay residuals, etc.

[0113] (2-2) The Loran C time difference observation equation is as follows:

[0114] For the Loran C station layout with one main station (M) and two auxiliary stations (S1, S2), the time difference method is used to construct the observation equations (eliminating common errors from receiver clock bias and ionospheric / tropospheric delay):

[0115] The receiver location is The main stage location is The secondary station (S1) is located at... The secondary station (S2) is located at... The actual distances from the receiver to the Roland C main station (M), secondary station (S1), and secondary station (S2) are as follows:

[0116] ;

[0117] ;

[0118] ;

[0119] The time difference observation equations for the main station (M) and the secondary station (S1) are as follows:

[0120] ;

[0121] The time difference observation equations for the main station (M) and the secondary station (S2) are as follows:

[0122] ;

[0123] in, The time difference observations between the main station (M) and the secondary station (S1) The time difference between the main station (M) and the secondary station (S2) is the observed value, where c is the speed of light. The clock difference between the secondary station (S1) and the primary station (M) is as follows: Measurement error from the main station (M) to the auxiliary station (S1) (ground wave interference, noise, etc.); The clock difference between the secondary station (S2) and the primary station (M) is as follows: Measurement error from the main station (M) to the auxiliary station (S1) (ground wave interference, noise, etc.).

[0124] (3) Construct the noise variance matrix.

[0125] (3-1) Measurement noise variance matrix ( )as follows:

[0126] The measurement noise variance matrix characterizes the statistical properties of GNSS and Loran C observation noise and is constructed in a block diagonal matrix form:

[0127] ;

[0128] in, For GNSS pseudorange measurement noise submatrix; This is the Loran C time difference measurement noise submatrix.

[0129] (3-2) State noise variance matrix ( )as follows:

[0130] The state noise variance matrix characterizes the statistical properties of the system process noise, matches the dimension of the state vector, and is constructed in a block diagonal matrix form:

[0131] ;

[0132] in, Here is the standard deviation of the position noise, and the standard deviation of the velocity noise is... GNSS receiver clock bias noise standard deviation Loran C receiver clock noise standard deviation .

[0133] (4) Obtain the entropy of the observation information.

[0134] (4-1) GNSS pseudorange observation information entropy ( ).

[0135] No. pseudorange observation sequence of satellites ( (where the sliding window length is 10-20 filter cycles). First, calculate the... The probability density function of pseudorange observations of satellites The kernel density estimation method was used for fitting:

[0136] ;

[0137] in For Gaussian kernel function, For bandwidth parameters;

[0138] Based on the Shannon entropy definition, the first The information entropy of pseudorange observations from the satellite is:

[0139] ;

[0140] The combined pseudorange observation information entropy of the three satellites is:

[0141] ;

[0142] The overall uncertainty of pseudorange data from the three satellites was quantified, especially when GNSS is affected by obstruction or multipath propagation. Significantly increased when the signal stabilizes. It remains at a low level.

[0143] (4-2) Loran C time difference observation information entropy ( ).

[0144] Two time difference observation sequences for Loran C, consisting of one main station and two secondary stations. , Similarly, calculate the first... Group Probability density function of time difference observations :

[0145] ;

[0146] in, For Gaussian kernel function, For bandwidth parameters;

[0147] Based on Shannon's definition of entropy, we define its information entropy:

[0148] ;

[0149] Loran C's overall time difference observation entropy is:

[0150] ;

[0151] The overall uncertainty of Loran C time difference data from one master station and two slave stations was quantified, influenced by ASF time delay disturbances and ground wave transmission characteristics. It will dynamically adjust according to changes in terrain or ionosphere.

[0152] It is understandable that information entropy, as a core indicator for measuring information uncertainty, can effectively reflect the observation quality of the data source. Its characteristics are: the larger the error, the higher the information entropy, and the smaller the corresponding weight. In the above (4) to obtain the observation information entropy, for the preprocessed GNSS and Loran C data, an information entropy calculation model is constructed. The data uncertainty is quantified by calculating the information entropy value of each data source (where the higher the information entropy value, the lower the data credibility and the stronger the uncertainty), so as to realize the data source credibility quantification based on information entropy.

[0153] (5) Dynamic weight allocation based on information entropy.

[0154] Traditional AEKF uses fixed empirical weights to fuse GNSS and Loran C data. This application constructs dynamic weight coefficients through information entropy normalization.

[0155] Normalize the information entropy of GNSS and Loran-C:

[0156] ;

[0157] ;

[0158] Define the dynamic weighting coefficients of the GNSS observation matrix Dynamic weighting coefficients of the Loran C observation matrix :

[0159] ;

[0160] ;

[0161] satisfy This refers to an adaptive allocation that reduces the weight of high-entropy data sources and increases the weight of low-entropy data sources. When three GNSS signals are blocked... When it increases, Automatically lower, Corresponding improvement; when Loran C is affected by ASF disturbances leading to When it increases, reduce, promote.

[0162] It is understandable that in the above (5) dynamic weight allocation based on information entropy, a dynamic weighted allocation algorithm is designed to map the information entropy value to the fusion weight coefficient, so as to realize the dynamic allocation of high confidence data with high weight and low confidence / incomplete data with low weight.

[0163] (6) Information fusion is performed based on the information entropy weighted improvement AEKF model to achieve integrated navigation.

[0164] (6-1) Prior estimation of the system state and error covariance matrix is ​​performed as follows:

[0165] State prediction: Based on the system state equations, perform prior state estimation.

[0166] ;

[0167] in, Indicates the first State prior estimation over one filtering cycle Represents the state transition matrix. Indicates the first The state vector under each filtering cycle;

[0168] Prediction of prior error covariance matrix:

[0169] ;

[0170] in, Indicates the first Prior estimation of error covariance over 1 filter cycle (as the current filter cycle), Represents the state transition matrix. Indicates the first The error covariance matrix over each filtering cycle (as the previous filtering cycle) Represents the process noise driving matrix. This represents the state noise variance matrix.

[0171] (6-2) Information entropy calculation and weight allocation: Based on the GNSS pseudorange observations and Loran C time difference observations within the sliding window, calculate... , And solve for the dynamic weight coefficients. , Correct the observation matrix and the measurement noise variance matrix.

[0172] Corrected observation matrix ( )for:

[0173] ;

[0174] in, , As the observation matrix for GNSS and Loran C, the weighting coefficients directly affect the observation matrix, realizing differentiated weighting of heterogeneous data sources.

[0175] Corrected measurement noise variance matrix ( )for:

[0176] ;

[0177] in, The original GNSS measurement noise variance matrix ( A diagonal matrix, where the diagonal lines represent the pseudorange noise variance of a single satellite. Loran C's original measurement noise variance matrix ( (Diagonal matrix, where the diagonal lines represent the variance of single-channel time difference noise).

[0178] (6-3) Kalman Gain Update: Calculate the Kalman gain by combining the corrected observation matrix and the measurement noise matrix.

[0179] .

[0180] (6-4) Based on the updated Kalman gain, the posterior estimation of the system state and error covariance matrix is ​​performed as follows:

[0181] State update: Based on the combined observation equation, the posterior state estimation is completed.

[0182] ;

[0183] in, For the first The combined observation vector under each filtering period (composed of GNSS pseudorange observations and Loran C time difference observations) It is a nonlinear observation function;

[0184] Error covariance matrix update:

[0185] ;

[0186] in, Represents the identity matrix. for The first-order partial derivative matrix, Indicates the first The observed Jacobian matrix under each filtering period can be obtained by solving... The first-order partial derivative matrix, using the first-order partial derivative matrix as... .

[0187] (6-5) Iteration loop: The iteration of the next filtering cycle is executed as (6-1), (6-2), (6-3) and (6-4) above.

[0188] It is understandable that in the above (6) information fusion based on information entropy weighting to improve the AEKF model to achieve integrated navigation, information entropy weighting is introduced into the AEKF framework. By dynamically quantifying the observation quality of each data source, the weights are adaptively allocated, ensuring fault tolerance and fusion accuracy, and improving the overall performance of the integrated navigation system under the condition of incomplete GNSS.

[0189] Example 2: The integrated navigation method of the improved AEKF algorithm under incomplete GNSS conditions provided in this application is illustrated by simulation experiments.

[0190] To verify the effectiveness of the information entropy-weighted improved AEKF model in a low-redundancy Loran C scenario with 3 satellites, 1 master station, and 2 slave stations, a combined navigation simulation system was built using Python. The longitude, latitude, and altitude errors of the receiver were quantitatively analyzed using RMSE (Root Mean Square Error). The RMSE was primarily used as the quantitative indicator of positioning accuracy, and the positioning error was analyzed from three directions: longitude, latitude, and altitude.

[0191] A combined navigation system based on an information entropy-weighted improved AEKF model was simulated using Python in a Loran C low-redundancy scenario with 3 satellites, 1 master station, and 2 slave stations. The simulation time was 800 seconds. The GNSS sampling period was 1 second with a standard deviation of 3 m, and the Loran C sampling period was 4.5 seconds with a standard deviation of 30 m. The simulation results for the northward and eastward position errors in the static experiment are as follows: Figure 1 , Figure 2 As shown.

[0192] from Figure 1 It can be seen that within 0~800s, the maximum positional error in the north direction is no more than 32m, and the maximum positional error in the east direction is no more than 22m.

[0193] The changes in channel weights and information entropy in integrated navigation based on the information entropy-weighted improved AEKF model in a Loran C low-redundancy scenario with 3 satellites, 1 master station, and 2 slave stations are as follows: Figure 3 The figure shows the trends in weight and information entropy changes of three GNSS signals and two Loran C signals within 0-100s during a static experiment. Since the accuracy of Loran C is much lower than that of GNSS, a basic weight allocation was performed based on the accuracy settings of Loran C and GNSS, with a weight allocation ratio of 1:9. After the basic weight allocation, each channel was divided according to the signal strength of each signal-to-noise ratio signal. Figure 3 It can be clearly seen that the smaller the information entropy, the greater the weight.

[0194] The dynamic experiment set up straight-line and turning motion trajectories from 0 to 800 seconds, and the trajectory diagram is as follows. Figure 4 As shown, Figure 4 The solid blue line in the middle represents the actual trajectory. Figure 4 The red dashed line represents the estimated trajectory. GNSS sampling time is 1 second with a standard deviation of 3 meters. Loran C sampling time is 4.5 seconds with a standard deviation of 30 meters. The base weights are set in the same way as in the static experiment.

[0195] like Figure 4 As shown, the position error is significant when turning at the starting position of the motion, and smaller when stationary and moving at a constant speed in a straight line.

[0196] Northward position error and eastward position error, as follows Figure 5 , Figure 6 As shown.

[0197] from Figure 5 and Figure 6 It can be seen that the northward and eastward position errors in the dynamic test are both within the range of 0 to 60m. During uniform linear motion, the northward and eastward position errors are within the range of 0 to 20m. When turning, the northward and eastward position errors suddenly increase to about 40m or 60m.

[0198] Dynamic experimental information entropy weighting, such as Figure 7 As shown, the weights of each observed signal and the information entropy are inversely proportional.

[0199] To further simulate and improve the algorithm, we assume signal suppression during the 20-60s period of uniform linear motion of the GNSS pseudorange 2 within the 0-100s range. The changes in signal weights and information entropy, as well as the position error curves, are shown below. Figure 8As shown, when the GNSS pseudorange 2 signal is suppressed, the weight of GNSS pseudorange 2 decreases and its information entropy increases, while the weights of GNSS pseudorange 1 and GNSS pseudorange 3 increase, and their information entropy decreases. When one of the signals is suppressed, the position error range increases to 30m~90m. The improved algorithm can quickly adjust the weight ratios of other signals when one of the signals is suppressed.

[0200] Based on the methods in the above embodiments, this application provides an electronic device, such as... Figure 10 As shown, the electronic device may include a processor 810, a communications interface 820, a memory 830, and a communication bus 840, wherein the processor 810, the communications interface 820, and the memory 830 communicate with each other through the communication bus 840. The processor 810 can call logical instructions in the memory 830 to execute the methods in the above embodiments.

[0201] Furthermore, the logical instructions in the aforementioned memory 830 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the 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 to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application.

[0202] Based on the methods in the above embodiments, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0203] Based on the methods in the above embodiments, this application provides a computer program product that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0204] It is understood that the processor in the embodiments of this application can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. A general-purpose processor can be a microprocessor or any conventional processor.

[0205] The method steps in this application embodiment can be implemented in hardware or by a processor executing software instructions. The software instructions can consist of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, portable hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can reside in an ASIC.

[0206] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0207] It is understood that the various numerical designations used in the embodiments of this application are merely for the convenience of description and are not intended to limit the scope of the embodiments of this application.

[0208] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A method for improving an AEKF algorithm for integrated navigation under GNSS imperfection, characterized in that, This includes performing the following operations in each filtering cycle of the AEKF algorithm: Based on the state transition matrix and the state vector of the previous filtering cycle, the prior state estimate for the current filtering cycle is determined. The state vector is constructed based on the receiver's position, receiver speed, and GNSS receiver clock error. Based on the state noise variance matrix and the error covariance matrix of the previous filtering cycle, the prior estimate of the error covariance in the current filtering cycle is determined. Based on the dynamic weighting coefficients of the GNSS observation matrix and the Loran C observation matrix, the observation matrix and the measurement noise variance matrix are corrected to obtain the corrected observation matrix and the corrected measurement noise variance matrix. The dynamic weighting coefficients are determined based on the GNSS pseudorange observation information entropy and the Loran C time difference observation information entropy. Based on the prior estimation of error covariance, the corrected observation matrix, and the corrected measurement noise variance matrix, the Kalman gain for the current filtering period is obtained. Based on the Kalman gain under the current filtering cycle, update the state prior estimate and the error covariance prior estimate, and obtain the state vector and error covariance matrix under the current filtering cycle.

2. The integrated navigation method of claim 1, wherein, The dynamic weighting coefficients are obtained using the following formula: ； ； ； ； in, This represents the entropy of GNSS pseudorange observation information. This represents the entropy of Loran C time difference observation information. and for and The normalization result, Represents the dynamic weighting coefficients of the GNSS observation matrix. This represents the dynamic weighting coefficients of the Loran C observation matrix.

3. The integrated navigation method of claim 1, wherein, The determination of the prior state estimate for the current filtering cycle based on the state transition matrix and the state vector from the previous filtering cycle includes determining the prior state estimate for the current filtering cycle using the following formula: ； wherein, denotes the state prior estimate at the filter cycle, denotes the state transition matrix, denotes the state vector at the filter cycle.

4. The integrated navigation method of claim 1, wherein, The step of determining the prior estimate of the error covariance in the current filtering cycle based on the state noise variance matrix and the error covariance matrix of the previous filtering cycle includes determining the prior estimate of the error covariance in the current filtering cycle using the following formula: ； in, Indicates the first Prior estimation of error covariance over one filtering cycle Represents the state transition matrix. Indicates the first Error covariance matrix under each filtering period Represents the process noise driving matrix. This represents the state noise variance matrix.

5. The integrated navigation method of claim 1, wherein, The formula used to correct the observation matrix is ​​as follows: ； wherein, denotes the modified observation matrix, denotes a dynamic weight coefficient of the GNSS observation matrix, denotes a dynamic weight coefficient of the Loran C observation matrix, denotes the original observation matrix.

6. The integrated navigation method of claim 1, wherein, The formula used to correct the measurement noise variance matrix is ​​as follows: ； in, This represents the corrected measurement noise variance matrix. Represents the dynamic weighting coefficients of the GNSS observation matrix. This represents the dynamic weighting coefficients of the Loran C observation matrix. This represents the original GNSS measurement noise variance matrix. This represents the original measurement noise variance matrix of LoranC.

7. An electronic device, characterized in that, include: Memory and one or more processors; The memory is coupled to the one or more processors, and the memory is used to store computer program code, the computer program code including computer instructions; The one or more processors invoke the computer instructions to cause the electronic device to perform the method as described in any one of claims 1-6.

8. A computer-readable storage medium comprising instructions, characterized in that: When the instructions are executed on an electronic device, the electronic device causes the electronic device to perform the method as described in any one of claims 1-6.

Images