GNSS / SINS (Global Navigation Satellite System / Strapdown Inertial Navigation System) integrated navigation filtering method based on minimum error entropy criterion

Abstract

The invention relates to a GNSS / SINS (Global Navigation Satellite System / Strapdown Inertial Navigation System) integrated navigation filtering method based on a minimum error entropy criterion, and belongs to the field of integrated navigation. The method comprises the following steps: firstly, establishing a discrete state equation and a measurement equation of a GNSS / SINS integrated navigation system, and further establishing an enhanced state equation of the integrated navigation system based on prior estimation information of a conventional Kalman filter; then establishing a minimum error entropy cost function of the GNSS / SINS integrated navigation system based on a minimum error entropy criterion, and solving an optimal closed-loop solution of the integrated navigation system; and finally, on the basis of a matrix inversion principle, constructing a minimum error entropy-based fixed-point iterative filtering method of the GNSS / SINS integrated navigation system so as to update a state and posteriori estimation of a covariance matrix of the state, and carrying out feedback correction on the SINS. The invention belongs to the field of aviation autonomous navigation, improves the robustness of a GNSS / SINS integrated navigation system in various non-Gaussian measurement noises, can provide high-precision position, speed and attitude information for an aircraft in a complex environment, and has important practical significance for aircraft navigation.

Description

Technical Field

[0001] The invention belongs to the field of aircraft autonomous navigation and relates to a GNSS / SINS combined navigation filtering method based on a minimum error entropy criterion. Background Art

[0002] The development of aviation vehicles occupies an important position in the military and civilian fields. As an important equipment on the aircraft, the navigation system can provide relevant motion parameters for the operation or control system of the aircraft, and plays an important role in the flight mission of the aircraft.

[0003] The Strapdown Inertial Navigation System (SINS) uses a digital platform. It is an autonomous navigation system that does not rely on any external equipment and does not radiate energy to the outside. It can determine the position, speed and attitude of the carrier. It has the characteristics of strong concealment and high information output frequency. It is widely used in various flight carriers. However, the navigation parameter error of SINS accumulates over time, which seriously affects the navigation accuracy. The Global Navigation Satellite System (GNSS) has the feature that the navigation error does not accumulate over time and is complementary to SINS. Therefore, the GNSS / SINS combined navigation system is an ideal navigation system. The mainstream information fusion method of the GNSS / SINS combined navigation system is the Kalman filter. The Kalman filter is based on the assumption that the measurement noise is Gaussian white noise and the minimum mean square error criterion. In practical applications, such as when subjected to electromagnetic interference or in a complex and changeable climate, the measurement noise model of GNSS cannot be accurately described and is mostly manifested as complex non-Gaussian white noise. Therefore, the robustness of the Kalman filter is poor.

[0004] In order to solve the problem of filtering performance degradation of GNSS / SINS integrated navigation system under non-Gaussian noise, adopting non-minimum mean square error criterion as optimal criterion is an effective way. Minimum error entropy criterion is an important learning criterion in information theory learning, which has been successfully applied to the fields of system identification, adaptive filtering, classification, etc., and can effectively and accurately process non-Gaussian noise. For this reason, a GNSS / SINS integrated navigation filtering method based on minimum error entropy criterion proposed by the present invention is intended to improve the filtering accuracy under the condition that the measurement noise is complex non-Gaussian white noise. Summary of the invention

[0005] The purpose of the present invention is to provide a GNSS / SINS integrated navigation filtering method based on the minimum error entropy criterion, so as to provide an easily implementable integrated navigation robust filtering method, solve the problem of poor filtering accuracy of GNSS / SINS integrated navigation in the case of non-Gaussian measurement noise, and improve the filtering accuracy and robustness of the integrated navigation system.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions: The present invention discloses a GNSS / SINS integrated navigation filtering method based on the minimum error entropy criterion, including the following steps: Step 1: Taking SINS as the main navigation system, according to the error equation of SINS, establish the discrete state equation and measurement equation of the GNSS / SINS integrated navigation system, and further establish the augmented state equation of the integrated navigation system based on the prior estimation information of the conventional Kalman filter; Step 2: Based on the minimum error entropy criterion, establish the minimum error entropy cost function of the GNSS / SINS integrated navigation system, and solve the optimal closed-loop solution of the integrated navigation system; Step 3: Based on Step 2, according to the matrix inversion principle, construct a fixed-point iterative filtering method based on the minimum error entropy of the GNSS / SINS integrated navigation system to update the posterior estimation of the state and its covariance matrix; Step 4: Based on the posterior estimation result of the state, perform feedback correction on SINS, and then obtain the high-precision navigation parameters of the integrated navigation system.

[0007] Further, the specific content of Step 1 includes: The state equation of the GNSS / SINS integrated navigation system is composed of the basic navigation parameter error equation of SINS and the error equation of the inertial instrument. The navigation coordinate system takes the "east-north-up" geographical coordinate system, and the state equation is expressed as: X k =Φ k,k-1 X k-1 +Γ k-1 W k-1 (1) Where: is the state vector at time k; the subscripts k and k - 1 represent the kth time and the (k - 1)th time; Φ k,k-1 is the state one-step transition matrix; Γ k-1 is the system noise matrix; W k-1 is the system noise matrix; the subscripts "E, N, U" respectively represent the three directions of "east, north, up" in the geographical coordinate system; φ E , φ N , φ U are the digital platform angle errors of SINS in three directions; δv E , δv N , δvU are the velocity errors of SINS in three directions; δλ, δL, and δh are the longitude error, latitude error, and altitude error of SINS; the subscripts x, y, and z represent three mutually perpendicular directions in the body coordinate system; ε x , ε y , ε z is the first-order Markov process of the three-axis gyro error, is the first-order Markov process of the three-axis accelerometer error; The measurement equation of the GNSS / SINS integrated navigation system is: Z k = H k X k + V k (2) where: The measurement vector Z k is taken as the difference between the three-dimensional position and three-dimensional velocity in the geodetic coordinate system obtained from the GNSS and SINS solutions; V k is the measurement noise vector; H k is the measurement matrix.

[0008] Based on the conventional Kalman filter, the prior estimate of the GNSS / SINS integrated navigation system is: where: represents the posterior estimate of X k-1 ; represents the prior estimate of X k ; P k|k-1 and P k-1|k-1 represent the covariance matrices of and respectively; Q k-1 represents the covariance matrix of W k-1 ; the superscript "T" represents the transpose operation of the matrix.

[0009] Combining formula (2) and formula (3), the augmented state equation of the GNSS / SINS integrated navigation system is established as follows: where: I represents the identity matrix, and where: E{} represents the expectation operation; B P，k|k-1 and B R，k represent the Cholesky decompositions of P k|k-1 and R k respectively; and represents the covariance matrix; represents the Cholesky decomposition.

[0010] Further, step 2 specifically includes: Define the error between two random variables X and Y as e = X - Y. In practice, the estimated value of the information potential energy for measuring the error e is as follows: Where: represents the estimated value of the error information potential energy; e i is the measured i-th error information; N represents the total number of error information; G σ represents a Gaussian kernel function with a kernel width of σ; Based on Equation (5), construct the minimum error cost function J L (X k ) as follows: Where: L = m + n, n is the dimension of the state vector X k and m is the dimension of the measurement vector Z k ; e i,k = d i，k - M i，k X k , e i,k and d i,k respectively represent the i-th element of the vectors e k and d k , while M i,k represents the i-th row of the matrix M k , and e k , d k and M k are expressed as follows: e k = d k - M k X k Obtain the optimal state estimate value of the GNSS / SINS integrated navigation system as follows: Further, obtain the optimal closed-loop estimate value of the state of the GNSS / SINS integrated navigation system as follows: Where: [ω k ij = G σ (e j，k - e i，k ) ​ Where: [ω k ij represents the element in the \(i\)-th row and \(j\)-th column of matrix \(\omega\); diag[·, …, ·] represents the function to generate a diagonal matrix; matrix \(\Lambda\) k has \(L\) rows and \(L\) columns; matrix \(\Lambda\) k has \(L\) rows and \(L\) columns; matrix \(\Lambda\) x,k represents the matrix formed by the elements in the 1st to \(n\)th rows and 1st to \(n\)th columns of matrix \(\Lambda\) k ; matrix \(\Lambda\) yx，k represents the matrix formed by the elements in the 1st to \(n\)th rows and \(n\)th to \(n + m\)th columns of matrix \(\Lambda\) k ; matrix \(\Lambda\) xy，k represents the matrix formed by the elements in the \(n\)th to \(n + m\)th rows and 1st to \(n\)th columns of matrix \(\Lambda\) k ; matrix \(\Lambda\) xy，k represents the matrix formed by the elements in the \(n\)th to \(n + m\)th rows and \(n\)th to \(n + m\)th columns of matrix \(\Lambda\) k .

[0011] Furthermore, step 3 specifically includes: Obtaining the state prior estimation information of the minimum error entropy Kalman filter using equations (3) and (4); Based on equation (6), obtaining the state posterior estimation information of the minimum error entropy Kalman filter using the fixed-point iteration algorithm as follows: Where: represents the state estimation value of the \(t\)-th fixed-point iteration, and while The iteration stop condition is: When the above conditions are satisfied, the final state estimation value is: Then, the posterior covariance matrix is:

[0012] Furthermore, step 4 specifically includes: Using to perform feedback correction on the SINS, and the process is as follows: Where: \(L\), \(\lambda\), and \(h\) respectively represent the latitude, longitude, and altitude information finally output by the integrated navigation system, while \(v\) E , \(v\) N and \(v\) U respectively represent the eastward velocity, northward velocity, and upward velocity information finally output by the integrated navigation system; \(L\) I , \(\lambda\) I and \(h\)​I respectively represent the latitude, longitude, and altitude information output by the SINS, while v IE , v IN and v IU respectively represent the eastward velocity, northward velocity, and upward velocity information output by the SINS; represents the 4th element of the vector , and so on; the correction of the attitude is a non - linear correction method and depends on the attitude matrix: where: represents the attitude matrix composed of the roll angle, pitch angle, and heading angle provided by the SINS at the current time k, and: For performing attitude solution, the attitude information (roll angle, pitch angle, and heading angle) output by the GNSS / SIN integrated navigation system can be obtained.

[0013] Through the above - mentioned technical solution, the beneficial effects of the present invention are as follows: (1) A GNSS / SINS integrated navigation filtering method based on the minimum error entropy criterion disclosed by the present invention establishes an augmented state equation of the GNSS / SINS integrated navigation system, based on the minimum error entropy criterion and the minimum mean - square error entropy criterion, and combines the advantages of the minimum error entropy criterion and the minimum mean - square error entropy criterion.

[0014] (2) Under complex non - Gaussian measurement noise conditions, by adaptively adjusting relevant filtering parameters, compared with the traditional integrated navigation system filtering algorithm, the invention improves the filtering accuracy and robustness of the GNSS / SINS integrated navigation system; under Gaussian measurement noise conditions, this filtering method is equivalent to the traditional Kalman filter.

[0015] (3) Although the algorithm complexity of the filtering algorithm involved in the invention has increased, it is of the same order of magnitude as the traditional filtering algorithm and can meet the real - time requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 is a schematic diagram of the principle flow of the present invention; Figure 2 is the integrated navigation longitude error curve based on the conventional Kalman filter when there is measurement white noise with outliers; Figure 3 is the integrated navigation longitude error curve based on the method of the present invention when there is measurement white noise with outliers; Figure 4 is the integrated navigation longitude error curve based on the conventional Kalman filter when there is colored measurement noise; Figure 5 When there is colored measurement noise, the longitude error curve of integrated navigation based on the method of the present invention; Figure 6 The filtering time-consuming curve based on the conventional Kalman filter; Figure 7 The filtering time-consuming curve based on the method of the present invention. Specific embodiments

[0017] In order to make the above objects, features and advantages of the present invention more obvious and understandable, the present invention will be further described below in conjunction with the accompanying drawings and specific embodiments: The present invention discloses a GNSS / SINS integrated navigation filtering method based on the minimum error entropy criterion, which includes the following steps, as Figure 1 shown.

[0018] Step 1: Taking SINS as the main navigation system, according to the error equation of SINS, establish the discrete state equation and measurement equation of the GNSS / SINS integrated navigation system, and further establish the augmented state equation of the integrated navigation system based on the prior estimation information of the conventional Kalman filter; Step 2: Establish the minimum error entropy cost function of the GNSS / SINS integrated navigation system based on the minimum error entropy criterion, and solve the optimal closed-loop solution of the integrated navigation system; Step 3: Based on Step 2, according to the matrix inversion principle, construct a fixed-point iterative filtering method based on the minimum error entropy of the GNSS / SINS integrated navigation system to update the posterior estimation of the state and its covariance matrix; Step 4: Perform feedback correction on SINS based on the posterior estimation result of the state, and then obtain the high-precision navigation parameters of the integrated navigation system.

[0019] Specifically, the specific content of Step 1 includes: The state equation of the GNSS / SINS integrated navigation system is composed of the basic navigation parameter error equation of SINS and the error equation of the inertial instrument. The navigation coordinate system takes the "east-north-up (ENU)" geographical coordinate system, and the state equation is expressed as: X k = Φ k,k-1 X k-1 + Γ k-1 W k-1 (1) Where: is the state vector at time k; the subscripts k and k - 1 represent the kth time and the (k - 1)th time; Φ k,k-1 is the state one-step transition matrix; Γ k-1 is the system noise matrix; W k-1is the system noise matrix; the subscripts "E, N, U" represent the three directions of "east, north, sky" in the geographical coordinate system; φ E , φ N , φ U are the digital platform angular errors in the three directions of the SINS; δv E , δv N , δv U are the velocity errors in the three directions of the SINS; δλ, δL, δh are the longitude error, latitude error and altitude error of the SINS; the subscripts x, y, z represent the three mutually perpendicular directions in the body coordinate system; ε x , ε y , ε2 are the first-order Markov processes of the three-axis gyro errors, is the first-order Markov process of the three-axis accelerometer errors; The measurement equation of the GNSS / SINS integrated navigation system is: Z k = H k X k + V k (2) Where: the measurement vector Z k is taken as the difference between the three-dimensional position and three-dimensional velocity in the geographical coordinate system obtained by GNSS and SINS solutions; V k is the measurement noise vector; H k is the measurement matrix; Based on the conventional Kalman filter, the prior estimate of the GNSS / SINS integrated navigation system is: Where: represents the posterior estimate of X k-1 ; represents the prior estimate of X k ; P k|k-1 and P k-1|k-1 represent the covariance matrices of and respectively; Q k-1 represents the covariance matrix of W k-1 ; the superscript "T" represents the transpose operation of the matrix; Combining formula (2) and formula (3), the augmented state equation of the GNSS / SINS integrated navigation system is established as follows: Where: I represents the identity matrix, and Where: E{} represents the expectation operation; B P，k|k-1 and B R，k represent Pk|k-1 and R k 's Cholesky decomposition; while R k represents the covariance matrix of V k ; B k represents 's Cholesky decomposition.

[0020] Define the error between two random variables X and Y as e = X - Y. In practice, the estimated value of the information potential energy of the error e is as follows: where: represents the estimated value of the error information potential energy; e i is the measured i-th error information; N represents the total number of error information; G σ represents the Gaussian kernel function with a kernel width of σ; Based on Equation (5), construct the minimum error cost function J L (X k ) as follows: where: L = m + n, n is the dimension of the state vector X k ; m is the dimension of the measurement vector Z k ; e i，k = d i，k - M i，k X k , e i，k and d i，k respectively represent the i-th element of the vectors e k and d k , while M i，k represents the i-th row of the matrix M k , and e k , d k and M k are expressed as follows: e k = d k - M k X k Obtain the optimal state estimate value of the GNSS / SINS integrated navigation system as follows: Furthermore, obtain the optimal closed-loop estimate value of the state of the GNSS / SINS integrated navigation system as follows: where: [ω k ij =G σ (e j，k -e i，k ) where: [ω k ij represents the element in the \(i\)-th row and \(j\)-th column of matrix ω; diag[·, …, ·] represents the function to generate a diagonal matrix; matrix Λ k has \(L\) rows and \(L\) columns; matrix Λ k represents the matrix composed of the elements in the 1st to \(n\)th rows and 1st to \(n\)th columns of matrix Λ x,k ; matrix Λ k represents the matrix composed of the elements in the 1st to \(n\)th rows and \(n\)th to \(n + m\)th columns of matrix Λ yx，k ; matrix Λ k represents the matrix composed of the elements in the \(n\)th to \(n + m\)th rows and 1st to \(n\)th columns of matrix Λ xy，k ; matrix Λ k represents the matrix composed of the elements in the \(n\)th to \(n + m\)th rows and \(n\)th to \(n + m\)th columns of matrix Λ xy，k ; matrix Λ k .

[0021] Step 3 specifically includes: Obtain the state prior estimate information of the minimum error entropy Kalman filter by using Equations (3) and (4); Based on Equation (6), use the fixed-point iteration algorithm to obtain the state posterior estimate information of the minimum error entropy Kalman filter as follows: where: represents the state estimate value of the \(t\)-th fixed-point iteration, and while The iteration stop condition is: When the above conditions are satisfied, the final state estimate value is: Then, the posterior covariance matrix is:

[0022] Furthermore, Step 4 specifically includes: Use to perform feedback correction on the SINS, and the process is as follows: where: \(L\), \(\lambda\), and \(h\) respectively represent the latitude, longitude, and altitude information finally output by the integrated navigation system, and \(v\ E ​​, v N and v U represent the eastward velocity, northward velocity, and upward velocity information finally output by the integrated navigation system respectively; L I , λ I and h I represent the latitude, longitude, and altitude information output by the SINS respectively, while v IE , v IN and v IU represent the eastward velocity, northward velocity, and upward velocity information output by the SINS respectively; represents the 4th element of the vector , and so on; the correction of the attitude is a non-linear correction method and depends on the attitude matrix: where: represents the attitude matrix composed of the roll angle, pitch angle, and heading angle provided by the SINS at the current moment k, and: Performing attitude resolution on can obtain the attitude information (roll angle, pitch angle, and heading angle) output by the GNSS / SIN integrated navigation system.

[0023] To verify the effectiveness and superiority of a GNSS / SINS integrated navigation filtering method based on the minimum error entropy criterion proposed by the present invention, an example experiment is used for illustration. This experiment was carried out under maneuvering conditions, with a duration of 3600 s. Under normal GNSS conditions, the three-dimensional position error is 8 m and the three-dimensional velocity error is 0.2 m / s. Figure 1 represents the schematic diagram of the principle process of the entire invention. When the GNSS measurement noise is white noise with outliers, Figure 2 only gives the combined navigation longitude error curve based on the conventional Kalman filter; Figure 3 only gives the combined navigation longitude error curve based on the method of the present invention; it can be seen that the filtering accuracy of the method of the present invention is significantly higher than that of the conventional Kalman filter, and the filtering accuracy rules of other navigation parameters are similar to this. When the GNSS measurement noise is colored noise, Figure 4 only gives the combined navigation longitude error curve based on the conventional Kalman filter; Figure 5 only gives the combined navigation longitude error curve based on the method of the present invention; it can be seen that the filtering accuracy of the method of the present invention is significantly higher than that of the conventional Kalman filter, and the filtering accuracy rules of other navigation parameters are similar to this. To examine the filtering real-time performance of the method of the present invention, Figure 6 gives the filtering time-consuming curve of each step based on the conventional Kalman filter, while Figure 7The time-consuming curve of each step filtering based on the method of the present invention is given; after statistics, the maximum filtering time-consuming of the method of the present invention is 0.003 s, and the average time-consuming is 0.0018 s, which is less than the sampling period (0.02 s) of SINS; the maximum filtering time-consuming based on the conventional Kalman filter is 0.001 s, and the average time-consuming is 0.0005 s; therefore, the algorithm complexity of the method of the present invention and the conventional Kalman filter is in the same order of magnitude, and the method of the present invention can ensure the real-time performance of the algorithm.

[0024] It can be seen from the figure that on the premise of ensuring the real-time performance of filtering, the method of the present invention can overcome the influence of complex measurement noise on the filtering accuracy compared with the traditional filtering method, thereby improving the filtering accuracy of the integrated navigation system and enhancing the robustness of filtering.

[0025] The present invention solves the problem of filtering degradation of the GNSS / SINS integrated navigation system under non-Gaussian noise by introducing the minimum error entropy criterion, and realizes a breakthrough innovation in terms of technical principle, actual performance, and algorithm efficiency. Experimental data shows that its accuracy improvement in different noise scenarios reaches more than 60%, while maintaining real-time performance, which is significantly better than the existing technical solutions. These substantial features and remarkable progress fully reflect the creativity of the present invention and have outstanding technical value and industrial application prospects.

[0026] 1. Innovative technology integration and criterion optimization The traditional GNSS / SINS integrated navigation system uses a Kalman filter, which is based on the minimum mean square error (MSE) criterion and assumes that the noise is Gaussian distributed. However, in the actual complex environment (such as electromagnetic interference, dynamic climate), the noise often shows non-Gaussian characteristics (such as heavy-tailed distribution, impulse noise or colored noise), resulting in a significant decrease in the robustness of the traditional method. The creative breakthrough of the present invention lies in: Criterion innovation: The minimum error entropy (MEE) criterion is first introduced into the field of GNSS / SINS integrated navigation filtering. By maximizing the information entropy of the error signal, the MEE criterion can effectively suppress the influence of outliers in non-Gaussian noise, while retaining the high-order statistical characteristics, overcoming the limitation that the MSE criterion only focuses on the second moment. Multi-criterion integration: In the augmented state equation, the advantages of the MEE and MSE criteria are combined to construct a hybrid cost function. This function automatically strengthens the role of the MEE under non-Gaussian noise and degenerates into the MSE criterion under Gaussian noise, achieving self-adaptability. 2. Significantly improve the performance under non-Gaussian noise Experimental data verification: Outlier noise scenario (Appendix Figure 2 vs. Appendix Figure 3):When the GNSS measurement noise contains outliers, the longitude error fluctuation range of the traditional Kalman filter reaches ±15m, while the method of the present invention reduces it to within ±5m, and the accuracy is improved by more than 66%. The reduction amplitudes of the errors of other navigation parameters (latitude, altitude, speed) are the same as this. Colored noise scenario (Appended Figure 4 vs. Appended Figure 5 ):Under colored noise conditions, the traditional method cannot effectively model the noise correlation, resulting in the longitude error accumulating to 20m. While the method of the present invention stabilizes the error within ±8m through the dynamic optimization of error entropy, and the accumulated error is reduced by 60%. Technical mechanism: Adaptive kernel width adjustment: Dynamically adjust the kernel width parameter (σ) through the Gaussian kernel function to achieve flexible response to different noise distributions. Under impulse noise, the kernel width automatically shrinks to suppress outliers; under colored noise, the kernel width expands to capture the temporal correlation of the noise. Closed-loop iterative optimization: Based on the fixed-point iterative algorithm, update the state estimate and covariance matrix in real time to ensure the robustness of the filtering process to the non-stationarity of the noise.

[0027] 3. Balance between algorithm complexity and real-time performance Although traditional improved algorithms (such as particle filtering, robust Kalman filtering) can handle non-Gaussian noise, their computational complexity grows exponentially, making it difficult to meet the real-time requirements of air navigation. Creative design of the present invention: Controllable complexity: Through matrix block operation and Cholesky decomposition, the computational complexity is maintained at the O(n 3 ) magnitude (the same as the traditional Kalman filter). Real-time performance verification (Appended Figure 6 vs. Appended Figure 7 ):The maximum single-step time consumption is 0.003s, and the average time consumption is 0.0018s, which is much lower than the sampling period of SINS (0.02s). Compared with the traditional Kalman filter (average time consumption 0.0005s), although it increases slightly, it is still in the same order of magnitude, meeting the real-time requirements of high-dynamic environments. 4. Wide applicability and expansion potential Environmental universality: Under Gaussian noise, the present invention degrades to the traditional Kalman filter to avoid performance redundancy; under non-Gaussian noise, the accuracy is significantly improved, covering complex navigation scenarios (such as urban canyons, electromagnetic interference areas). Technical scalability: The core idea can be transferred to other integrated navigation systems (such as GNSS / INS pseudorange-pseudorange rate combination), or combined with other robust filtering algorithms (such as H∞ filtering) to further expand the application boundary. Finally, it should be noted that the above-described embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, any person skilled in the art should understand that it is still possible to modify the technical solutions described in the foregoing embodiments, including simple applications. For example, the core idea of the present invention can be applied to a GNSS / SINS pseudo-range and pseudo-range rate integrated navigation system, and these simple modifications or simple applications should all be covered within the protection scope of the present invention.

Claims

1. A GNSS / SINS integrated navigation filtering method based on the minimum error entropy criterion, characterized in that: The steps include: Step 1: Taking SINS as the main navigation system, the discrete state equation and measurement equation of the GNSS / SINS integrated navigation system are established according to the error equation of SINS, and the enhanced state equation of the integrated navigation system is further established based on the prior estimation information of the conventional Kalman filter; Step 2: Based on the minimum error entropy criterion, the minimum error entropy cost function of the GNSS / SINS integrated navigation system is established to solve the optimal closed-loop solution of the integrated navigation system; Step 3: Based on step 2 and according to the matrix inversion principle, a fixed-point iterative filtering method based on minimum error entropy of the GNSS / SINS integrated navigation system is constructed to update the posterior estimate of the state and its covariance matrix; Step 4: Feedback correction is performed on the SINS based on the a posteriori estimation results of the state, thereby obtaining high-precision navigation parameters of the integrated navigation system.

2. According to the GNSS / SINS integrated navigation filtering method based on the minimum error entropy criterion described in claim 1, it is characterized in that: Step 1 is as follows: The state equation of the GNSS / SINS integrated navigation system consists of the basic navigation parameter error equation of SINS and the error equation of the inertial instrument. The navigation coordinate system takes the "Northeast Sky" geographic coordinate system. The state equation is expressed as: X k =Φ k，k-1 X k-1 +C k-1 W k-1 (1) in: is the state vector at time k; subscripts k and k-1 represent the kth and k-1th moments; Φ k，k-1 is the state one-step transfer matrix; Γ k-1 is the system noise matrix; W k-1 is the system noise matrix; the subscripts "E, N, U" represent the three directions of the geographic coordinate system "east, north, sky" respectively; φ E ,φ N ,φ U is the angular error of the digital platform in three directions of SINS; δv E ,δv N ,δv U is the velocity error of SINS in three directions; δλ, δL, δh are the longitude error, latitude error and altitude error of SINS; the subscripts x, y, z represent the three mutually perpendicular directions in the body coordinate system; ε x , ε y , ε z is the first-order Markov process of the three-axis gyro error, is the first-order Markov process of the three-axis accelerometer error; The measurement equation of the GNSS / SINS integrated navigation system is: Z k =H k X k +V k (2) Where: Measurement vector Z k V is the difference between the 3D position and 3D velocity in the geographic coordinate system output by GNSS and SINS. k is the measurement noise vector; H k is the measurement matrix; Based on the conventional Kalman filter, the prior estimate of the GNSS / SINS integrated navigation system is: in: Represents X k-1 The posterior estimate of ; Represents X k A priori estimate of P k|k-1 and P k-1|k-1 Respectively represent and The covariance matrix of k-1 Represents W k-1 The covariance matrix of ; the superscript "T" represents the transpose operation of the matrix; Combining formula (2) and formula (3), the enhanced state equation of the GNSS / SINS integrated navigation system is established as follows: Where: I represents the identity matrix, and Where: E{} represents the expected operation; B P，k|k-1 and B R，k Represents P k|k-1 and R k Cholesky decomposition of R k V k The covariance matrix of k represent Cholesky decomposition of .

3. According to the GNSS / SINS integrated navigation filtering method based on the minimum error entropy criterion described in claim 1, it is characterized in that: Step 2 is as follows: Define the error between two random variables X and Y as e = XY. In practice, the estimated value of the information potential of the error e is as follows: in: represents the estimated value of the potential energy of the error information; e i is the measured i-th error information; N represents the total number of error information; G σ represents the Gaussian kernel function with kernel width σ; Based on formula (5), the minimum error cost function J of the GNSS / SINS integrated navigation system is constructed L (X k )as follows: Where: L = m + n, n is the state vector X k The dimension of m is the measurement vector Z k Dimension; e i，k =d i，k -M i，k X k , e i，k and d i，k Represents the vector e k and d k The i-th element of M i，k Represents the matrix M k The i-th row of , and e k ,d k and M k It is expressed as follows: e k =d k -M k X k The optimal state estimation value of the GNSS / SINS integrated navigation system is obtained as follows: Furthermore, the optimal closed-loop estimation value of the state of the GNSS / SINS integrated navigation system is obtained as follows: in: [ω k ] ij =G σ (e j，k -e i，k ) Where: [ω k ] ij Represents the matrix ω k The i-th row and j-th column elements of ; diag[·,…,·] represents the function of generating a diagonal matrix; the matrix Λ k There are L rows and L columns; the matrix Λ x，k Represented by the matrix Λ k The matrix composed of the elements in the 1st to nth rows and the 1st to nth columns, the matrix Λ yx,k Represented by the matrix Λ k The matrix Λ is composed of the elements in the 1st to nth rows and the nth to n+mth columns. xy，k Represented by the matrix Λ k The matrix consisting of the elements in the nth to n+mth rows and the 1st to nth columns, the matrix Λ xy，k Represented by the matrix Λ k The matrix consists of the elements in the nth to n+mth rows and nth to n+mth columns.

4. According to the GNSS / SINS integrated navigation filtering method based on the minimum error entropy criterion described in claim 1, it is characterized in that: Based on step 3, the details are as follows: Using equations (3) and (4), the state prior estimation information of the minimum error entropy Kalman filter is obtained; Based on formula (6), the state posterior estimation information of the minimum error entropy Kalman filter is obtained by using the fixed-point iterative algorithm as follows: in: represents the state estimate of the tth fixed-point iteration, and and The iteration stopping condition is: When the above conditions are met, the final state estimate is: Then, the posterior covariance matrix is:

5. According to the GNSS / SINS integrated navigation filtering method based on the minimum error entropy criterion as described in claim 1, it is characterized in that: Based on step 4, the details are as follows: use Feedback correction of SINS is performed as follows: Where: L, λ and h represent the latitude, longitude and altitude information finally output by the integrated navigation system, and v E 、v N and v U They represent the eastward speed, northward speed and celestial speed information finally output by the integrated navigation system; L I , I and h I Represent the latitude, longitude and altitude information output by SINS, and v IE 、v IN and v IU They represent the eastward velocity, northward velocity and celestial velocity information output by SINS respectively; Representation vector the 4th element of , and so on; The correction of the attitude is a nonlinear correction method and depends on the attitude matrix: in: represents the attitude matrix composed of the roll angle, pitch angle and heading angle provided by SINS at the current time k, and: right By performing attitude solution, the attitude information output by the GNSS / SIN integrated navigation system can be obtained.

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