CN115291266B - Satellite inertial tight combination real-time navigation positioning method based on information filtering algorithm - Google Patents
Satellite inertial tight combination real-time navigation positioning method based on information filtering algorithm Download PDFInfo
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Abstract
The application relates to a satellite inertial tight combination real-time navigation positioning method based on an information filtering algorithm, which comprises the following steps: by carrying out dimension transformation on the system error state vector, a new time update equation and a new measurement update equation are deduced on the basis of the system error state equation and a tightly combined measurement equation, the system error state vector after dimension transformation participates in new information filtering model calculation, the system error state vector at the current moment before dimension transformation is obtained, and the system error state vector at the current moment is used for correcting the navigation result at the current moment. By adopting the method, the calculation of the high-dimensional matrix inversion can be avoided, the precision advantage of the tightly combined navigation is exerted under the condition of a large number of observed values, the calculated amount and the calculated error in the measurement updating process are effectively reduced, the real-time performance of the tightly combined navigation system is improved, and the possibility is provided for realizing the functions of coarse error detection, integrity real-time calculation and the like.
Description
Technical Field
The application relates to the technical field of satellite and inertial combination, in particular to a satellite inertial tight combination real-time navigation positioning method based on an information filtering algorithm.
Background
The integrated navigation system is characterized in that a plurality of different navigation devices are combined in a proper mode, better navigation performance is realized by utilizing the complementary characteristics of the performance of the integrated navigation system, and the integrated navigation scheme of satellites and inertia is the most widely used at present. The satellite navigation system can provide global all-weather position and speed information, has long-term stable precision, and can correct the accumulated error of inertial navigation through filtering; the inertial navigation has higher update rate and various navigation information, and can assist in detection and elimination of the guard observation faults, but errors can be accumulated gradually over time and cannot work independently for a long time. The satellite navigation system and the inertial navigation system are combined, so that complementary advantages can be realized, the precision and stability of the combined system are improved, and information such as the position, the speed, the gesture, the acceleration, the angular speed and the like of the carrier is output.
Depending on the manner of assembly, the integrated navigation system can be divided into three types, loosely-Coupled, compact Tightly-Coupled, and deep Deeply-Coupled. The combination module estimates and compensates errors of the satellite navigation subsystem and the inertial navigation subsystem, so that a positioning result with higher precision is obtained, and the system has obvious performance advantages.
The common data fusion method used by the satellite and inertial integrated navigation system is based on a Kalman filtering algorithm, but in consideration of limited data processing capacity of the miniaturized integrated navigation system, when the number of available satellites is large, the dimension of the equation for measurement update is large, and the calculation time of using the Kalman filtering algorithm is long, so that the time update, coarse error detection, integrity calculation and other works can be influenced.
Disclosure of Invention
Based on the above, it is necessary to provide a satellite inertial tight combination real-time navigation positioning method based on an information filtering algorithm, which can solve the problem that when the number of available satellites is large, the dimension of an equation for measurement update is large, and the calculation time of a traditional kalman filtering algorithm is long, so that the time update, coarse detection and integrity calculation are affected.
An information filtering algorithm-based satellite inertial tight combination real-time navigation positioning method, comprising the following steps:
Multiplying the system error state vector by two coefficient matrixes to obtain a system error state vector after dimension transformation; the two coefficient matrixes are a first error state coefficient matrix and a second error state coefficient matrix respectively;
establishing a system error state equation after dimension transformation according to the system error state vector at the previous moment after dimension transformation; according to the system error state vector at the current moment after dimension transformation, a tightly combined measurement equation after dimension transformation is established;
Obtaining a time update equation of information filtering according to the system error state equation after dimension transformation; the time update equation comprises a time updated information error state vector and a time updated information matrix;
Based on the measurement update of the tightly combined measurement equation and the time update equation after dimension transformation, establishing a measurement update equation of information filtering; the measurement update equation comprises a measurement updated information error state vector and a measurement updated information matrix;
Obtaining a system error state variance matrix at the current moment after dimension transformation according to the information matrix after measurement and update; obtaining a system error state vector at the current moment after dimension transformation according to the information error state vector after measurement updating and the system error state variance matrix at the current moment after dimension transformation;
Obtaining a current moment system error state vector before dimension transformation according to the current moment system error state vector after dimension transformation, the first error state coefficient matrix and the second error state coefficient matrix; and obtaining the system error state variance matrix of the current moment before dimension transformation according to the system error state variance matrix of the current moment after dimension transformation, the first error state coefficient matrix and the second error state coefficient matrix.
In one embodiment, the method further comprises: multiplying the system error state vector delta X by two coefficient matrixes to obtain a system error state vector delta X 'after dimension transformation, wherein the system error state vector delta X' is as follows:
The systematic error state vector δx 15×1 is a 15-dimensional systematic error state vector δx expressed as follows:
Wherein δr 3×1 represents a position error vector, δv 3×1 represents a velocity error vector, δΦ 3×1 represents an attitude error vector, δb g,3×1 represents a gyro zero offset error vector, and δx represents an accelerometer zero offset error vector;
c 1,15×15 represents a first error state coefficient matrix C 1;C2,15×15 of 15 dimensions and a second error state coefficient matrix C 2 of 15 dimensions.
In one embodiment, the method further comprises: constructing a first error state coefficient matrix with zero elements except diagonal elements according to the radius of curvature of the earth meridian, the radius of curvature of the earth prime circle, the altitude of the carrier and the latitude of the carrier; the first error state coefficient matrix C 1 enables the weft warp high error to be converted into the north-east position error;
Constructing a second error state coefficient matrix with zero elements except diagonal elements according to the diagonal elements of the first error state coefficient matrix C 1 and the main diagonal elements of the system error state variance matrix; wherein, the second error state coefficient matrix C 2 makes the diagonal element of the system error state variance matrix after dimension transformation equal to 1.
In one embodiment, the method further comprises: the calculation formulas of the diagonal elements of the first error state coefficient matrix C 1 and the diagonal elements of the second error state coefficient matrix C 2 are respectively:
Wherein C 1,15×1 represents the diagonal element values of the first error state coefficient matrix C 1 of 15 dimensions; c 2,15×1 represents the diagonal element value of the second error state coefficient matrix C 2 of 15 dimensions, R n is the radius of curvature of the earth's meridian, R e represents the radius of curvature of the earth's circle of mortise and tenon, h represents the altitude of the carrier, B represents the latitude of the carrier, K 1 (i) represents the i-th element of the main diagonal of the matrix C 1, and σ i represents the i-th element of the main diagonal of the system error state variance matrix.
In one embodiment, the method further comprises: an inertial navigation system error state equation is established by using a 15-dimensional system error state vector delta X' after the dimension transformation, and the formula is as follows:
wherein, A. B and C are derived from an inertial navigation mechanics programming equation, epsilon g,3×1 represents a random error vector of the gyroscope, epsilon a,3×1 represents a random error vector of the accelerometer;
converting the continuous time system into a discrete time system, and obtaining a system error state equation after discretization linearization according to a system error state vector at the previous moment after dimension transformation, wherein the system error state equation is as follows:
δX′k/k-1＝Φ′k/k-1δX′k-1/k-1+Γ′k/k-1Wk-1′
wherein the expression of each variable is as follows:
δX′k/k-1＝(C2,kC1,k)·δXk/k-1
δX′k-1/k-1＝(C2,k-1C1,k-1)·δXk-1/k-1
Wk-1′＝CεWk-1
Φ′k/k-1＝(C2,kC1,k)·Φk/k-1·(C2,k-1C1,k-1)-1
δx k-1/k-1 represents a system error state vector at a previous time, W k-1 represents a system noise vector, obeys normal distribution of a covariance matrix of Q k-1, and the specific parameter is determined by inertial navigation device performance, C ε represents a dimensional transformation coefficient matrix, Φ k/k-1 represents an error state transition matrix from the previous time to the current time, Γ k/k-1 represents a system noise transition matrix, and the calculation formulas of Φ k/k-1 and Γ k/k-1 are as follows:
Γk/k-1＝G·Δt
Wherein the time interval Δt=t k-tk-1, italic I denotes an identity matrix, F denotes a coefficient matrix, and G denotes a noise driving matrix.
In one embodiment, the method further comprises: according to the system error state vector delta X' k/k at the current moment after the dimension transformation, a tightly combined measurement equation after the dimension transformation is established, and the formula is as follows:
Zk＝Hk′δX′k/k+ξk
wherein, H k represents a measurement information geometric matrix, ζ k represents a measurement error vector, the zero-mean multidimensional n-Tai distribution obeying the covariance matrix is R k, the specific parameters of R k are obtained by carrying out error modeling on the hygienically measured information, Z k represents a hygienically measured information vector at the time t k, and the calculation formula of Z k is as follows:
Wherein δP (t k) represents single-difference error observables among pseudo-range satellites, δDelta tφ(tk represents double-difference error observables among carrier phase satellites, the double-difference error observables are obtained by calculation of satellite navigation original observation data and inertial navigation forecast antenna positions, the column vectors are n-1-dimensional, and n represents visible satellite particles.
In one embodiment, the method further comprises: definition of dimension transformed information matrixInformation error State vector/>Two auxiliary transition matrices/>N＝MΓ′(Γ′TMΓ′+Q′-1)-1Γ′T；
According to the time update of the system error state equation after dimension transformation, obtaining a time update equation of information filtering, which comprises the following steps:
Ι′k/k-1＝(I-N)M
the time update is a transformation process from the previous moment to the current moment of the system error state vector after dimension transformation;
Wherein S 'k/k-1 represents a time-updated information error state vector, i' k/k-1 represents a time-updated information matrix, and i 'k/k-1 is used for describing the degree of dispersion of error state distribution, that is, the size of the information content in S' k/k-1; p represents a systematic error state vector variance matrix, Q represents a systematic noise variance matrix, P 'represents a dimensional transformed systematic error state variance matrix, Q' represents a dimensional transformed systematic noise variance matrix, and P 'and Q' are respectively:
P′＝(C2·C1)·P·(C2·C1)T
Q′＝Cε·Q·Cε T
wherein, the diagonal line element of C ε is obtained by the open root number of the diagonal line element of Q, and the rest elements are all zero.
In one embodiment, the method further comprises: according to the calculation results of the dimension transformed tight combination measurement equation and the time update equation, introducing the sanitation measurement information to carry out measurement update on the S 'k/k-1 and the I' k/k-1, and establishing the measurement update equation of the information filtering as follows:
Wherein S 'k/k represents a measurement updated information error state vector, and i' k/k represents a measurement updated information matrix.
In one embodiment, the method further comprises: according to the updated information matrix I 'k/k, a system error state variance matrix P' k/k at the current moment after dimension transformation is obtained, and the formula is expressed as follows:
According to the information error state vector S ' k/k after the measurement update and the system error state variance array P ' k/k at the current moment after the dimension transformation, a system error state vector delta X ' k/k at the current moment after the dimension transformation is obtained, and the formula is expressed as follows:
δX′k/k＝P′k/k·S′k/k。
In one embodiment, the method further comprises: according to the system error state vector delta X' k/k at the current time after the dimension transformation, the first error state coefficient matrix C 1 and the second error state coefficient matrix C 2, the system error state vector delta X k/k at the current time before the dimension transformation is obtained, and the formula is expressed as follows:
δXk/k＝(C2·C1)-1·δX′k/k
According to the system error state variance matrix P' k/k, the first error state coefficient matrix C 1 and the second error state coefficient matrix C 2 at the current time after the dimension transformation, the system error state variance matrix P k/k at the current time before the dimension transformation is obtained, which is shown as follows:
Pk/k＝(C2·C1)-1Pk′/k(C2·C1)-T。
According to the satellite inertial tightly-combined real-time navigation positioning method based on the information filtering algorithm, the improved information filtering method and the tightly-combined navigation method are combined, the dimension transformation is carried out on the system error state vector, a new time update equation and a new measurement update equation are deduced, calculation of high-dimensional matrix inversion is avoided, under the condition that the number of observed values is large, the accuracy advantage of tightly-combined navigation is exerted, the calculated amount and the calculated error in the measurement update process are effectively reduced, the real-time performance of the tightly-combined navigation system is improved, and the possibility is provided for achieving functions such as rough detection and integrity real-time calculation.
Drawings
FIG. 1 is a flow chart of a satellite inertial compact real-time navigation positioning method based on an information filtering algorithm in one embodiment;
FIG. 2 is a flow diagram of integrated satellite/inertial navigation system information processing in one embodiment;
FIG. 3 is a flow diagram of information processing for an information filtering algorithm in one embodiment;
FIG. 4 is a comparison of time spent for sequential Kalman filtering and information filtering measurement updates in another embodiment;
FIG. 5 is a graph of the variation of the ratio of the time of sequential Kalman filtering to the time of information filtering in one embodiment;
FIG. 6 is a diagram of a horizontal motion profile of a vehicle in one embodiment;
FIG. 7 is a graph of a three-dimensional positioning error of a vehicle in one embodiment;
FIG. 8 is a graph of three-dimensional velocity variation of a vehicle in one embodiment;
FIG. 9 is a graph of three-dimensional attitude change of a vehicle in one embodiment;
Fig. 10 is an internal structural view of a computer device in one embodiment.
Detailed Description
The present application will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present application more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the application.
In one embodiment, as shown in fig. 1, there is provided a method for positioning satellite inertial close-up real-time navigation based on an information filtering algorithm, which can be applied to a terminal, and includes the following steps:
Step 102, multiplying the system error state vector by two coefficient matrixes to obtain a system error state vector after dimension transformation; the two coefficient matrixes are a first error state coefficient matrix and a second error state coefficient matrix respectively.
It can be understood that in the traditional information filtering calculation process, there are two places where high-dimensional matrix inversion calculation is needed, and the situation that the inversion accuracy is poor or irreversible may occur, so that in order to avoid the situation, the invention constructs two coefficient matrixes with zero elements except diagonal elements, multiplies the two coefficient matrixes to the left of the system error state vector to obtain a system error state vector after dimension conversion, and converts the dimension of the system error state vector to enable the diagonal elements of (Γ TMΓ+Q-1) to be approximately equal and the diagonal elements of the information matrix I to be approximately normalized, thereby effectively improving the calculation accuracy in the matrix inversion process.
104, Establishing a system error state equation after dimension transformation according to the system error state vector at the previous moment after dimension transformation; and establishing a tightly combined measurement equation after dimension transformation according to the system error state vector at the current moment after dimension transformation.
It will be appreciated that the system error state equation is based on the carrier error of the tightly combined navigation system and the tightly combined measurement equation is based on the satellite navigation measurement equation for pseudorange and carrier phase.
Step 106, obtaining a time update equation of information filtering according to the system error state equation after dimension transformation; the time update equation includes a time updated information error state vector and a time updated information matrix.
Specifically, the information matrix after dimension transformation, the information error state vector and the two auxiliary transition matrices are predefined, and a process of deducing the information error state vector after time update and the information matrix after time update based on a discrete form of system error state equation is called as a time update equation of information filtering.
Step 108, based on the measurement update of the tightly combined measurement equation and the time update equation after dimension transformation, establishing a measurement update equation of information filtering; the measurement update equation includes a measurement updated information error state vector and a measurement updated information matrix.
Specifically, based on the calculation result of the time update equation, introducing the sanitation measurement information to perform measurement update on the time updated information error state vector and the time updated information matrix to obtain a process of measuring the updated information error state vector and the time updated information matrix, which is called as a measurement update equation of information filtering.
Step 110, obtaining a system error state variance matrix at the current moment after dimension transformation according to the information matrix after measurement and update; and obtaining the system error state vector at the current moment after dimension transformation according to the information error state vector after measurement updating and the system error state variance matrix at the current moment after dimension transformation.
Specifically, performing inverse operation on the information matrix after measurement update to obtain a system error state variance matrix at the current moment after dimension transformation; multiplying the information error state vector after measurement update by the system error state variance matrix at the current moment after dimension transformation to obtain the system error state vector at the current moment after dimension transformation.
Step 112, obtaining a system error state vector at the current moment before dimension transformation according to the system error state vector at the current moment after dimension transformation, the first error state coefficient matrix and the second error state coefficient matrix; and obtaining the system error state variance matrix of the current moment before dimension transformation according to the system error state variance matrix of the current moment after dimension transformation, the first error state coefficient matrix and the second error state coefficient matrix.
It will be appreciated that the systematic error state vector at the current time before the dimensional transformation is used to correct the navigation results (parameters such as carrier position, speed and attitude) at the current time.
According to the satellite inertial tightly-combined real-time navigation positioning method based on the information filtering algorithm, the improved information filtering method and the tightly-combined navigation method are combined, the dimension transformation is carried out on the system error state vector, a new time update equation and a new measurement update equation are deduced, calculation of high-dimensional matrix inversion is avoided, under the condition that the number of observed values is large, the accuracy advantage of tightly-combined navigation is exerted, the calculated amount and the calculated error in the measurement update process are effectively reduced, the real-time performance of the tightly-combined navigation system is improved, and the possibility is provided for achieving functions such as rough detection and integrity real-time calculation.
In one embodiment, multiplying the systematic error state vector by two coefficient matrices to obtain a dimensionally transformed systematic error state vector includes:
Multiplying the system error state vector delta X by two coefficient matrixes to obtain a system error state vector delta X 'after dimension transformation, wherein the system error state vector delta X' is as follows:
The systematic error state vector δx 15×1 is a 15-dimensional systematic error state vector δx expressed as follows:
Wherein δr 3×1 represents a position error vector, δv 3×1 represents a velocity error vector, δΦ 3×1 represents an attitude error vector, δb g,3×1 represents a gyro zero offset error vector, and δb a,3×1 represents an accelerometer zero offset error vector;
c 1,15×15 represents a first error state coefficient matrix C 1;C2,15×15 of 15 dimensions and a second error state coefficient matrix C 2 of 15 dimensions.
In one embodiment, a first error state coefficient matrix with all the elements except diagonal elements being zero is constructed according to the radius of curvature of the earth meridian, the radius of curvature of the earth prime circle, the altitude of the carrier and the latitude of the carrier; the first error state coefficient matrix C 1 enables the weft warp high error to be converted into the north-east position error; constructing a second error state coefficient matrix with zero elements except diagonal elements according to the diagonal elements of the first error state coefficient matrix C 1 and the main diagonal elements of the system error state variance matrix; wherein, the second error state coefficient matrix C 2 makes the diagonal element of the system error state variance matrix after dimension transformation equal to 1.
In another embodiment, the diagonal elements of the first error state coefficient matrix C 1 and the diagonal elements of the second error state coefficient matrix C 2 are respectively calculated according to the following formulas:
Wherein C 1,15×1 represents the diagonal element values of the first error state coefficient matrix C 1 of 15 dimensions; c 2,15×1 represents the diagonal element values of the second error state coefficient matrix C 2 of 15 dimensions; r n is the radius of curvature of the earth meridian, and the unit is m; r e represents the radius of curvature of the earth's prime ring, and the unit is m; h represents the altitude of the carrier in m; b represents the latitude of the carrier, and the unit is rad; k 1 (i) represents the ith element of the main diagonal of the C 1 matrix; σ i represents the i-th element of the system error state variance matrix main diagonal.
In another embodiment, the step of creating the system error state equation after the dimension transformation according to the system error state vector at the previous moment after the dimension transformation includes:
an inertial navigation system error state equation is established by using a 15-dimensional system error state vector delta X' after the dimension transformation, and the formula is as follows:
wherein, A. B and C are derived from an inertial navigation mechanics programming equation, epsilon g,3×1 represents a random error vector of the gyroscope, epsilon a,3×1 represents a random error vector of the accelerometer;
converting the continuous time system into a discrete time system, and obtaining a system error state equation after discretization linearization according to a system error state vector at the previous moment after dimension transformation, wherein the system error state equation is as follows:
δX′k/k-1＝Φ′k/k-1δX′k-1/k-1+Γ′k/k-1Wk-1′ (5)
wherein the expression of each variable is as follows:
δx k-1/k-1 represents a system error state vector at a previous time, C ε represents a dimensional transformation coefficient matrix, W k-1 represents a system noise vector, obeying a normal distribution of a covariance matrix of Q k-1, the specific parameter is determined by inertial navigation device performance, Φ k/k-1 represents an error state transition matrix from the previous time to the current time, Γ k/k-1 represents a system noise transition matrix, and the calculation formulas of Φ k/k-1 and Γ k/k-1 are as follows:
Γk/k-1＝G·Δt (8)
Wherein the time interval Δt=t k-tk-1, italic I denotes an identity matrix, F denotes a coefficient matrix, and G denotes a noise driving matrix.
In another embodiment, establishing a tightly combined measurement equation after dimension transformation according to the system error state vector at the current moment after dimension transformation comprises:
according to the system error state vector delta X' k/k at the current moment after the dimension transformation, a tightly combined measurement equation after the dimension transformation is established, and the formula is as follows:
Zk＝Hk′δX′k/k+ξk (9)
wherein, H k represents a measurement information geometric matrix, ζ k represents a measurement error vector, the zero-mean multidimensional n-Tai distribution obeying the covariance matrix is R k, the specific parameters of R k are obtained by carrying out error modeling on the hygienically measured information, Z k represents a hygienically measured information vector at the time t k, and the calculation formula of Z k is as follows:
Wherein δP (t k) represents single-difference error observables among pseudo-range satellites, δDelta tφ(tk represents double-difference error observables among carrier phase satellites, the double-difference error observables are obtained by calculation of satellite navigation original observation data and inertial navigation forecast antenna positions, the column vectors are n-1-dimensional, and n represents visible satellite particles.
In another embodiment, before obtaining the time update equation of the information filtering according to the time update of the system error state equation after the dimension transformation, the method further includes:
definition of dimension transformed information matrix Information error State vector/>Two auxiliary transition matrices/>N＝MΓ′(Γ′TMΓ′+Q′-1)-1Γ′T；
According to the time update of the system error state equation after dimension transformation, obtaining a time update equation of information filtering, which comprises the following steps:
the time update is a transformation process from the previous moment to the current moment of the system error state vector after dimension transformation;
Wherein S 'k/k-1 represents a time-updated information error state vector, i' k/k-1 represents a time-updated information matrix, and i 'k/k-1 is used for describing the degree of dispersion of error state distribution, that is, the size of the information content in S' k/k-1; p represents a systematic error state vector variance matrix, Q represents a systematic noise variance matrix, P 'represents a dimensional transformed systematic error state variance matrix, Q' represents a dimensional transformed systematic noise variance matrix, and P 'and Q' are respectively:
wherein, the diagonal line element of C ε is obtained by the open root number of the diagonal line element of Q, and the rest elements are all zero.
In another embodiment, establishing the measurement update equation for the information filtering based on the measurement update of the dimension transformed tightly-packed measurement equation and the time update equation includes:
According to the calculation results of the dimension transformed tight combination measurement equation and the time update equation, introducing the sanitation measurement information to carry out measurement update on the S 'k/k-1 and the I' k/k-1, and establishing the measurement update equation of the information filtering as follows:
Wherein S 'k/k represents a measurement updated information error state vector, and i' k/k represents a measurement updated information matrix.
In another embodiment, according to the information matrix i 'k/k after measurement update, a system error state variance matrix P' k/k at the current moment after dimension transformation is obtained, and the formula is expressed as follows:
According to the information error state vector S ' k/k after the measurement update and the system error state variance array P ' k/k at the current moment after the dimension transformation, a system error state vector delta X ' k/k at the current moment after the dimension transformation is obtained, and the formula is expressed as follows:
δX′k/k＝P′k/k·S′k/k (15)
In another embodiment, the system error state vector δx k/k at the current time before the dimensional transformation is obtained according to the system error state vector δx' k/k at the current time after the dimensional transformation, the first error state coefficient matrix C 1 and the second error state coefficient matrix C 2, and the formula is:
δXk/k＝(C2·C1)-1·δX′k/k (16)
According to the system error state variance matrix P' k/k, the first error state coefficient matrix C 1 and the second error state coefficient matrix C 2 at the current time after the dimension transformation, the system error state variance matrix P k/k at the current time before the dimension transformation is obtained, which is shown as follows:
Pk/k＝(C2·C1)-1P′k/k(C2·C1)-T (17)
It should be understood that, although the steps in the flowchart of fig. 1 are shown in sequence as indicated by the arrows, the steps are not necessarily performed in sequence as indicated by the arrows. The steps are not strictly limited to the order of execution unless explicitly recited herein, and the steps may be executed in other orders. Moreover, at least some of the steps in fig. 1 may include multiple sub-steps or stages that are not necessarily performed at the same time, but may be performed at different times, nor do the order in which the sub-steps or stages are performed necessarily performed in sequence, but may be performed alternately or alternately with at least a portion of other steps or sub-steps of other steps.
In another specific embodiment, with reference to fig. 2 and fig. 3, the method for positioning satellite inertial tight combination real-time navigation based on the information filtering algorithm in the present invention is further described:
The integrated navigation receiver is connected with the guide receiving antenna by using the radio frequency cable, the power supply is switched on, and the alignment mode of the integrated navigation system is set: "assignment alignment" or "dynamic satellite aiding alignment" sets the lever arm vector from the inertial navigation center to the satellite antenna center.
Based on the time update of the system error state equation, the position, the speed, the posture, the coefficient matrix F, the noise driving matrix G, the system error state variance matrix P 'after dimension transformation, the system noise variance matrix Q' after dimension transformation, the error state transition matrix phi 'k/k-1 and the system noise transition matrix gamma' k/k-1 of the carrier are calculated.
Taking a certain vehicle-mounted test as an example, the sanitation-navigation data and the inertia-navigation data near the time t= 134117.5036s are selected, and a coefficient matrix F and a noise driving matrix G in an error state equation are calculated first:
When the discretized time interval is defined as Δt=8ms, the discretized error state transition matrix Φ k/k-1 and the system noise transition matrix Γ k/k-1 in the formula (1) can be obtained according to the formulas (7) and (8), the system error state variance matrix P 'after the dimension transformation and the system noise variance matrix Q' after the dimension transformation can be obtained by the formula (12), and the information matrix and the information error state vector after the time update can be calculated by the formula (11).
After time update, the carrier position at t= 134117.5036s is obtained through inertial navigation recursion
BLH= [ 4.927X 10 -1 1.972 4.008×101 ] rad, carrier speed
Vector= [ -9.693 x 10 -3 -1.290×10-2 -1.166×10-2 ] m/s, carrier pose
Att＝[-9.459×10-4 -4.603×10-3 3.142]rad。
When time-synchronized preamble data is received, the system enters a measurement update step. At this time, at time t= 134177.5s of the satellite observation data, available satellites include 14 Beidou satellites and 8 GPS satellites, wherein the Beidou satellites have 3 frequency points, and the GPS satellites have 2 frequency points.
Firstly, using single-difference observation values among pseudo-range satellites and double-difference observation values among carrier phase epochs to establish a measurement information vector Z and a measurement information geometric matrix H, then carrying out measurement updating on an information matrix I 'and an information error state vector S' according to a formula (13), wherein the information error state vector after measurement updating is as follows:
From the information error state vector S ', the system error state vector δx' after the dimensional transformation is calculated according to the equations (14) and (15), since the diagonal elements of the information matrix I have been approximately normalized, the following inversion process errors are small:
According to equation (16), the systematic error state vector δx before the dimensional transformation can be calculated from the error state coefficient matrices C 2 and C 1, and since both C 2 and C 1 are diagonal matrices, the inversion operation in equation (12) can be actually converted into division calculation without affecting the calculation efficiency, and the systematic error state vector δx before the dimensional transformation is:
the position, velocity and attitude of the carrier are corrected using the systematic error state vector δx before the measurement-updated dimensional transformation. Calculated to measure the updated carrier position
Blh= [4.927 ×10 -1rad 1.972rad 4.017×101 m ], carrier speed
Vector= [ -3.270 X10 -3m/s -3.688×10-3m/s 2.053×10-2 m/s ], carrier pose
Att= [ -4.489 x 10 -3rad -3.319×10-3 rad 3.140rad ]. On the basis, inertial measurement data can be continuously read, and the time update process is carried out forward.
In this embodiment, based on the performance analysis of the improved information filtering algorithm in the tightly-combined navigation system, by processing a set of vehicle-mounted test data with a duration of 9min, and comparing and verifying the calculation efficiency of the classical sequential kalman filtering algorithm and the information filtering algorithm used in the present invention, as can be seen from fig. 4 and fig. 5, the time used by the information filtering algorithm used in the present invention during a single measurement update period is about 1/13 of that used by the classical sequential kalman filtering algorithm, so that the calculation burden of the calculation main board is greatly reduced, and the statistical information of the specific use is shown in table 1.
Table 1 statistics table at single measurement update time
Then, respectively running two algorithms in the real-time navigation system of the invention, and comparing the single measurement update time of the two algorithms. The used computing main board is a Xilinx ZYNQ7020N development board, a dual-core ARM Cortex-A9 processing system is built in, the highest main frequency is 866MHz, and the operating system is Linux 3.15.0. The method comprises the steps of adopting a span K708 OEM board card and an STIM300 inertial navigation, observing the L1C, L W of a satellite channel as a GPS and the B1I, B2I, B I of a Beidou C01-C37 satellite, wherein the sampling rates are respectively 10Hz and 125Hz, and printing the measurement update time to a screen through a network port. In the experiment, the sequential Kalman filter measurement fluctuates between 15 and 17ms when updated, and the information filter measurement fluctuates between 2 and 3ms when updated.
Because the updating frequency of the inertial navigation module is 125HZ, and the corresponding time interval is 8ms, the calculation time of the sequential Kalman filtering algorithm is too long, the information filtering algorithm is shorter, the normal time updating step is not influenced, and the real-time performance is better.
In order to verify the accuracy index of the invention, the real-time navigation result of a vehicle-mounted test is analyzed, the carrier position track obtained by post calculation of RTKLIB software is used as a reference, the absolute position error is calculated, and the speed and gesture change curve is drawn. In fig. 6, the horizontal axis represents longitude, the vertical axis represents latitude, the real-time position of the integrated navigation system is represented by a red dotted line, the standard track calculated by using RTKLIB software is represented by a black solid line, and it can be seen that the two tracks are substantially identical. In fig. 7, the horizontal axis represents epoch time, the unit is seconds, the vertical axis is the position errors of north, east and earth, so that the positioning error is larger at the initial moment, the errors in the three directions after the post filtering convergence are basically within 1m, and the standard deviation of the errors is smaller as shown in table 2, because epoch differential carrier phase observables are introduced, the positioning result is smooth, the comprehensive positioning error is about 1m, and the method is obviously superior to loose combination navigation positioning precision and can be applied to lane-level navigation scenes.
Table 2 real-time positioning error statistics for tightly-integrated navigation systems
In fig. 8, the horizontal axis is epoch time, the time interval is 8ms, and the vertical axis is the velocity values in the north-east direction, and it can be seen that since the vehicle makes elliptical motion in the horizontal plane, the velocity values in the north direction and the east direction are larger, the velocity component values in the ground direction change periodically, and the velocity component values in the ground direction are smaller.
In fig. 9, the horizontal axis is epoch time, the time interval is 8ms, and the vertical axis is roll angle, pitch angle and yaw angle, and it can be seen that, since the vehicle makes elliptical motion in the horizontal plane, mainly the yaw angle periodically changes within the range of ±180 degrees, and the change amplitude of the roll angle and pitch angle is smaller.
From fig. 7, 8 and 9, it can be seen that the invention can output the position, speed and posture information of the carrier at the frequency of 125HZ, and the comprehensive positioning error is about 1m, so that the positioning accuracy of sub-meter level can be achieved in the horizontal plane, and the change condition of speed and posture is basically consistent with the actual movement condition.
In one embodiment, a computer device is provided, which may be a terminal, and an internal structure diagram thereof may be as shown in fig. 10. The computer device includes a processor, a memory, a network interface, a display screen, and an input device connected by a system bus. Wherein the processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage media. The network interface of the computer device is used for communicating with an external terminal through a network connection. The computer program, when executed by the processor, implements a satellite inertial close-up real-time navigation positioning method based on an information filtering algorithm. The display screen of the computer equipment can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer equipment can be a touch layer covered on the display screen, can also be keys, a track ball or a touch pad arranged on the shell of the computer equipment, and can also be an external keyboard, a touch pad or a mouse and the like.
It will be appreciated by those skilled in the art that the structure shown in FIG. 10 is merely a block diagram of some of the structures associated with the present inventive arrangements and is not limiting of the computer device to which the present inventive arrangements may be applied, and that a particular computer device may include more or fewer components than shown, or may combine some of the components, or have a different arrangement of components.
Those skilled in the art will appreciate that implementing all or part of the above described methods may be accomplished by way of a computer program stored on a non-transitory computer readable storage medium, which when executed, may comprise the steps of the embodiments of the methods described above. Any reference to memory, storage, database, or other medium used in embodiments provided herein may include non-volatile and/or volatile memory. The nonvolatile memory can include Read Only Memory (ROM), programmable ROM (PROM), electrically Programmable ROM (EPROM), electrically Erasable Programmable ROM (EEPROM), or flash memory. Volatile memory can include Random Access Memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms such as Static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double Data Rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (SYNCHLINK) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), among others.
The technical features of the above embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be considered as the scope of the description.
The above examples illustrate only a few embodiments of the application, which are described in detail and are not to be construed as limiting the scope of the application. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the application, which are all within the scope of the application. Accordingly, the scope of protection of the present application is to be determined by the appended claims.
Claims (4)
1. The method for positioning the satellite inertial tight combination real-time navigation based on the information filtering algorithm is characterized by comprising the following steps of:
multiplying the system error state vector by two coefficient matrixes to obtain a system error state vector after dimension transformation; the two coefficient matrixes are a first error state coefficient matrix and a second error state coefficient matrix respectively;
establishing a system error state equation after dimension transformation according to the system error state vector at the previous moment after dimension transformation; according to the system error state vector at the current moment after dimension transformation, a tightly combined measurement equation after dimension transformation is established;
Obtaining a time update equation of information filtering according to the time update of the system error state equation after dimension transformation; the time update equation comprises an information error state vector after time update and an information matrix after time update;
According to the measurement update of the tightly combined measurement equation after dimension transformation and the time update equation, establishing a measurement update equation of information filtering; the measurement update equation comprises a measurement updated information error state vector and a measurement updated information matrix;
obtaining a system error state variance matrix at the current moment after dimension transformation according to the information matrix after measurement updating; obtaining a system error state vector at the current moment after dimension transformation according to the information error state vector after dimension transformation and the system error state variance matrix at the current moment after dimension transformation;
obtaining a system error state vector at the current moment before dimension transformation according to the system error state vector at the current moment after dimension transformation, the first error state coefficient matrix and the second error state coefficient matrix; obtaining a system error state variance matrix of the current moment before dimension transformation according to the system error state variance matrix of the current moment after dimension transformation, the first error state coefficient matrix and the second error state coefficient matrix;
The multiplying the systematic error state vector by two coefficient matrixes to obtain a dimensional transformed systematic error state vector comprises the following steps:
Multiplying the system error state vector delta X by two coefficient matrixes to obtain a system error state vector delta X 'after dimension transformation, wherein the system error state vector delta X' is as follows:
the system error state vector δx 15×1 is a 15-dimensional system error state vector δx, and the expression is as follows:
Wherein δr 3×1 represents a position error vector, δv 3×1 represents a velocity error vector, δΦ 3×1 represents an attitude error vector, δb g,3×1 represents a gyro zero offset error vector, and δb a,3×1 represents an accelerometer zero offset error vector;
C 1,15×15 represents a first error state coefficient matrix C 1;C2,15×15 of 15 dimensions and a second error state coefficient matrix C 2 of 15 dimensions;
The step of establishing a system error state equation after dimension transformation according to the system error state vector at the previous moment after dimension transformation comprises the following steps:
an inertial navigation system error state equation is established by using a 15-dimensional system error state vector delta X' after the dimension transformation, and the formula is as follows:
wherein, A. B and C are derived from an inertial navigation mechanics programming equation, epsilon g,3×1 represents a random error vector of the gyroscope, epsilon a,3×1 represents a random error vector of the accelerometer;
converting the continuous time system into a discrete time system, and obtaining a system error state equation after discretization linearization according to a system error state vector at the previous moment after dimension transformation, wherein the system error state equation is as follows:
δX'k/k-1＝Φ'k/k-1δX'k-1/k-1+Γ'k/k-1Wk-1'
wherein the expression of each variable is as follows:
δX'k/k-1＝(C2,kC1,k)·δXk/k-1
δX'k-1/k-1＝(C2,k-1C1,k-1)·δXk-1/k-1
Wk-1'＝CεWk-1
Φ'k/k-1＝(C2,kC1,k)·Φk/k-1·(C2,k-1C1,k-1)-1
Γ'k/k-1＝(C2,kC1,k)·Γk/k-1·Cε -1
δx k-1/k-1 represents a system error state vector at a previous time, C ε represents a dimensional transformation coefficient matrix, W k-1 represents a system noise vector, obeying a normal distribution of a covariance matrix of Q k-1, the specific parameter is determined by inertial navigation device performance, Φ k/k-1 represents an error state transition matrix from the previous time to the current time, Γ k/k-1 represents a system noise transition matrix, and the calculation formulas of Φ k/k-1 and Γ k/k-1 are as follows:
Γk/k-1＝G·Δt
wherein, the time interval Δt=t k-tk-1, italic I represents an identity matrix, F represents a coefficient matrix, and G represents a noise driving matrix;
The method for establishing the tightly combined measurement equation after dimension transformation according to the system error state vector at the current moment after dimension transformation comprises the following steps:
according to the system error state vector delta X' k/k at the current moment after the dimension transformation, a tightly combined measurement equation after the dimension transformation is established, and the formula is as follows:
Zk＝Hk'δX′k/k+ξk
wherein, H k represents a measurement information geometric matrix, ζ k represents a measurement error vector, the zero-mean multidimensional n-Tai distribution obeying the covariance matrix is R k, the specific parameters of R k are obtained by carrying out error modeling on the hygienically measured information, Z k represents a hygienically measured information vector at the time t k, and the calculation formula of Z k is as follows:
Wherein δP (t k) represents single-difference error observables among pseudo-range satellites, δDelta tφ(tk represents double-difference error observables among carrier phase satellites, the double-difference error observables are obtained by calculation of satellite navigation original observation data and antenna positions of inertial navigation forecast, the column vectors are n-1 dimension, and n represents visible satellite particles;
according to the measurement update of the dimension transformed tightly combined measurement equation and the time update equation, establishing an information filtering measurement update equation, which comprises the following steps:
According to the calculation results of the dimension transformed tight combination measurement equation and the time update equation, introducing the guide measurement information to carry out measurement update on S 'k/k-1 and I' k/k-1, and establishing the measurement update equation of information filtering as follows:
Wherein S 'k/k represents a measurement updated information error state vector, and I' k/k represents a measurement updated information matrix
Obtaining a system error state variance matrix at the current moment after dimension transformation according to the information matrix after measurement updating; obtaining a system error state vector of the current moment after dimension transformation according to the information error state vector after dimension transformation and the system error state variance matrix of the current moment after dimension transformation, comprising:
According to the information matrix I 'k/k after measurement update, a system error state variance matrix P' k/k at the current moment after dimension transformation is obtained, and the formula is expressed as follows:
And obtaining a system error state vector delta X ' k/k of the current moment after dimension transformation according to the information error state vector S ' k/k after dimension transformation and the system error state variance array P ' k/k of the current moment after dimension transformation, wherein the formula is as follows:
δX′k/k＝P′k/k·S′k/k；
The system error state vector at the current moment before dimension transformation is obtained according to the system error state vector at the current moment after dimension transformation, the first error state coefficient matrix and the second error state coefficient matrix; obtaining a system error state variance matrix of the current moment before dimension transformation according to the system error state variance matrix of the current moment after dimension transformation, the first error state coefficient matrix and the second error state coefficient matrix, wherein the system error state variance matrix comprises the following components:
Obtaining a system error state vector delta X k/k at the current moment before dimension transformation according to the system error state vector delta X' k/k at the current moment after dimension transformation, the first error state coefficient matrix C 1 and the second error state coefficient matrix C 2, wherein the formula is as follows:
δXk/k＝(C2·C1)-1·δX′k/k
Obtaining a system error state variance matrix P k/k of the current moment before dimension transformation according to the system error state variance matrix P' k/k of the current moment after dimension transformation, the first error state coefficient matrix C 1 and the second error state coefficient matrix C 2, which are shown as follows:
Pk/k＝(C2·C1)-1P′k/k(C2·C1)-T。
2. The method according to claim 1, wherein the method further comprises:
constructing a first error state coefficient matrix with zero elements except diagonal elements according to the radius of curvature of the earth meridian, the radius of curvature of the earth prime circle, the altitude of the carrier and the latitude of the carrier; the first error state coefficient matrix C 1 enables the weft warp high error to be converted into the north-east position error;
Constructing a second error state coefficient matrix with zero elements except diagonal elements according to the diagonal elements of the first error state coefficient matrix C 1 and the main diagonal elements of the system error state variance matrix; wherein, the second error state coefficient matrix C 2 makes the diagonal element of the system error state variance matrix after dimension transformation equal to 1.
3. The method according to claim 2, wherein the method further comprises:
The calculation formulas of the diagonal elements of the first error state coefficient matrix C 1 and the diagonal elements of the second error state coefficient matrix C 2 are respectively:
Wherein C 1,15×1 represents the diagonal element values of the first error state coefficient matrix C 1 of 15 dimensions; c 2,15×1 represents the diagonal element value of the second error state coefficient matrix C 2 of 15 dimensions, R n is the radius of curvature of the earth's meridian, R e represents the radius of curvature of the earth's circle of mortise and tenon, h represents the altitude of the carrier, B represents the latitude of the carrier, K 1 (i) represents the i-th element of the main diagonal of the matrix C 1, and σ i represents the i-th element of the main diagonal of the system error state variance matrix.
4. The method of claim 1, further comprising, prior to deriving the time update equation for the information filtering, based on the time update of the dimensional transformed system error state equation:
definition of dimension transformed information matrix Information error State vector/>Two auxiliary transition matrices/>N＝MΓ′(Γ′TMΓ′+Q′-1)-1Γ′T；
Obtaining a time update equation of information filtering according to the time update of the system error state equation after dimension transformation, wherein the time update equation comprises the following steps:
Ι′k/k-1＝(I-N)M
The time update is a transformation process of the system error state vector after dimension transformation from the previous moment to the current moment;
Wherein S 'k/k-1 represents a time-updated information error state vector, i' k/k-1 represents a time-updated information matrix, and i 'k/k-1 is used for describing the degree of dispersion of error state distribution, that is, the size of the information content in S' k/k-1; p represents a systematic error state vector variance matrix, Q represents a systematic noise variance matrix, P 'represents a systematic error state variance matrix after dimension transformation, Q' represents a systematic noise variance matrix after dimension transformation, and the calculation formulas of P 'and Q' are respectively as follows:
P'＝(C2·C1)·P·(C2·C1)T
Q'＝Cε·Q·Cε T
wherein, the diagonal line element of C ε is obtained by the open root number of the diagonal line element of Q, and the rest elements are all zero.
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