CN115291266A - Satellite inertia tight combination real-time navigation positioning method based on information filtering algorithm - Google Patents
Satellite inertia 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 inertia tight integration 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, deriving a new time updating equation and a new measurement updating equation on the basis of the system error state equation and the tightly combined measurement equation, participating the system error state vector after the dimension transformation in new information filtering model calculation, thus obtaining the system error state vector at the current moment before the dimension transformation, and using the system error state vector at the current moment for correcting the navigation result at the current moment. By adopting the method, the calculation of high-dimensional matrix inversion can be avoided, under the condition of more observed values, the precision advantage of the tight combination navigation is exerted, the calculated amount and the calculation error in the measurement updating process are effectively reduced, the real-time performance of the tight combination navigation system is improved, and the possibility is provided for realizing the functions of gross error detection, integrity real-time calculation and the like.
Description
Technical Field
The application relates to the technical field of satellite and inertia combination, in particular to a satellite inertia tight combination real-time navigation positioning method based on an information filtering algorithm.
Background
The combined navigation system is characterized in that various navigation devices are combined in a proper mode, and the complementary characteristics of the performance of the navigation devices are utilized to realize better navigation performance, so that the most widely applied scheme is a satellite and inertia combined navigation scheme. The satellite navigation system can provide global and all-weather position and speed information, has long-term stable precision, and can correct the accumulated error of inertial navigation through filtering; inertial navigation has higher update rate and various navigation information, and can also assist detection and elimination of the satellite-guided observation quantity faults, but errors can be gradually accumulated along with time, and the long-time independent work cannot be realized. The satellite navigation system and the inertial navigation system are combined, so that the advantage complementation can be realized, the precision and the stability of the combined system are improved, and the information such as the position, the speed, the attitude, the acceleration, the angular velocity and the like of a carrier is output.
The integrated navigation system can be classified into a loose integration (Loosely-Coupled), a tight integration (Tightly-Coupled), and a deep integration (deep-Coupled) according to the combination method. The loose combination uses the result of satellite navigation single-point positioning and speed fixing and the inertial navigation data to carry out fusion filtering, the tight combination navigation system uses pseudo range and Doppler observation information output by a satellite receiver to combine with the inertial navigation system, and the combination module estimates and compensates errors of satellite navigation and inertial navigation subsystems, so that a positioning result with higher precision is obtained, and the loose combination navigation system has obvious performance advantages.
The common data fusion method used by the satellite and inertial integrated navigation system is based on a Kalman (Kalman) filtering algorithm, but considering that the data processing capacity of the miniaturized integrated navigation system is limited, when the number of available satellites is large, the equation dimension for measurement update is large, the calculation time using the Kalman filtering algorithm is long, and the work of time update, gross error detection, integrity calculation and the like can be influenced.
Disclosure of Invention
Therefore, in order to solve the technical problems, it is necessary to provide a satellite inertia 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, and the equation dimension of measurement update is large, the calculation time of the traditional kalman filtering algorithm is long, so that the time update, the gross error detection and the integrity calculation are affected.
A satellite inertia tight combination real-time navigation positioning method based on an information filtering algorithm comprises the following steps:
the system error state vector is multiplied by the two coefficient matrixes to obtain the system error state vector after dimension transformation; the two coefficient matrixes are respectively a first error state coefficient matrix and a second error state coefficient matrix;
establishing a system error state equation after dimension transformation according to the system error state vector at the previous moment after dimension transformation; establishing a tightly-combined measurement equation after dimension transformation according to the system error state vector at the current moment after dimension transformation;
obtaining a time updating equation of information filtering according to the system error state equation after dimension transformation; the time updating equation comprises a time updated information error state vector and a time updated information matrix;
establishing a measurement updating equation of information filtering based on measurement updating of a tightly combined measurement equation and a time updating equation after dimension transformation; the measurement updating 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 updated information matrix after measurement; 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 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 array at the current moment before dimension transformation according to the system error state variance array at 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 the following steps: the system error state vector delta X is multiplied 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:
system error state vector deltax 15×1 Is a 15-dimensional system error state vector δ X, expressed as follows:
wherein, δ r 3×1 Indicating the position error vector, δ v 3×1 Representing the velocity error vector, δ φ 3×1 Representing the attitude error vector, δ b g,3×1 Representing a gyro zero offset error vector, and delta X representing an accelerometer zero offset error vector;
C 1,15×15 representing a 15-dimensional first error state coefficient matrix C 1 ；C 2,15×15 Representing a second error state coefficient matrix C of 15 dimensions 2 。
In one embodiment, the method further comprises the following steps: constructing a first error state coefficient matrix with zero elements except diagonal elements according to the meridian curvature radius of the earth, the curvature radius of the earth prime circle, the altitude of the carrier and the latitude of the carrier; wherein the first error state coefficient matrix C 1 So that the high latitude and longitude error is converted into a north east position error;
according to the first error state coefficient matrix C 1 Constructing a second error state coefficient matrix with zero other elements except the diagonal elements; wherein the second error state coefficient matrix C 2 The diagonal elements of the dimension transformed system error state variance matrix are made equal to 1.
In one embodiment, the method further comprises the following steps: first errorState coefficient matrix C 1 Diagonal elements of and a second error state coefficient matrix C 2 The calculation formula of the diagonal elements is respectively as follows:
wherein, C 1,15×1 Representing a 15-dimensional first error state coefficient matrix C 1 A diagonal element value of (a); c 2,15×1 Representing a 15-dimensional second error state coefficient matrix C 2 Diagonal element value of R n Radius of curvature of meridian of the earth, R e Representing the curvature radius of the earth-shaped unitary space ring, h representing the altitude of the carrier, B representing the latitude of the carrier, and K 1 (i) Is represented by C 1 The ith element, σ, of the main diagonal of the matrix i The ith element representing the main diagonal of the variance matrix of the state of the system error.
In one embodiment, the method further comprises the following steps: using the 15-dimensional system error state vector delta X' after dimension transformation to establish an inertial navigation system error state equation, wherein the equation is as follows:
wherein the content of the first and second substances,
A. b and C are derived from an inertial navigation mechanics arrangement equation g,3×1 Representing the random error vector, ε, of a gyroscope a,3×1 A random error vector representing an 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 as follows:
δX′ k/k-1 ＝Φ′ k/k-1 δX′ k-1/k-1 +Γ′ k/k-1 W k-1 ′
wherein the expressions of the variables are as follows:
δX′ k/k-1 ＝(C 2,k C 1,k )·δX k/k -1
δX′ k-1/k-1 ＝(C 2,k-1 C 1,k-1 )·δX k-1/k-1
W k-1 ′＝C ε W k-1
Φ′ k/k-1 ＝(C 2,k C 1,k )·Φ k/k-1 ·(C 2,k-1 C 1,k-1 ) -1
δX k-1/k-1 representing the state vector of the system error at the previous instant, W k-1 Representing the system noise vector obeying a covariance matrix of Q k-1 The specific parameters are determined by the performance of the inertial navigation device, C ε Representing a matrix of dimension transformation coefficients, phi k/k-1 Representing the error state transition matrix, Γ, from the previous time to the current time k/k-1 Representing the system noise transfer matrix, phi k/k-1 And gamma k/k-1 The calculation formula of (c) is as follows:
Γ k/k-1 ＝G·Δt
wherein the time interval Δ t = t k -t k-1 Italics I denotes an identity matrix, F denotes a coefficient matrix, and G denotes a noise driving matrix.
In one embodiment, the method further comprises the following steps: system error state vector delta X 'at current moment after dimension transformation' k/k Establishing a tightly-combined measurement equation after dimension transformation, wherein the formula is as follows:
Z k ＝H k ′δX′ k/k +ξ k
wherein the content of the first and second substances,
H k geometrical matrix, xi, representing measurement information k Representing the measurement error vector obeying a covariance matrix of R k Zero mean multidimensional positive space distribution, R k Is obtained by error modeling of satellite navigation measurement information, Z k Denotes t k Satellite derived measurement information vector of time, Z k The calculation formula of (c) is as follows:
wherein δ P (t) k ) Represents the observed quantity of single-difference error between pseudo-range stars, delta t φ(t k ) The double-difference error observed quantity between the carrier phase inter-satellite epochs is obtained by calculating satellite navigation original observation data and an antenna position predicted by inertial navigation, is a column vector with n-1 dimensions, and n represents the number of visible satellites.
In one embodiment, the method further comprises the following steps: defining a dimension transformed information matrix
Information error state vector
And two auxiliary transition matrices
N＝MΓ′(Γ′ T MΓ′+Q′ -1 ) -1 Γ′ T ；
Obtaining a time updating equation of information filtering according to the time updating of the system error state equation after dimension transformation, wherein the time updating equation comprises the following steps:
Ι′ k/k-1 ＝(I-N)M
the time updating is the conversion process of the system error state vector after dimension conversion from the previous moment to the current moment;
wherein, S' k/k-1 Indicates the information error state vector, I 'after time update' k/k-1 Represents the information matrix I 'after the time update' k/k-1 For describing the degree of dispersion of the error state distribution, i.e. S' k/k-1 The size of the contained information volume; p represents a system error state vector variance matrix, Q represents a system noise variance matrix, P 'represents the system error state variance matrix after dimension transformation, Q' represents the system noise variance matrix after dimension transformation, and P 'and Q' are respectively:
P′＝(C 2 ·C 1 )·P·(C 2 ·C 1 ) T
Q′＝C ε ·Q·C ε T
wherein, C ε The diagonal elements of (a) are obtained by root-opening the diagonal elements of Q, and the other elements are all zero.
In one embodiment, the method further comprises the following steps: introducing satellite navigation measurement information pairs S 'according to the calculation results of the closely combined measurement equation and the time updating equation after dimension transformation' k/k-1 And l' k/k-1 And (3) carrying out measurement updating, and establishing a measurement updating equation of information filtering as follows:
wherein, S' k/k Represents the updated information error state vector, I' k/k Representing the updated information matrix of the measurement.
In one embodiment, the method further comprises the following steps: according to the updated information matrix I 'after measurement' k/k Obtaining a system error state variance matrix P 'at the current moment after dimension transformation' k/k The formula is expressed as:
according to the measured and updated information error state vector S' k/k And current time system error state variance matrix P 'after dimension transformation' k/k Obtaining a system error state vector delta X 'of the current time after dimension transformation' k/k The formula is expressed as:
δX′ k/k ＝P′ k/k ·S′ k/k 。
in one embodiment, the method further comprises the following steps: according to the system error state vector delta X 'at the current moment after dimension transformation' k/k A first error state coefficient matrix C 1 And a second error state coefficient matrix C 2 Obtaining the system error state vector delta X at the current moment before dimension transformation k/k The formula is expressed as:
δX k/k ＝(C 2 ·C 1 ) -1 ·δX′ k/k
according to the current time system error state variance matrix P 'after dimension transformation' k/k A first error state coefficient matrix C 1 And a second error state coefficient matrix C 2 Obtaining the system error state variance matrix P at the current moment before dimension transformation k/k The notations are represented as:
P k/k ＝(C 2 ·C 1 ) -1 P k ′ /k (C 2 ·C 1 ) -T 。
according to the satellite inertia tight combination real-time navigation positioning method based on the information filtering algorithm, the improved information filtering method and the tight combination navigation method are combined, dimension transformation is carried out on a system error state vector, a new time updating equation and a new measurement updating equation are derived, calculation of inversion of a high-dimensional matrix is avoided, under the condition that the number of observed values is large, the precision advantage of tight combination navigation is exerted, the calculated amount and the calculated error in the measurement updating process are effectively reduced, the real-time performance of the tight combination navigation system is improved, and the possibility is provided for realizing functions of gross error detection, integrity real-time calculation and the like.
Drawings
FIG. 1 is a schematic flow chart of a satellite inertia tight integration real-time navigation positioning method based on an information filtering algorithm in an embodiment;
FIG. 2 is a flow diagram illustrating information processing for a combined satellite/inertial navigation system according to one embodiment;
FIG. 3 is a flow diagram of information processing by the information filtering algorithm in one embodiment;
FIG. 4 is a comparison of sequential Kalman filtering and information filtering measurement updates in another embodiment;
FIG. 5 is a graph illustrating a variation of a ratio of sequential Kalman filtering to information filtering in one embodiment;
FIG. 6 is a diagram of a horizontal movement trajectory of a vehicle in one embodiment;
FIG. 7 is a three-dimensional positioning error plot for a vehicle according to one embodiment;
FIG. 8 is a graph illustrating a three-dimensional velocity profile of a vehicle according to one embodiment;
FIG. 9 is a graph illustrating a three-dimensional attitude change of a vehicle according to an embodiment;
fig. 10 is an internal structural diagram of a computer device in one embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
In one embodiment, as shown in fig. 1, there is provided a satellite inertia tight combination real-time navigation positioning method based on an information filtering algorithm, which can be applied in a terminal, and includes the following steps:
102, multiplying the system error state vector by two coefficient matrixes to obtain a system error state vector after dimension transformation; the two coefficient matrices 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, two positions need to be subjected to high-dimensional matrix inversion calculation, the condition of irreversibility or poor inversion precision can occur, in order to avoid the condition, the invention constructs two coefficient matrixes of which the other elements except diagonal elements are zero, the system error state vector is subjected to left multiplication by the two coefficient matrixes to obtain the system error state vector after dimension transformation, and the dimension of the system error state vector is transformed to enable the (gamma) to be obtained T MΓ+Q -1 ) The diagonal elements of the matrix I are approximately equal, and the diagonal elements of the information matrix I are approximately normalized, so that the calculation accuracy in the matrix inversion process is effectively improved.
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 coupled navigation system and the tightly coupled measurement equation is based on the satellite navigation measurement equations for pseudorange and carrier phase.
Specifically, a process of predefining an information matrix after dimension transformation, an information error state vector and two auxiliary transition matrices and deriving a time-updated information error state vector and a time-updated information matrix based on a discrete-form system error state equation is called as an information filtering time update equation.
Specifically, on the basis of the calculation result of the time update equation, the measurement update is performed on the time-updated information error state vector and the time-updated information matrix by introducing satellite-guided measurement information, and a process of obtaining the measurement-updated information error state vector and the measurement-updated information matrix is called as a measurement update equation of information filtering.
Specifically, performing inverse operation on the information matrix after measurement updating to obtain a system error state variance matrix at the current moment after dimension transformation; and multiplying the information error state vector after measurement updating with the system error state variance matrix at the current moment after dimension conversion to obtain the system error state vector at the current moment after dimension conversion.
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 at the current moment before dimension transformation according to the system error state variance matrix at the current moment after dimension transformation, the first error state coefficient matrix and the second error state coefficient matrix.
It can be understood that the system error state vector at the current moment before dimension transformation is used for correcting the navigation result (parameters such as position, speed and attitude of the carrier) at the current moment.
According to the satellite inertia tight combination real-time navigation positioning method based on the information filtering algorithm, the improved information filtering method and the tight combination navigation method are combined, dimension transformation is carried out on a system error state vector, a new time updating equation and a new measurement updating equation are derived, calculation of inversion of a high-dimensional matrix is avoided, under the condition that the number of observed values is large, the precision advantage of tight combination navigation is exerted, the calculated amount and the calculated error in the measurement updating process are effectively reduced, the real-time performance of the tight combination navigation system is improved, and the possibility is provided for realizing functions of gross error detection, integrity real-time calculation and the like.
In one embodiment, the step of left-multiplying the system error state vector by two coefficient matrixes to obtain a dimension-transformed system error state vector includes:
the system error state vector delta X is multiplied 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:
system error state vector deltax 15×1 Is a 15-dimensional system error state vector δ X, expressed as follows:
wherein, δ r 3×1 Indicating the position error vector, δ v 3×1 Representing the velocity error vector, δ φ 3×1 Representing the attitude error vector, δ b g,3×1 Representing the gyro zero-offset error vector, δ b a,3×1 Representing an accelerometer zero offset error vector;
C 1,15×15 first error state coefficient matrix C representing 15 dimensions 1 ；C 2,15×15 Representing a 15-dimensional second error state coefficient matrix C 2 。
In one embodiment, a first error state coefficient matrix with zero elements except diagonal elements is constructed according to the radius of curvature of the earth meridian, the radius of curvature of the earth prime unit circle, the altitude of a carrier and the latitude of the carrier; wherein the first error state coefficient matrix C 1 So that the high latitude and longitude error is converted into the northeast position error; according to the first error state coefficient matrix C 1 The diagonal elements and the system error state variance matrix main diagonal elements of (1) are constructed by dividing the diagonal elementsA second error state coefficient matrix with all other elements except the elements being zero; wherein the second error state coefficient matrix C 2 The diagonal elements of the dimension transformed system error state variance matrix are made equal to 1.
In another embodiment, the first error state coefficient matrix C 1 Diagonal elements of and a second error state coefficient matrix C 2 The calculation formula of (a) is respectively as follows:
wherein, C 1,15×1 First error state coefficient matrix C representing 15 dimensions 1 A diagonal element value of (a); c 2,15×1 Representing a second error state coefficient matrix C of 15 dimensions 2 A diagonal element value of; r n Is the radius of curvature of the earth in the meridian, and the unit is m; r e The curvature radius of the earth prime circle is represented, and the unit is m; h represents the carrier altitude in m; b represents the latitude of the vector, and the unit is rad; k 1 (i) Is represented by C 1 The ith element of the main diagonal of the matrix; sigma i The ith element representing the main diagonal of the variance matrix in the state of the system error.
In another embodiment, the step of establishing the dimension-transformed system error state equation according to the dimension-transformed system error state vector of the previous time comprises:
using the 15-dimensional system error state vector delta X' after dimension transformation to establish an inertial navigation system error state equation, wherein the equation is as follows:
wherein, the first and the second end of the pipe are connected with each other,
A. b and C are derived from an inertial navigation mechanics arrangement equation g,3×1 Representing the random error vector, ε, of the gyroscope a,3×1 Indicating accelerationA random error vector of the meter;
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 as follows:
δX′ k/k-1 ＝Φ′ k/k-1 δX′ k-1/k-1 +Γ′ k/k-1 W k-1 ′ (5)
wherein the expressions for the variables are as follows:
δX k-1/k-1 representing the state vector of the systematic error at the previous moment, C ε Representing a matrix of dimensional transformation coefficients, W k-1 Representing the system noise vector obeying a covariance matrix of Q k-1 The specific parameter is determined by the performance of the inertial navigation device, phi k/k-1 Representing the error state transition matrix, Γ, from the previous time to the current time k/k-1 Representing the system noise transfer matrix, phi k/k-1 And gamma k/k-1 The calculation formula of (c) is as follows:
Γ k/k-1 ＝G·Δt (8)
wherein the time interval Δ t = t k -t k-1 Italicized I denotes an identity matrix, F denotes a coefficient matrix, and G denotes a noise driving matrix.
In another embodiment, the step of establishing the dimension-transformed tightly-combined measurement equation according to the dimension-transformed current-time system error state vector comprises the following steps:
according to the system error state vector delta X 'at the current moment after dimension transformation' k/k Establishing a tightly-combined measurement equation after dimension transformation, wherein the formula is as follows:
Z k ＝H k ′δX′ k/k +ξ k (9)
wherein the content of the first and second substances,
H k geometrical matrix, ξ, representing measurement information k Representing the measurement error vector obeying a covariance matrix of R k Zero mean multidimensional positive space distribution, R k Is obtained by error modeling of satellite navigation measurement information, Z k Represents t k Time of day satellite-guided measurement information vector, Z k The calculation formula of (c) is as follows:
wherein δ P (t) k ) Representing single-difference error observations, δ Δ, between pseudo-range stars t φ(t k ) The double-difference error observed quantity between the carrier phase inter-satellite epochs is obtained by calculating satellite navigation original observation data and an antenna position predicted by inertial navigation, is a column vector with n-1 dimensions, and n represents the number of visible satellites.
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:
defining a dimension transformed information matrix
Information error state vector
And two auxiliary transition matrices
N＝MΓ′(Γ′ T MΓ′+Q′ -1 ) -1 Γ′ T ；
Obtaining a time updating equation of information filtering according to the time updating of the system error state equation after dimension transformation, wherein the time updating equation comprises the following steps:
the time updating is the conversion process of the system error state vector after dimension conversion from the previous moment to the current moment;
wherein, S' k/k-1 Represents the information error state vector, I 'after the time update' k/k-1 Represents the information matrix I 'after the time update' k/k-1 Describing the degree of dispersion of the error state distribution, i.e. S' k/k-1 The size of the contained information volume; p represents a system error state vector variance array, Q represents a system noise variance array, P 'represents a system error state variance array after dimension transformation, Q' represents a system noise variance array after dimension transformation, and P 'and Q' respectively are as follows:
wherein, C ε The diagonal elements of (a) are obtained by root-opening the diagonal elements of Q, and the other elements are all zero.
In another embodiment, the establishing of the information-filtered measurement update equation according to the measurement update of the immediately combined measurement equation and time update equation after the dimension transformation comprises:
introducing guard guide measurement information pair S 'according to the calculation result of the closely combined measurement equation and the time updating equation after dimension transformation' k/k-1 And I' k/k-1 And (3) carrying out measurement updating, and establishing a measurement updating equation of information filtering as follows:
wherein, S' k/k Represents the updated information error state vector, I' k/k Representing the updated information matrix of the measurement.
In another embodiment, the updated information matrix I 'is measured' k/k Obtaining a system error state variance matrix P 'at the current moment after dimension transformation' k/k The formula is expressed as:
according to the measurement updated information error state vector S' k/k And current time system error state variance matrix P 'after dimension transformation' k/k Obtaining a system error state vector delta X 'at the current time after dimension transformation' k/k The formula is expressed as:
δX′ k/k ＝P′ k/k ·S′ k/k (15)
in another embodiment, the system error state vector δ X 'is transformed according to dimension at the current time' k/k A first error state coefficient matrix C 1 And a second error state coefficient matrix C 2 Obtaining the system error state vector delta X at the current moment before dimension transformation k/k The formula is expressed as:
δX k/k ＝(C 2 ·C 1 ) -1 ·δX′ k/k (16)
according to the system error state variance array P 'at the current moment after dimension transformation' k/k A first error state coefficient matrix C 1 And a second error state coefficient matrix C 2 Obtaining the system error state variance matrix P at the current moment before dimension transformation k/k The notations are represented as:
P k/k ＝(C 2 ·C 1 ) -1 P′ k/k (C 2 ·C 1 ) -T (17)
it should be understood that, although the steps in the flowchart of fig. 1 are shown in order as indicated by the arrows, the steps are not necessarily performed in order as indicated by the arrows. The steps are not performed in the exact order shown and described, and may be performed in other orders, unless explicitly stated otherwise. Moreover, at least a portion of the steps in fig. 1 may include multiple sub-steps or multiple stages that are not necessarily performed at the same time, but may be performed at different times, and the order of performance of the sub-steps or stages is not necessarily sequential, but may be performed in turn or alternately with other steps or at least a portion of the sub-steps or stages of other steps.
In another embodiment, the information filtering algorithm based satellite inertia tight combination real-time navigation positioning method of the present invention is further described with reference to fig. 2 and fig. 3:
connecting the combined navigation receiver with the guide receiving antenna by using a radio frequency cable, switching on a power supply, and setting an alignment mode of the combined navigation system: and assigning alignment or dynamic satellite navigation auxiliary alignment, and setting a lever arm vector from an inertial navigation center to the center of the satellite antenna.
Based on time updating of the system error state equation, calculating a position, a speed, an attitude and a coefficient matrix F, a noise driving matrix G, a dimension-transformed system error state variance matrix P ', a dimension-transformed system noise variance matrix Q', an error state conversion matrix phi 'of the carrier' k/k-1 And a system noise transfer matrix gamma' k/k-1 。
Taking a certain vehicle-mounted test as an example, satellite navigation and inertial 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 firstly calculated:
when the discretization time interval is defined as Δ t =8ms, the discretized error state transition matrix Φ in equation (1) is set to be smaller than the discretized error state transition matrix Φ k/k-1 And the system noise transfer matrix Γ k/k-1 The system error state variance matrix P' after dimension transformation and the system noise after dimension transformation can be obtained according to the formula (7) and the formula (8)The variance matrix Q' can be obtained by equation (12), and the time-updated information matrix and the information error state vector are calculated by equation (11).
After time updating, the position of the carrier at t =134117.5036s can be obtained by inertial navigation recursion
BLH＝[4.927×10 -1 1.972 4.008×10 1 ]rad, carrier velocity
Vel＝[-9.693×10 -3 -1.290×10 -2 -1.166×10 -2 ]m/s, carrier attitude
Att＝[-9.459×10 -4 -4.603×10 -3 3.142]rad。
When receiving the time-synchronized satellite data, the system enters a measurement update step. At the time t =134177.5s of the satellite navigation observation data, the 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, establishing a measurement information vector Z and a measurement information geometric matrix H by using pseudo-range inter-satellite single-difference observed values and carrier phase inter-satellite double-difference observed values, and then measuring and updating an information matrix I 'and an information error state vector S' according to a formula (13), wherein the information error state vector after measurement and update is as follows:
from equations (14) and (15), the dimension-transformed system error state vector δ X 'is calculated from the information error state vector S', and since the diagonal elements of the information matrix I have been approximately normalized, the following inversion process error is small:
from equation (16), the error state coefficient matrix C 2 And C 1 Calculating the systematic error state vector deltaX before dimension transformation, due to C 2 And C 1 Are all diagonal matrices, so the inversion operation in equation (12) is realThe method can be converted into division calculation without influencing the calculation efficiency, and the system error state vector delta X before dimension conversion is as follows:
and correcting the position, the speed and the posture of the carrier by using the system error state vector delta X before the measurement updating dimension transformation. Calculated, updated carrier position is measured
BLH＝[4.927×10 -1 rad 1.972rad 4.017×10 1 m]Speed of carrier
Vel＝[-3.270×10 -3 m/s -3.688×10 -3 m/s 2.053×10 -2 m/s]Attitude of carrier
Att＝[-4.489×10 -3 rad -3.319×10 -3 rad 3.140rad]. On the basis, inertial navigation measurement data can be continuously read, and a time updating process is carried out forward.
In this embodiment, based on the performance analysis of the improved tightly-combined navigation system of the information filtering algorithm, the calculation efficiency of the classical sequential kalman filtering algorithm and the calculation efficiency of the information filtering algorithm used in the present invention are verified by comparing a set of vehicle-mounted test data with a duration of 9min, as can be seen from fig. 4 and 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 of the classical sequential kalman filtering algorithm, so that the calculation burden of the calculation motherboard is greatly reduced, and the statistical information during specific use is shown in table 1.
TABLE 1 statistical information Table for single measurement update
Then, two algorithms are respectively operated in the real-time navigation system of the invention, and the time spent by single measurement update is compared. 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 southwestern K708 OEM board card and STIM300 inertial navigation, observing satellite channels of L1C and L2W of a GPS and B1I, B2I and B3I of a Beidou C01-C37 satellite, wherein sampling rates are respectively 10Hz and 125Hz, and printing measurement update time on a screen through a network port. In the test, the time for updating the sequential Kalman filtering measurement fluctuates between 15 and 17ms, and the time for updating the information filtering measurement fluctuates between 2 and 3 ms.
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 time consumption of the information filtering algorithm is short, the normal time updating step cannot be influenced, and the real-time performance is better.
In order to verify the precision index of the invention, the real-time navigation result of a one-time vehicle-mounted test is analyzed, the position track of the carrier obtained by the subsequent calculation of RTKLIB software is used as the reference, the absolute position error is calculated, and the speed and attitude change curve is drawn. In fig. 6, the horizontal axis represents longitude and the vertical axis represents latitude, the real-time position of the integrated navigation system is represented by a red dotted line, and the standard trajectory calculated using the RTKLIB software is represented by a black solid line, and it can be seen that the two trajectories are substantially identical. In fig. 7, the horizontal axis represents epoch time, the unit is second, the vertical axis represents position errors in the north direction, the east direction and the ground direction, it can be seen that the positioning error is large due to misalignment at the initial time, the errors in the three directions after post-filtering convergence are basically within 1m, and meanwhile, as can be seen from table 2, the standard deviation of the errors is small, because epoch differential carrier phase observed quantity is introduced, the positioning result is smoothed, the comprehensive positioning error is about 1m, which is obviously superior to the loose combination navigation positioning accuracy, and can be applied to a lane-level navigation scene.
TABLE 2 real-time positioning error statistics for tightly-integrated navigation systems
In fig. 8, the abscissa represents epoch time, the time interval is 8ms, and the ordinate represents velocity values in the three north-east directions, and it can be seen that since the vehicle makes an elliptical motion in the horizontal plane, velocity values in the north direction and the east direction are large and vary periodically, and velocity component values in the ground direction are small.
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 an elliptical motion in the horizontal plane, the yaw angle mainly changes periodically within a range of ± 180 degrees, and the change ranges of the roll angle and the pitch angle are small.
As can be seen from fig. 7, 8 and 9, the present invention can output the position, speed and attitude information of the carrier at a frequency of 125HZ, and the integrated positioning error is about 1m, the sub-meter level positioning accuracy can be achieved in the horizontal plane, and the variation of the speed and attitude substantially conforms to the actual motion situation.
In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram 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 comprises a nonvolatile 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 an operating system and computer programs in the non-volatile storage medium. The network interface of the computer device is used for communicating with an external terminal through a network connection. The computer program is executed by a processor to realize a satellite inertia compact combination 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, a key, a track ball or a touch pad arranged on the shell of the computer equipment, an external keyboard, a touch pad or a mouse and the like.
Those skilled in the art will appreciate that the architecture shown in fig. 10 is merely a block diagram of some of the structures associated with the disclosed aspects and is not intended to limit the computing devices to which the disclosed aspects apply, as particular computing devices may include more or less components than those shown, or may combine certain components, or have a different arrangement of components.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by hardware instructions of a computer program, which can be stored in a non-volatile computer-readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. Any reference to memory, storage, database, or other medium used in the embodiments provided herein may include non-volatile and/or volatile memory, among others. Non-volatile 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 DRAM (SLDRAM), rambus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).
The technical features of the above embodiments can be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the above embodiments are not described, but should be considered as the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is specific and detailed, but not to be understood as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (10)
1. A satellite inertia tight combination real-time navigation positioning method based on an information filtering algorithm is characterized by comprising the following steps:
the system error state vector is multiplied by the two coefficient matrixes to obtain the system error state vector after dimension transformation; the two coefficient matrixes are respectively a first error state coefficient matrix and a second error state coefficient matrix;
establishing a system error state equation after dimension transformation according to the system error state vector at the previous moment after dimension transformation; establishing a tightly combined measurement equation after dimension transformation according to the system error state vector at the current moment after dimension transformation;
according to the time update of the system error state equation after the dimension transformation, obtaining a time update equation of information filtering; the time updating equation comprises a time updated information error state vector and a time updated information matrix;
establishing a measurement updating equation of information filtering according to the measurement updating of the closely combined measurement equation after the dimension transformation and the time updating equation; 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 conversion according to the information error state vector after measurement updating and the system error state variance matrix at the current moment after dimension conversion;
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 a system error state variance array at the current moment before dimension transformation according to the system error state variance array at the current moment after dimension transformation, the first error state coefficient matrix and the second error state coefficient matrix.
2. The method of claim 1, wherein the pre-multiplying the systematic error state vector by two matrices of coefficients to obtain a dimension transformed systematic error state vector comprises:
the system error state vector delta X is multiplied by two coefficient matrixes to the left, and the system error state vector delta X' after dimension transformation is obtained and is:
the system error state vector deltaX 15×1 Is a 15-dimensional system error state vector δ X, expressed as follows:
wherein, δ r 3×1 Indicating the position error vector, δ v 3×1 Representing the velocity error vector, δ φ 3×1 Representing the attitude error vector, δ b g,3×1 Representing the gyro zero-offset error vector, δ b a,3×1 Representing an accelerometer zero offset error vector;
C 1,15×15 first error state coefficient matrix C representing 15 dimensions 1 ；C 2,15×15 Representing a 15-dimensional second error state coefficient matrix C 2 。
3. The method of claim 2, further comprising:
constructing a first error state coefficient matrix with zero elements except diagonal elements according to the meridian curvature radius of the earth, the curvature radius of the earth fourth unit circle, the altitude of the carrier and the latitude of the carrier; wherein the first error state coefficient matrix C 1 So that the high latitude and longitude error is converted into the northeast position error;
according to the first error state coefficient momentMatrix C 1 Constructing a second error state coefficient matrix with zero other elements except the diagonal elements; wherein the second error state coefficient matrix C 2 The diagonal elements of the dimension transformed system error state variance matrix are made equal to 1.
4. The method of claim 3, further comprising:
first error state coefficient matrix C 1 Diagonal elements of and a second error state coefficient matrix C 2 The calculation formula of (a) is respectively as follows:
wherein, C 1,15×1 First error state coefficient matrix C representing 15 dimensions 1 A diagonal element value of; c 2,15×1 Representing a 15-dimensional second error state coefficient matrix C 2 Diagonal element value of R n Radius of curvature of meridian of the earth, R e Representing the curvature radius of the earth-shaped unitary space ring, h representing the altitude of the carrier, B representing the latitude of the carrier, and K 1 (i) Is represented by C 1 The ith element, σ, of the principal diagonal of the matrix i The ith element representing the main diagonal of the variance matrix of the state of the system error.
5. The method of claim 1, wherein the step of establishing a dimension-transformed system error state equation based on the dimension-transformed system error state vector at the previous time comprises:
using the 15-dimensional system error state vector delta X' after dimension transformation to establish an inertial navigation system error state equation, wherein the equation is as follows:
wherein the content of the first and second substances,
A. b and C are derived from an inertial navigation mechanics arrangement equation g,3×1 Representing the random error vector, ε, of the gyroscope a,3×1 A random error vector representing the accelerometer;
converting the continuous time system into a discrete time system, and obtaining a discretized and linearized system error state equation according to a system error state vector at the previous moment after dimension transformation, wherein the discretized and linearized system error state equation comprises the following steps:
δX' k/k-1 ＝Φ' k/k-1 δX' k-1/k-1 +Γ' k/k-1 W k-1 '
wherein the expressions of the variables are as follows:
δX' k/k-1 ＝(C 2,k C 1,k )·δX k/k-1
δX' k-1/k-1 ＝(C 2,k-1 C 1,k-1 )·δX k-1/k-1
W k-1 '＝C ε W k-1
Φ' k/k-1 ＝(C 2,k C 1,k )·Φ k/k-1 ·(C 2,k-1 C 1,k-1 ) -1
δX k-1/k-1 representing the state vector of the systematic error at the previous moment, C ε Representing a matrix of dimensional transformation coefficients, W k-1 Representing the system noise vector obeying a covariance matrix of Q k-1 The specific parameter is determined by the performance of the inertial navigation device, phi k/k-1 Representing the error state transition matrix, Γ, from the previous time to the current time k/k-1 Representing the system noise transfer matrix, phi k/k-1 And gamma k/k-1 The calculation formula of (a) is as follows:
Γ k/k-1 ＝G·Δt
wherein the time interval Δ t = t k -t k-1 Italicized I denotes an identity matrix, F denotes a coefficient matrix, and G denotes a noise driving matrix.
6. The method of claim 1, wherein establishing a dimension-transformed, tightly-combined measurement equation based on the dimension-transformed, current-time systematic error state vector comprises:
system error state vector delta X 'at current moment after dimension transformation' k/k Establishing a tightly-combined measurement equation after dimension transformation, wherein the formula is as follows:
Z k ＝H k 'δX′ k/k +ξ k
wherein the content of the first and second substances,
H k geometrical matrix, ξ, representing measurement information k Representing the measurement error vector obeying a covariance matrix of R k Zero mean multidimensional positive space distribution, R k Is obtained by error modeling of satellite navigation measurement information, Z k Represents t k Time of day satellite-guided measurement information vector, Z k The calculation formula of (a) is as follows:
wherein δ P (t) k ) Representing single-difference error observations, δ Δ, between pseudo-range stars t φ(t k ) The double-difference error observed quantity between the carrier phase inter-satellite epochs is obtained by calculating satellite navigation original observation data and an antenna position predicted by inertial navigation, is a column vector of n-1 dimension, and n represents the number of visible satellites.
7. The method of claim 1, wherein before obtaining the time update equation for information filtering according to the time update of the dimension-transformed system error state equation, further comprising:
defining a dimension transformed information matrix
Information error state vector
And two auxiliary transition matrices
N＝MΓ′(Γ′ T MΓ′+Q′ -1 ) -1 Γ′ T ；
Obtaining a time update equation of information filtering according to the time update of the system error state equation after the dimension transformation, wherein the time update equation comprises the following steps:
Ι′ k/k-1 ＝(I-N)M
the time updating 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 Indicates the information error state vector, I 'after time update' k/k-1 Represents the information matrix I 'after the time update' k/k-1 Describing the degree of dispersion of the error state distribution, i.e. S' k/k-1 The size of the contained information volume; p represents a system error state vector variance array, Q represents a system noise variance array, P 'represents the system error state variance array after dimension transformation, Q' represents the system noise variance array after dimension transformation, and the calculation formulas of P 'and Q' are respectively as follows:
P'＝(C 2 ·C 1 )·P·(C 2 ·C 1 ) T
Q'＝C ε ·Q·C ε T
wherein, C ε The diagonal element of (b) is obtained by root-opening the diagonal element of Q, and the other elements are all zero.
8. The method of claim 1, wherein building an information filtered measurement update equation based on the measurement update of the dimension transformed immediate combination measurement equation and the time update equation comprises:
introducing guard guide measurement information pair S 'according to the calculation results of the closely combined measurement equation and the time updating equation after dimension transformation' k/k-1 And I' k/k-1 And (3) carrying out measurement updating, and establishing a measurement updating equation of information filtering as follows:
S′ k/k ＝S′ k/k-1 +H′ k T R k -1 Z k
Ι′ k/k ＝Ι′ k/k-1 +H′ k T R k -1 H k
wherein, S' k/k Represents the updated information error state vector, I' k/k Representing the updated information matrix of the measurement.
9. The method according to claim 1, wherein a system error state variance matrix at the current time after dimension transformation is obtained according to the updated information matrix after measurement; obtaining a dimension-converted current-time system error state vector according to the measurement-updated information error state vector and the dimension-converted current-time system error state variance matrix, including:
according to the information matrix I 'after the measurement update' k/k Obtaining a system error state variance matrix P 'at the current moment after dimension transformation' k/k The formula is expressed as:
according to the measurement updated information error state vector S' k/k And the system error state variance array P 'at the current moment after dimension transformation' k/k Obtaining a system error state vector delta X 'at the current time after dimension transformation' k/k The formula is expressed as:
δX′ k/k ＝P′ k/k ·S′ k/k 。
10. the method according to claim 1, wherein the current-time system error state vector before dimension transformation is obtained according to the current-time system error state vector after dimension transformation, the first error state coefficient matrix and the second error state coefficient matrix; obtaining a system error state variance matrix at the current moment before dimension transformation according to the system error state variance matrix at the current moment after dimension transformation, the first error state coefficient matrix and the second error state coefficient matrix, and the method comprises the following steps:
according to the system error state vector delta X 'at the current moment after dimension transformation' k/k The first error state coefficient matrix C 1 And the second error state coefficient matrix C 2 Obtaining the system error state vector delta X at the current moment before dimension transformation k/k The formula is expressed as:
δX k/k ＝(C 2 ·C 1 ) -1 ·δX′ k/k
according to the current time system error state variance array P 'after dimension transformation' k/k The first error state coefficient matrix C 1 And the second error state coefficient matrix C 2 Obtaining the system error state variance matrix P at the current moment before dimension transformation k/k The notations are represented as:
P k/k ＝(C 2 ·C 1 ) -1 P′ k/k (C 2 ·C 1 ) -T 。
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