CN112697154B - Self-adaptive multi-source fusion navigation method based on vector distribution - Google Patents
Self-adaptive multi-source fusion navigation method based on vector distribution Download PDFInfo
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- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/20—Instruments for performing navigational calculations
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
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- G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
- G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
- G01C21/165—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation combined with non-inertial navigation instruments
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Abstract
The invention discloses a self-adaptive multi-source fusion navigation method based on vector distribution. The method comprises the following steps: selecting a northeast coordinate system as a navigation system, selecting an 18-dimensional system error as a state quantity, establishing a federal filtering combined navigation model according to the output characteristics of each sensor, and designing a federal filter; designing a method for detecting and isolating faults through vector distribution, and detecting and isolating the information of fault dimensions of each sensor; and (3) constructing vector distribution coefficients for each dimension of information of each sub-filter by using the information obtained in the fault detection in the step (2), and carrying out information fusion in the main filter to obtain a global optimal estimation result. The invention improves the navigation positioning precision of the multi-source fusion combined navigation system in a strong interference environment, enhances the fault tolerance performance and the robustness of the system, can select a proper navigation sensor according to different navigation requirements, and improves the flexibility of the navigation system.
Description
Technical Field
The invention relates to the technical field of integrated navigation, in particular to a self-adaptive multi-source fusion navigation method based on vector distribution.
Background
In recent years, with the development and application of GNSS systems, satellite navigation technology has been widely used not only in war but also in informatization industry. The navigation industry and the technical support and application of the navigation industry are not separated from the personal travel, transportation, weather prediction, map mapping, disaster relief and flood control and mobile communication. However, GNSS system design is only initially designed as a navigation aid in a war environment, and thus, there are inherent drawbacks in BDS systems in china, GPS systems in the united states, GLONASS systems in russia, galileo systems in europe, and small navigation systems and regional navigation systems in some other countries and regions, and the signal power of the signal reaching the ground is extremely low, so that the receiver is easily deceptively and disturbed, and the service performance is seriously degraded in physical signal blocking environments such as indoor, underwater, underground and urban canyons, and in electromagnetic interference environments, which seriously may lead to serious challenges for military security.
Based on the above, the combined mode of the single navigation subsystem auxiliary inertial navigation system cannot meet the requirements of high precision and high reliability of the navigation system.
Disclosure of Invention
The invention aims to provide a vector distribution-based self-adaptive multi-source fusion navigation method, which is based on the technology of Federal Kalman multi-source data filtering, performs fault diagnosis and information distribution in a vector distribution mode, realizes the self-adaptive distribution of information factors of all Federal sub-filters, improves the information utilization rate of all sensors, and optimizes the optimal estimation of the Federal filters.
The technical solution for realizing the purpose of the invention is as follows: an adaptive multi-source fusion navigation method based on vector allocation comprises the following steps:
step 1: selecting a northeast coordinate system as a navigation system, selecting an 18-dimensional system error as a state quantity, establishing a federal filtering combined navigation model according to the output characteristics of each sensor, and designing a federal filter;
step 2: designing a method for detecting and isolating faults through vector distribution, and detecting and isolating the information of fault dimensions of each sensor;
step 3: and (3) constructing vector distribution coefficients for each dimension of information of each sub-filter by using the information obtained in the fault detection in the step (2), and carrying out information fusion in the main filter to obtain a global optimal estimation result. .
Compared with the prior art, the invention has the remarkable advantages that: (1) On the basis of a conventional GNSS/SINS integrated navigation algorithm, a multi-source navigation system based on a Federal Kalman filtering algorithm and with SINS as a reference system and with the combination of SINS/GNSS and SINS/odometer is designed, so that the navigation positioning accuracy of the integrated navigation system is improved; (2) Aiming at the difference of estimation precision between each sensor and each observation component of the same sensor, an algorithm for fault diagnosis and information distribution in a vector distribution mode is designed to form a self-adaptive federal fault-tolerant filter, so that the utilization rate of the system to navigation information is improved, and the precision and reliability of the multi-source navigation system are enhanced.
Drawings
FIG. 1 is a flow chart of the adaptive multi-source fusion navigation method based on vector allocation of the present invention.
FIG. 2 is a schematic diagram of the structure of an improved Federal Kalman filter used in the adaptive multi-source fusion navigation method based on vector distribution of the present invention.
Detailed Description
According to the environmental characteristics and the working characteristics of the navigation system, the invention is based on an inertial/satellite integrated navigation system with mature technology and unique advantages, and combines the output information of the navigation sensors with different working characteristics to form the integrated navigation system based on multi-source information fusion, so that the service defects and the capacity deficiency caused by the inherent vulnerability of GNSS are overcome, the precision of the whole navigation system is improved, and the navigation system can accurately and reliably complete tasks for a long time.
The invention discloses a self-adaptive multi-source fusion navigation method based on vector allocation, which comprises the following steps:
step 1: selecting a northeast coordinate system as a navigation system, selecting an 18-dimensional system error as a state quantity, establishing a federal filtering combined navigation model according to the output characteristics of each sensor, and designing a federal filter;
step 2: designing a method for detecting and isolating faults through vector distribution, and detecting and isolating the information of fault dimensions of each sensor;
step 3: and constructing vector distribution coefficients for each dimension of information of each sub-filter by using the output result of each sub-filter, and carrying out information fusion in the main filter to obtain a global optimal estimation result.
Further, in the step 1, the northeast and north coordinate system is selected as a navigation system, 18-dimensional system errors are selected as state quantities, a federal filter combined navigation model is established according to the output characteristics of each sensor, and a federal filter is designed, specifically as follows:
(2.1) firstly, building a federal filtering combined navigation system model under a navigation coordinate system; the error model of the inertial navigation system selects a universal error model, the common error reference system selects an inertial navigation system, the navigation coordinate system selects a northeast geographic coordinate system, and the state vector X of the system is
Wherein the method comprises the steps ofIs an attitude angle error in the northeast direction; δV (delta V) E 、δV N 、δV U Is a speed error in the northeast sky direction; δl, δλ, δh are positional errors in the warp and weft directions; epsilon bx 、ε by 、ε bz Random drift of the gyroscope in three axial directions; epsilon rx 、ε ry 、ε rz Random noise is a first-order Markov process of the gyroscope in three axes; (V) x 、▽ y 、▽ z Constant deviations of the accelerometer in three axial directions are obtained;
equation of state of systemThe method comprises the following steps:
wherein F (t) is a state transition matrix of the system, G (t) is an error coefficient matrix, W (t) is a white noise random error vector, and the specific form is as follows:
state transition matrix F (t):
f in the formula N As a systematic error matrix, F s Error transformation matrix for inertial device, F M The noise matrix of the inertial device is specifically as follows:
wherein the method comprises the steps ofIs a gesture conversion matrix;
wherein T is g Representing the related time of the gyro, T a Representing the relative time of the accelerometer, wherein x, y and z respectively represent the triaxial directions of the carrier system;
the error coefficient matrix G (t) is:
the white noise random error vector W (t) is:
W(t)＝[w gx w gy w gz w rx w ry w rz w ax w ay w az ] T (8)
wherein w is g Representing white noise of gyro, w r Represent Ma Shibai noise, w a Representing accelerometer white noise;
the measurement equation Z (t) of the system is:
Z(t)＝H(t)X(t)+V(t) (9)
where X (t) is the state vector of the system, V (t) = [ N E N N N U ] T To measure noise, N E 、N N 、N U Measuring noise in the direction, wherein H (t) is a measuring matrix of the system, and the measuring matrix is selected differently according to different sub-filters; the continuous system model is not easy to realize in a computer, so that the system model needs to be discretized, and the state equation (2) and the measurement equation (9) need to be discretized, so that the method can be obtained
Wherein X is k Is the state vector at time k, Φ k|k-1 At k-1 to kSystem for engraving one-step transfer matrix Γ k-1 For the noise matrix of the system, it characterizes that each system noise from k-1 to k affects the brightness of each state at k time, W k-1 Is the system noise at time k-1, Z k For the measurement vector at time k, H k For the measurement matrix at time k, V k Measurement noise for time k
In the middle of
Wherein T is an iteration period, T k The k time is k;
(2.2) design of a federal filter:
each sub-filter adopts a Kalman filtering mode, and the specific steps are as follows:
state one-step prediction equation:
in the method, in the process of the invention,is made use of->Calculating to obtain X k Is predicted in one step;
state estimation equation:
is to predict +.>Based on the measured value, the true value X k Wherein K is k Is the filtering gain;
kalman gain equation:
wherein P is kk-1 The mean square error is predicted for one step; r is R k A variance matrix for measuring noise;
one-step prediction mean square error equation:
mean square error estimation equation:
wherein P is kk To estimateIs determined according to the estimated mean square error equation;
the position information representing the inertial navigation system is
Lambda in I 、L I 、H I Lambda is a measurement value of latitude, longitude and altitude of inertial navigation system t 、L t 、H t The true values of the latitude, longitude and altitude of the vehicle-mounted device are shown as delta lambda, delta L and delta H, and the measured error values of the latitude, longitude and altitude of the inertial navigation system are shown as delta lambda, delta L and delta H;
the speed information representing the inertial navigation system is
V in IN 、v IE 、v IU V, a measurement of the velocity of the inertial navigation system in the northeast-north direction N 、v E 、v U Is true value of the speed of the vehicle-mounted device in the northeast and north directions, δv N 、δv E 、δv U Measuring error values of the speed of the inertial navigation system in the northeast direction;
the position information representing the satellite navigation system is
Lambda in G 、L G 、H G Lambda is the measured value of latitude, longitude and altitude of satellite navigation system t 、L t 、H t True value of latitude, longitude and altitude of vehicle-mounted device, N E 、N N 、N U Measuring error values for the northeast direction position of the satellite navigation system;
the speed information representing the satellite navigation system is
V in GE 、v GN 、v GU V, a measurement of the velocity of a satellite navigation system in the northeast-north direction N 、v E 、v U Is true value of the speed of the vehicle-mounted device in the northeast and north directions, M N 、M E 、M U Measuring error values of the speed of the inertial navigation system in the northeast direction; in order to cooperate with the dimensions of longitude and latitude of the inertial navigation system, position measurement value N and velocity measurement value M are converted;
the speed information representing the odometer is
V in OE 、v ON 、v OU V, a measurement of the speed of the odometer in the northeast direction N 、v E 、v U Is true value of the speed of the vehicle-mounted device in the northeast and north directions, O N 、O E 、O U Measuring error value of speed of the odometer in northeast day direction;
the height information representing the height gauge is
H a ＝H U -A (23)
H in a H is the measurement of the height of the altimeter U The true value of the vehicle-mounted device in the upward position is shown, and A is the measurement error value of the altimeter in the height;
(2.2.1) designing SINS/BDS sub-filters
The state equation of the SINS/BDS sub-filter is known as (2.1)
Measuring method of SINS/BDS sub-filter
Wherein the method comprises the steps of
V G (t)＝[N N N E N U M E M N M U ] T (27)
The measured noise is treated as white noise, and its variance is respectivelyR M 、R N Respectively a long radius and a short radius of the earth;
(2.2.2) designing SINS/odometer sub-filters
According to (2.1), the state equation of the SINS/BDS sub-filter is
The measurement equation of the SINS/odometer sub-filter is
Wherein the method comprises the steps of
H O (t)＝[0 3×3 diag[1 1 1] 0 3×12 ] (30)
V G (t)＝[O E O N O U ] T (31)
The measurement noise is treated as white noise with the mean value of 0;
(2.2.3) design of Federal Filter Main Filter
The federal filter is a two-stage filtering structure, and the output X of the common reference subsystem SINS k On one hand, the main filter and on the other hand, each sub-filter are used as measurement values; the output of each subsystem is only given to the respective filter, the local estimation value X of each sub-filter i And its covariance matrix P i The estimation values sent into the main filter and the main filter are fused together to obtain a global estimation value;
global optimum estimation synthesized by main filter and sub-filterAnd its corresponding covariance matrix P g Is amplified to +.>And then feeding back to the sub-filter to reset the estimation value of the sub-filter, namely: />The co-equation matrix of the main filter is +.>β i Determining according to an information distribution principle;
the invention comprehensively considers the filtering precision and the structural performance of the system, and designs a self-adaptive information fusion method based on vector distribution from the basis of a covariance matrix of the system and the observability of the system.
Further, in the step 2, the fault detection and isolation method is designed by vector distribution, and the fault dimension information of each sensor is detected and isolated, specifically as follows:
(3.1) sub-filter time update:
wherein i represents the i-th sub-filter;
(3.2) fault diagnosis:
the following fault diagnosis function is first constructed:
Λ i,k ＝r i,k (r i,k ) T [H i,k P i,k|k-1 (H i,k ) T +R i,k ] -1 (33)
wherein r is i,k Representing the residual error of system i at time k, Λ i,k Is a matrix of m rows and m columns, which can be expressed as:
Λ when no fault occurs in the sub-filter i,k Each element on the diagonal of the array should obey x with the degree of freedom of 1 2 And (3) distributing, namely when a sensor in the system fails, not meeting the condition, setting a proper threshold value at the moment, and establishing the following judgment rule:
defining the measured noise figure B of the ith sub-filter i,k The method comprises the following steps:
wherein the method comprises the steps of
By the obtained measured noise figure B i,k Reconstructing a measurement noise matrix
In the formula (37), when one dimension of the equivalent measurement information is judged to be normal, B i,k The corresponding diagonal element is set to 1, otherwise to 0, so that the measurement noise matrix reconstructed in equation (39)For normal measurement variables, the adjusted corresponding noise variance is unchanged; for fault measurement variables, the adjusted corresponding noise variance tends to infinity, so that the dimension information of the sensor fault is dynamically isolated;
(3.3) sub-Filter measurement update
After the sub-filters are measured and updated, the filtering result of the fault dimension information of the isolation sensor is sent to the main filter to perform the next information fusion.
Further, in step 3, the output result of each sub-filter is used to construct a vector distribution coefficient for each dimension of information of each sub-filter, and information fusion is performed in the main filter to obtain a global optimal estimation result, which specifically includes the following steps:
covariance matrix P of sub-filter i,k|k The estimation precision of the sub-filters can be reflected, and the observability of the system can reflect the structural performance of the system; conventional adaptive information allocation methods use trace (P i,k|k ) Calculating information distribution coefficients, wherein each sub-filter generally comprises more than one measurement variable in an actual federal filtering model, and each measurement variable has different estimation precision even in the same filter; the invention designs a self-adaptive information distribution coefficient algorithm based on vector distribution based on covariance matrix of a sub-filter and observability of a system;
first, a sub-filter covariance matrix P i,k|k And (3) performing eigenvalue decomposition:
P i,k|k ＝D i,k Λ i,k (D i,k ) T (41)
in the middle of
Wherein lambda is n,i,k Is the ith sub-filter covariance matrix P i,k|k Is the nth characteristic value of D i,k Is an orthogonal matrix generated by eigenvalue decomposition; defining distribution coefficient matrix A i,k The method comprises the following steps:
in the middle of
A i,k Meets the theorem of conservation of information
The distribution coefficient matrix C is constructed by observability of the sub-filters i,k Assuming that the observability matrix of the sub-filter i is Q i,k For Q i,k Singular value decomposition
Q i,k ＝U i,k S i,k (V i,k ) T (46)
Wherein U is i,k And V i,k Is an orthogonal matrix, S i,k The method comprises the following steps:
wherein the method comprises the steps ofσ n,i,k (n＝1,2,…r i )，r i Respectively Q i,k Singular values and ranks of (2);
then measure coefficient C i,k The definition is as follows:
wherein the method comprises the steps of
C i,k Meets the theorem of conservation of information
Then the vector-based information distribution coefficient B i,k The method comprises the following steps:
at this time, the information distribution coefficient still satisfies the principle of information conservation:
the asymmetry of the error covariance matrix of the system can destroy the consistent convergence stability of the Kalman filter, increase the filtering error and even lose the filtering effect; in order to ensure the symmetry of the error covariance matrix, the information distribution mode is as follows:
the invention will be described in further detail with reference to the accompanying drawings and specific examples.
Examples
Referring to fig. 1, the invention provides a self-adaptive multi-source fusion navigation method based on vector allocation, which comprises the following steps:
step 1: selecting a northeast coordinate system as a navigation system, selecting an 18-dimensional system error as a state quantity, establishing a federal filtering combined navigation model according to the output characteristics of each sensor, and designing a federal filter;
referring to fig. 2, in the federal kalman filtering of the present invention, 3 navigation information sources are used, so that SINS/GNSS, SINS/odometer sub-filters and a main filter for information fusion are used, information is distributed between each sub-filter and the main filter by using an information distribution principle, each sub-filter processes the respective measurement information and obtains local estimation, and then information fusion is performed in the main filter to obtain optimal estimation.
(1.1) firstly, building a federal filtering combined navigation system model under a navigation coordinate system; the error model of the inertial navigation system selects a universal error model, the common error reference system selects an inertial navigation system, the navigation coordinate system selects a northeast geographic coordinate system, and the state vector X of the system is
Wherein the method comprises the steps ofIs an attitude angle error in the northeast direction; δV (delta V) E 、δV N 、δV U Is a speed error in the northeast sky direction; δl, δλ, δh are positional errors in the warp and weft directions; epsilon bx 、ε by 、ε bz Random drift of the gyroscope in three axial directions; epsilon rx 、ε ry 、ε rz Random noise is a first-order Markov process of the gyroscope in three axes; (V) x 、▽ y 、▽ z Constant deviations of the accelerometer in three axial directions are obtained;
equation of state of systemThe method comprises the following steps:
wherein F (t) is a state transition matrix of the system, G (t) is an error coefficient matrix, W (t) is a white noise random error vector, and the specific form is as follows:
state transition matrix F (t):
f in the formula N As a systematic error matrix, F s Error transformation matrix for inertial device, F M The noise matrix of the inertial device is specifically as follows:
wherein the method comprises the steps ofIs a gesture conversion matrix;
wherein T is g Representing the related time of the gyro, T a Indicating the relative time of the accelerometer, x, y and z respectively indicate the three axis directions of the carrier.
The error coefficient matrix G (t) is:
the white noise random error vector W (t) is:
W(t)＝[w gx w gy w gz w rx w ry w rz w ax w ay w az ] T (1.8)
wherein w is g Representing white noise of gyro, w r Represent Ma Shibai noise, w a Representing accelerometer white noise.
The measurement equation Z (t) of the system is:
Z(t)＝H(t)X(t)+V(t) (1.9)
where X (t) is the state vector of the system, V (t) = [ N E N N N U ] T To measure noise, N E 、N N 、N U Measuring noise in the direction, wherein H (t) is a measuring matrix of the system, and the measuring matrix is selected differently according to different sub-filters; the continuous system model is not easy to realize in a computer, so that the system model needs to be discretized, and the state equation (2) and the measurement equation (9) need to be discretized, so that the method can be obtained
Wherein X is k Is the state vector at time k, Φ k|k-1 For the system one-step transfer matrix of k-1 to k moments Γ k-1 For the noise matrix of the system, it characterizes that each system noise from k-1 to k affects the brightness of each state at k time, W k-1 Is the system noise at time k-1, Z k For the measurement vector at time k, H k For the measurement matrix at time k, V k Measurement noise for time k
In the middle of
Wherein T is an iteration period, T k The k time is k;
(1.2) design of a federal filter:
each sub-filter adopts a Kalman filtering mode, and the specific steps are as follows:
state one-step prediction equation:
in the method, in the process of the invention,is made use of->Calculating to obtain X k Is predicted in one step;
state estimation equation:
is to predict +.>Based on the measured value, the true value X k Wherein K is k Is the filtering gain;
kalman gain equation:
wherein P is k|k-1 The mean square error is predicted for one step; r is R k A variance matrix for measuring noise;
one-step prediction mean square error equation:
mean square error estimation equation:
wherein P is k|k To estimateIs described.
The position information representing the inertial navigation system is
Lambda in I 、L I 、H I Lambda is a measurement value of latitude, longitude and altitude of inertial navigation system t 、L t 、H t The true values of the latitude, longitude and altitude of the vehicle-mounted device are shown as delta lambda, delta L and delta H, and the measured error values of the latitude, longitude and altitude of the inertial navigation system are shown as delta lambda, delta L and delta H;
the speed information representing the inertial navigation system is
V in IN 、v IE 、v IU V, a measurement of the velocity of the inertial navigation system in the northeast-north direction N 、v E 、v U Is true value of the speed of the vehicle-mounted device in the northeast and north directions, δv N 、δv E 、δv U Measuring error values of the speed of the inertial navigation system in the northeast direction;
the position information representing the satellite navigation system is
Lambda in G 、L G 、H G Lambda is the measured value of latitude, longitude and altitude of satellite navigation system t 、L t 、H t True value of latitude, longitude and altitude of vehicle-mounted device, N E 、N N 、N U Measuring error values for the northeast direction position of the satellite navigation system;
the speed information representing the satellite navigation system is
V in GE 、v GN 、v GU V, a measurement of the velocity of a satellite navigation system in the northeast-north direction N 、v E 、v U Is true value of the speed of the vehicle-mounted device in the northeast and north directions, M N 、M E 、M U Measuring error values of the speed of the inertial navigation system in the northeast direction; in order to cooperate with the dimensions of longitude and latitude of the inertial navigation system, position measurement value N and velocity measurement value M are converted;
the speed information representing the odometer is
V in OE 、v ON 、v OU V, a measurement of the speed of the odometer in the northeast direction N 、v E 、v U Is true value of the speed of the vehicle-mounted device in the northeast and north directions, O N 、O E 、O U Measuring error value of speed of the odometer in northeast day direction;
the height information representing the height gauge is
H a ＝H U -A(1.23)
H in a H is the measurement of the height of the altimeter U The true value of the vehicle-mounted device in the upward position is shown, and A is the measurement error value of the altimeter in the height;
(1.2.1) designing SINS/BDS sub-filters
The state equation of the SINS/BDS sub-filter is known as (2.1)
Measuring method of SINS/BDS sub-filter
Wherein the method comprises the steps of
V G (t)＝[N N N E N U M E M N M U ] T (1.27)
The measured noise is treated as white noise, and its variance is respectivelyR M 、R N Respectively a long radius and a short radius of the earth;
(1.2.2) designing SINS/odometer sub-Filter
According to (1.1), the state equation of the SINS/BDS sub-filter is
The measurement equation of the SINS/odometer sub-filter is
Wherein the method comprises the steps of
H O (t)＝[0 3×3 diag[1 1 1] 0 3×12 ] (1.30)
V G (t)＝[O E O N O U ] T (1.31)
The measurement noise is treated as white noise with the mean value of 0;
(1.2.3) design of Federal Filter Main Filter
The federal filter is a two-stage filter structure, common referenceOutput X of subsystem SINS k The main filter on the one hand and the sub-filters on the other hand are used as measurement values. The outputs of the subsystems are only provided to the respective filters. Local estimation value X of each sub-filter i And its covariance matrix P i The estimation values sent into the main filter and the main filter are fused together to obtain a global estimation value;
global optimum estimation synthesized by main filter and sub-filterAnd its corresponding covariance matrix P g Is amplified as
And then feeding back to the sub-filter to reset the estimation value of the sub-filter, namely: />The co-equation matrix of the main filter is +.>β i And determining according to the information distribution principle.
The invention comprehensively considers the filtering precision and the structural performance of the system, and designs a self-adaptive information fusion method based on vector distribution from the basis of a covariance matrix of the system and the observability of the system.
Step 2: after the output results of the sub-filters in the step 1 are obtained, fault detection is performed by a vector distribution mode
Isolation, the specific method is as follows:
(2.1) sub-filter time update:
where i denotes the i-th sub-filter.
(2.2) fault diagnosis. The following fault diagnosis function is first constructed:
wherein r is i,k Representing the residual error of system i at time k, Λ i,k Is a matrix of m rows and m columns, which can be expressed as:
Λ when no fault occurs in the sub-filter i,k Each element on the diagonal of the array should obey x with the degree of freedom of 1 2 Distribution, which is no longer satisfied when there is a sensor failure in the system. At this time, a proper threshold is set, and the following judgment rule is established:
defining the measured noise figure B of the ith sub-filter i,k The method comprises the following steps:
wherein the method comprises the steps of
By the obtained measured noise figure B i,k Reconstructing a measurement noise matrix
In the formula (37), when one dimension of the equivalent measurement information is judged to be normal, B i,k The corresponding diagonal element is set to 1, otherwise to 0, so that the measurement noise matrix reconstructed in equation (39)For normal measurement variables, the adjusted corresponding noise variance is unchanged; for fault measurement variables, the adjusted corresponding noise variance tends to infinity, so that the dimension information of the sensor fault is dynamically isolated.
(2.3) sub-Filter measurement update
After the sub-filters are measured and updated, the filtering result of the fault dimension information of the isolation sensor is sent to the main filter to perform the next information fusion.
Step 3: and (3) constructing vector distribution coefficients for each dimension of information of each sub-filter by using the information obtained in the fault detection in the step (2), and carrying out information fusion in the main filter to obtain a global optimal estimation result. The method comprises the following steps:
covariance matrix P of sub-filter i,k|k The estimation precision of the sub-filters can be reflected, and the observability of the system can reflect the structural performance of the system. Conventional adaptive information allocation methods use trace (P i,k|k ) The information distribution coefficients are calculated, but in an actual federal filtering model, each sub-filter typically contains more than one measured variable, and even in the same filter, each measured variable may have different estimation accuracy. The invention designs a self-adaptive information distribution coefficient algorithm based on vector distribution based on covariance matrix of a sub-filter and observability of a system.
First, a sub-filter covariance matrix P i,k|k Proceeding featureValue decomposition:
P i,k|k ＝D i,k Λ i,k (D i,k ) T (1.41)
in the middle of
Wherein lambda is n,i,k Is the ith sub-filter covariance matrix P i,k|k Is the nth characteristic value of D i,k Is an orthogonal matrix generated by eigenvalue decomposition. Defining distribution coefficient matrix A i,k The method comprises the following steps:
A i,k meets the theorem of conservation of information
The distribution coefficient matrix C is constructed by observability of the sub-filters i,k Assuming that the observability matrix of the sub-filter i is Q i,k For Q i,k Singular value decomposition
Q i,k ＝U i,k S i,k (V i,k ) T (1.46)
Wherein U is i,k And V i,k Is an orthogonal matrix, S i,k The method comprises the following steps:
wherein the method comprises the steps ofσ n,i,k (n＝1,2,…r i )，r i Respectively Q i,k Singular values and ranks of (c).
Then measure coefficient C i,k The definition is as follows:
C i,k meets the theorem of conservation of information
Then the vector-based information distribution coefficient B i,k The method comprises the following steps:
at this time, the information distribution coefficient still satisfies the principle of information conservation:
the asymmetry of the error covariance matrix of the system can destroy the consistent convergence stability of the Kalman filter, increase the filtering error and even lose the filtering effect. In order to ensure the symmetry of the error covariance matrix, the information distribution mode is as follows:
in summary, the invention designs a multi-source navigation system based on the federal Kalman filtering algorithm based on the conventional GNSS/SINS combined navigation algorithm, which uses SINS as a reference system and combines SINS/GNSS and SINS/odometer, thereby improving the navigation positioning accuracy of the combined navigation system; aiming at the difference of estimation precision between each sensor and each observation component of the same sensor, an algorithm for fault diagnosis and information distribution in a vector distribution mode is designed to form a self-adaptive federal fault-tolerant filter, so that the utilization rate of the system to navigation information is improved, and the precision and reliability of the multi-source navigation system are enhanced.
Claims (1)
1. The self-adaptive multi-source fusion navigation method based on vector allocation is characterized by comprising the following steps of:
step 1: selecting a northeast coordinate system as a navigation system, selecting an 18-dimensional system error as a state quantity, establishing a federal filtering combined navigation model according to the output characteristics of each sensor, and designing a federal filter;
step 2: designing a method for detecting and isolating faults through vector distribution, and detecting and isolating the information of fault dimensions of each sensor;
step 3: constructing vector distribution coefficients for each dimension of information of each sub-filter by using the output result of each sub-filter, and carrying out information fusion in a main filter to obtain a global optimal estimation result;
in the step 1, the northeast coordinate system is selected as a navigation system, 18-dimensional system errors are selected as state quantities, a federal filtering combined navigation model is established according to the output characteristics of each sensor, and a federal filter is designed, wherein the method comprises the following steps:
(2.1) firstly, building a federal filtering combined navigation system model under a navigation coordinate system; the error model of the inertial navigation system selects a universal error model, the common error reference system selects an inertial navigation system, the navigation coordinate system selects a northeast geographic coordinate system, and the state vector X of the system is
Wherein the method comprises the steps ofIs an attitude angle error in the northeast direction; δV (delta V) E 、δV N 、δV U Is a speed error in the northeast sky direction; δl, δλ, δh are positional errors in the warp and weft directions; epsilon bx 、ε by 、ε bz Random drift of the gyroscope in three axial directions; epsilon rx 、ε ry 、ε rz Random noise is a first-order Markov process of the gyroscope in three axes; />Constant deviations of the accelerometer in three axial directions are obtained;
equation of state of systemThe method comprises the following steps:
wherein F (t) is a state transition matrix of the system, G (t) is an error coefficient matrix, W (t) is a white noise random error vector, and the specific form is as follows:
state transition matrix F (t):
f in the formula N As a systematic error matrix, F s Error transformation matrix for inertial device, F M The noise matrix of the inertial device is specifically as follows:
wherein the method comprises the steps ofIs a gesture conversion matrix;
wherein T is g Representing the related time of the gyro, T a Representing the relative time of the accelerometer, wherein x, y and z respectively represent the triaxial directions of the carrier system;
the error coefficient matrix G (t) is:
the white noise random error vector W (t) is:
W(t)＝[w gx w gy w gz w rx w ry w rz w ax w ay w az ] T (8)
wherein w is g Representing white noise of gyro, w r Represent Ma Shibai noise, w a Representing accelerometer white noise;
the measurement equation Z (t) of the system is:
Z(t)＝H(t)X(t)+V(t) (9)
where X (t) is the state vector of the system, V (t) = [ N E N N N U ] T To measure noise, N E 、N N 、N U Measuring noise in the direction, wherein H (t) is a measuring matrix of the system, and the measuring matrix is selected differently according to different sub-filters;
discretizing the system model, discretizing the state equation (2) and the measurement equation (9) to obtain
Wherein X is k Is the state vector at time k, Φ kk-1 For the system one-step transfer matrix of k-1 to k moments Γ k-1 For the noise matrix of the system, it characterizes that each system noise from k-1 to k affects the brightness of each state at k time, W k-1 Is the system noise at time k-1, Z k For the measurement vector at time k, H k For the measurement matrix at time k, V k Measurement noise for time k
In the middle of
Wherein T is an iteration period, T k The k time is k;
(2.2) design of a federal filter:
each sub-filter adopts a Kalman filtering mode, and the specific steps are as follows:
state one-step prediction equation:
in the method, in the process of the invention,is made use of->Calculating to obtain X k Is predicted in one step;
state estimation equation:
is to predict +.>Based on the measured value, the true value X k Wherein K is k Is the filtering gain;
kalman gain equation:
wherein P is kk-1 The mean square error is predicted for one step; r is R k A variance matrix for measuring noise;
one-step prediction mean square error equation:
mean square error estimation equation:
wherein P is kk To estimateIs determined according to the estimated mean square error equation;
the position information representing the inertial navigation system is
Lambda in I 、L I 、H I Lambda is a measurement value of latitude, longitude and altitude of inertial navigation system t 、L t 、H t The true values of the latitude, longitude and altitude of the vehicle-mounted device are shown as delta lambda, delta L and delta H, and the measured error values of the latitude, longitude and altitude of the inertial navigation system are shown as delta lambda, delta L and delta H;
the speed information representing the inertial navigation system is
V in IN 、v IE 、v IU V, a measurement of the velocity of the inertial navigation system in the northeast-north direction N 、v E 、v U Is true value of the speed of the vehicle-mounted device in the northeast and north directions, δv N 、δv E 、δv U Measuring error values of the speed of the inertial navigation system in the northeast direction;
the position information representing the satellite navigation system is
Lambda in G 、L G 、H G Lambda is the measured value of latitude, longitude and altitude of satellite navigation system t 、L t 、H t True value of latitude, longitude and altitude of vehicle-mounted device, N E 、N N 、N U Measuring error values for the northeast direction position of the satellite navigation system;
the speed information representing the satellite navigation system is
V in GE 、v GN 、v GU Is a satellite navigation systemIntegrating velocity measurements in northeast and north directions, v N 、v E 、v U Is true value of the speed of the vehicle-mounted device in the northeast and north directions, M N 、M E 、M U Measuring error values of the speed of the inertial navigation system in the northeast direction; in order to cooperate with the dimensions of longitude and latitude of the inertial navigation system, position measurement value N and velocity measurement value M are converted;
the speed information representing the odometer is
V in OE 、v ON 、v OU V, a measurement of the speed of the odometer in the northeast direction N 、v E 、v U Is true value of the speed of the vehicle-mounted device in the northeast and north directions, O N 、O E 、O U Measuring error value of speed of the odometer in northeast day direction;
the height information representing the height gauge is
H a ＝H U -A(23)
H in a H is the measurement of the height of the altimeter U The true value of the vehicle-mounted device in the upward position is shown, and A is the measurement error value of the altimeter in the height;
(2.2.1) designing SINS/BDS sub-filters
The state equation of the SINS/BDS sub-filter is known according to (2.1)
Measuring method of SINS/BDS sub-filter
Wherein the method comprises the steps of
V G (t)＝[N N N E N U M E M N M U ] T (27)
The measured noise is treated as white noise, and its variance is respectivelyR M 、R N Respectively a long radius and a short radius of the earth;
(2.2.2) designing SINS/odometer sub-filters
According to (2.1), the state equation of the SINS/BDS sub-filter is
The measurement equation of the SINS/odometer sub-filter is
Wherein the method comprises the steps of
H O (t)＝[0 3×3 diag[1 1 1]0 3×12 ] (30)
V G (t)＝[O E O N O U ] T (31)
The measurement noise is treated as white noise with the mean value of 0;
(2.2.3) design of Federal Filter Main Filter
The federal filter is a two-stage filtering structure, and the output X of the common reference subsystem SINS k On one hand, the main filter and on the other hand, each sub-filter are used as measurement values; the output of each subsystem is only given to the respective filter, the local estimation value X of each sub-filter i And its covariance matrix P i The estimation values sent into the main filter and the main filter are fused together to obtain a global estimation value;
global optimum estimation synthesized by main filter and sub-filterCorresponding covariance matrix P g Is amplified to +.>And then feeding back to the sub-filter to reset the estimation value of the sub-filter, namely: />The co-equation matrix of the main filter is +.>β i Determining according to an information distribution principle;
and 2, designing a fault detection and isolation method through vector distribution, and detecting and isolating information of fault dimensions of each sensor, wherein the method comprises the following steps of:
(3.1) sub-filter time update:
wherein i represents the i-th sub-filter;
(3.2) fault diagnosis:
the following fault diagnosis function is first constructed:
Λ i,k ＝r i,k (r i,k ) T [H i,k P i,k|k-1 (H i,k ) T +R i,k ] -1 (33)
wherein r is i,k Representing the residual error of system i at time k, Λ i,k Is a matrix of m rows and m columns, expressed as:
Λ when no fault occurs in the sub-filter i,k Each element on the diagonal of the array should obey x with the degree of freedom of 1 2 And (3) distributing, namely when a sensor in the system fails, not meeting the condition, setting a threshold value at the moment, and establishing the following judgment rule:
defining the measured noise figure B of the ith sub-filter i,k The method comprises the following steps:
wherein the method comprises the steps of
By the obtained measured noise figure B i,k Reconstructing a measurement noise matrix
In the formula (37), when one dimension of the equivalent measurement information is judged to be normal, B i,k The corresponding diagonal element is set to 1, otherwise to 0, so that the measurement noise matrix reconstructed in equation (39)For normal measurement variables, the adjusted corresponding noise variance is unchanged; for fault measurement variables, the adjusted corresponding noise variance tends to infinity, so that the dimension information of the sensor fault is dynamically isolated;
(3.3) sub-Filter measurement update
After the sub-filters are measured and updated, the filtering result of the fault dimension information of the isolation sensor is sent to the main filter to perform the next information fusion;
and 3, constructing vector distribution coefficients for each dimension of information of each sub-filter by using the output result of each sub-filter, and carrying out information fusion in the main filter to obtain a global optimal estimation result, wherein the method comprises the following specific steps of:
first, a sub-filter covariance matrix P i,k|k And (3) performing eigenvalue decomposition:
P i,k|k ＝D i,k Λ i,k (D i,k ) T (41)
in the middle of
Wherein lambda is n,i,k Is the ith sub-filter covariance matrix P i,k|k Is the nth characteristic value of D i,k Is an orthogonal matrix generated by eigenvalue decomposition; defining distribution coefficient matrix A i,k The method comprises the following steps:
in the middle of
A i,k Meets the theorem of conservation of information
Constructing distribution coefficient matrix C by observability of sub-filters i,k Assuming that the observability matrix of the sub-filter i is Q i,k For Q i,k Singular value decomposition
Q i,k ＝U i,k S i,k (V i,k ) T (46)
Wherein U is i,k And V i,k Is an orthogonal matrix, S i,k The method comprises the following steps:
wherein Λ r×r ＝diag{σ 1,i,k ,σ 2,i,k …σ ri,i,k }，σ n,i,k (n＝1,2,…r i )，r i Respectively Q i,k Singular values and ranks of (2);
then measure coefficient C i,k The definition is as follows:
wherein the method comprises the steps of
C i,k Meets the theorem of conservation of information
Then the vector-based information distribution coefficient B i,k The method comprises the following steps:
at this time, the information distribution coefficient still satisfies the principle of information conservation:
in order to ensure the symmetry of the error covariance matrix, the information distribution mode is as follows:
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