CN112697154A - 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 PDF

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CN112697154A
CN112697154A CN202110132460.XA CN202110132460A CN112697154A CN 112697154 A CN112697154 A CN 112697154A CN 202110132460 A CN202110132460 A CN 202110132460A CN 112697154 A CN112697154 A CN 112697154A
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information
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CN112697154B (en
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张孟军
赵海飞
王博浩
马永犇
程玉
陈帅
刘清秀
马一鸣
顾涛
王琮
姚晓涵
廖泽俣
蒋长辉
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Nanjing University of Science and Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • 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
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • 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
    • G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • 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
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • 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
    • G01C21/206—Instruments for performing navigational calculations specially adapted for indoor navigation

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 18-dimensional system errors as state quantities, establishing a federal filtering combined navigation model according to the output characteristics of each sensor, and designing a federal filter; designing a method for fault detection and isolation through vector distribution, and detecting and isolating information of fault dimensions of each sensor; and (3) constructing a vector distribution coefficient for each dimension of information of each sub-filter by using the information obtained in the step (2) fault detection, 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 robustness of the system, and can select a proper navigation sensor according to different navigation requirements, thereby improving the flexibility of the navigation system.

Description

Self-adaptive multi-source fusion navigation method based on vector distribution
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, the satellite navigation technology has been widely applied not only in war, but also the satellite navigation industry has become an important support for the information industry. The navigation industry and the support and application of the technology thereof cannot be separated from personal travel, transportation, weather prediction, mapping, disaster relief and flood control and mobile communication. However, the GNSS system is originally designed as a navigation aid in war environments, and therefore, the BDS system in china, the GPS system in the united states, the GLONASS system in russia, the galileo system in europe, or the small-scale navigation system and the regional navigation system in other countries and regions all have inherent disadvantages that the signal power of the signal reaching the ground is extremely low, so that the receiver is easily deceived and interfered, the service performance is seriously degraded in physical signal-blocking environments such as indoor, underwater, underground, and urban canyons, and in electromagnetic interference environments, and the military security is seriously challenged.
Based on the above, the combination mode of the single navigation subsystem assisted 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 the federal Kalman multi-source data filtering and carries out fault diagnosis and information distribution in a vector distribution mode, so that the self-adaptive distribution of information factors of all federal sub-filters is realized, the information utilization rate of all sensors is improved, and the optimal estimation of the federal filter is optimized.
The technical solution for realizing the purpose of the invention is as follows: a self-adaptive multi-source fusion navigation method based on vector distribution comprises the following steps:
step 1: selecting a northeast coordinate system as a navigation system, selecting 18-dimensional system errors as state quantities, 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 fault detection and isolation through vector distribution, and detecting and isolating information of fault dimensions of each sensor;
and step 3: and (3) constructing a vector distribution coefficient for each dimension of information of each sub-filter by using the information obtained in the step (2) fault detection, 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 following remarkable advantages: (1) on the basis of a conventional GNSS/SINS integrated navigation algorithm, a multi-source navigation system based on a Federal Kalman filtering algorithm is designed, an SINS is taken as a reference system, and an SINS/GNSS and an SINS/odometer are fused, so that the navigation positioning precision of the integrated navigation system is improved; (2) aiming at the difference of estimation precision among sensors and among observation components 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 a system to navigation information is improved, and the precision and the reliability of a multi-source navigation system are enhanced.
Drawings
FIG. 1 is a flow chart of the adaptive multi-source fusion navigation method based on vector distribution according to the present invention.
FIG. 2 is a structural schematic diagram of an improved Federal Kalman filter used in the adaptive multi-source fusion navigation method based on vector distribution.
Detailed Description
According to the environmental characteristics and the working characteristics of the navigation system, the invention combines the output information of navigation sensors with different working characteristics to form the integrated navigation system based on multi-source information fusion on the basis of an inertia/satellite integrated navigation system with mature technology and unique advantages, thereby overcoming the service defects and insufficient capability caused by the inherent vulnerability of the GNSS, improving the precision of the whole navigation system and leading the navigation system to be capable of accurately and reliably completing tasks for a long time.
The invention relates to a vector distribution-based self-adaptive multi-source fusion navigation method, which comprises the following steps of:
step 1: selecting a northeast coordinate system as a navigation system, selecting 18-dimensional system errors as state quantities, 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 fault detection and isolation through vector distribution, and detecting and isolating information of fault dimensions of each sensor;
and 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 performing information fusion in the main filter to obtain a global optimal estimation result.
Further, in the step 1, a 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, specifically as follows:
(2.1) firstly, establishing a federal filtering integrated navigation system model under a navigation coordinate system; the error model of the inertial navigation system adopts a universal error model, the public 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
Figure BDA0002925871360000021
Wherein
Figure BDA0002925871360000031
The attitude angle error in the northeast direction; delta VE、δVN、δVUIs the speed error in the northeast direction; δ L, δ λ, δ H are position errors in the weft height direction; epsilonbx、εby、εbzRandom drift of the gyroscope in three axial directions; epsilonrx、εry、εrzRandom noise is generated in a first-order Markov process of the gyroscope in three axial directions;
Figure BDA0002925871360000032
Figure BDA0002925871360000033
is a constant deviation of the accelerometer in three axial directions;
equation of state of system
Figure BDA0002925871360000034
Comprises the following steps:
Figure BDA0002925871360000035
wherein F (t) is a state transition matrix of the system, G (t) is an error coefficient matrix, and W (t) is a white noise random error vector, and the specific form is as follows:
state transition matrix f (t):
Figure BDA0002925871360000036
in the formula FNIs a systematic error matrix, FsError transformation matrix for inertial devices, FMThe noise matrix of the inertial device is as follows:
Figure BDA0002925871360000037
Figure BDA0002925871360000038
wherein
Figure BDA0002925871360000039
An attitude transformation matrix;
Figure BDA00029258713600000310
wherein, TgRepresenting the relevant time of the gyro, TaRepresenting the relevant time of the accelerometer, and x, y and z respectively representing the three-axis directions of the carrier system;
the error coefficient matrix g (t) is:
Figure BDA0002925871360000041
the white noise random error vector W (t) is:
W(t)＝[wgx wgy wgz wrx wry wrz wax way waz]T (8)
wherein, wgRepresenting white noise of the gyro, wrRepresenting March white noise, waRepresenting 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) ═ NE NN NU]TFor measuring noise, NE、NN、NUThe measurement noise in the direction, H (t), is the measurement matrix of the system, and is selected differently according to different sub-filters; since a continuous system model is not easily realized in a computer, it is necessary to discretize the system model and discretize the state equation (2) and the measurement equation (9) to obtain a system model
Figure BDA0002925871360000042
Wherein, XkIs the state vector at time k, phik|k-1For the system one-step transfer matrix, Γ, from time k-1 to time kk-1Is a noise matrix of the system, which characterizes that each system noise from k-1 to k time respectively influences the brightness of each state at k time, Wk-1System noise at time k-1, ZkIs the measurement vector at time k, HkIs a measurement matrix at time k, VkMeasurement noise at time k
In the formula
Figure BDA0002925871360000043
Figure BDA0002925871360000044
Where T is the iteration period, TkIs the k moment;
(2.2) design of a federal filter:
each sub-filter adopts a Kalman filtering mode, and the method specifically comprises the following steps:
one-step prediction equation of state:
Figure BDA0002925871360000051
in the formula (I), the compound is shown in the specification,
Figure BDA0002925871360000052
is to utilize
Figure BDA0002925871360000053
Calculating to obtain XkThe one-step prediction is carried out;
the state estimation equation:
Figure BDA0002925871360000054
Figure BDA0002925871360000055
is predicted in one step
Figure BDA0002925871360000056
Based on the measured value, the true value X is measuredkIs estimated, where KkIs the filter gain;
kalman gain equation:
Figure BDA0002925871360000057
in the formula, Pk|k-1Predicting the mean square error for one step; rkA variance matrix for the measured noise;
one-step prediction mean square error equation:
Figure BDA0002925871360000058
mean square error estimation equation:
Figure BDA0002925871360000059
in the formula, Pk|kTo estimate the value
Figure BDA00029258713600000510
The estimated mean square error equation of (a);
the position information representing the inertial navigation system is
Figure BDA00029258713600000511
In the formula ofI、LI、HIAs a measure of latitude, longitude, altitude, λ, of the inertial navigation systemt、Lt、HtThe latitude, longitude and altitude of the vehicle-mounted device are true values, and the delta lambda, delta L and delta H are measurement error values of the latitude, longitude and altitude of the inertial navigation system;
the velocity information representing the inertial navigation system is
Figure BDA0002925871360000061
In the formula vIN、vIE、vIUIs a measure of the velocity of the inertial navigation system in the northeast direction, vN、vE、vUIs the true value of the speed of the vehicle-mounted device in the northeast direction, delta vN、δvE、δvUMeasuring error value of the velocity of the inertial navigation system in the northeast direction;
the position information of the satellite navigation system is
Figure BDA0002925871360000062
In the formula ofG、LG、HGAs a measure of the satellite navigation system latitude, longitude, altitude, lambdat、Lt、HtIs the true value of latitude, longitude and altitude of the vehicle-mounted device, NE、NN、NUMeasuring error values of the satellite navigation system in the northeast direction;
the velocity information representing the satellite navigation system is
Figure BDA0002925871360000063
In the formula vGE、vGN、vGUAs a measure of the velocity of the satellite navigation system in the northeast direction, vN、vE、vUIs the true value of the speed of the vehicle-mounted device in the northeast direction, MN、ME、MUMeasuring error value of the velocity of the inertial navigation system in the northeast direction; the position measurement value N and the speed measurement value M are converted in order to be matched with the longitude and latitude dimensions of the inertial navigation system;
the speed information indicating the odometer is
Figure BDA0002925871360000064
In the formula vOE、vON、vOUAs a measure of the velocity of the odometer in the northeast direction, vN、vE、vUIs the true value of the speed of the vehicle-mounted device in the northeast direction, ON、OE、OUThe measurement error value of the speed of the odometer in the northeast direction is shown;
the altitude information indicating the altimeter is
Ha＝HU-A (23)
In the formula HaAs a measure of the height of the altimeter, HUThe altitude measurement error value A is a true value of the position of the vehicle-mounted device in the vertical direction, and A is a measurement error value of the altimeter in the altitude;
(2.2.1) design of SINS/BDS sub-filter
From (2.1), the equation of state of the SINS/BDS sub-filter is known as
Figure BDA0002925871360000071
Measuring method of SINS/BDS sub-filter
Figure BDA0002925871360000072
Wherein
Figure BDA0002925871360000073
VG(t)＝[NN NE NU ME MN MU]T (27)
The measured noise is treated as white noise, and its variance is respectively
Figure BDA0002925871360000074
RM、RNThe long radius and the short radius of the earth, respectively;
(2.2.2) design of SINS/odometer sub-filter
According to (2.1), the state equation of the SINS/BDS sub-filter is
Figure BDA0002925871360000075
The measurement equation of the SINS/odometer sub-filter is as follows
Figure BDA0002925871360000076
Wherein
HO(t)＝[03×3 diag[1 1 1] 03×12] (30)
VG(t)＝[OE ON OU]T (31)
Measuring the white noise with the average value of 0;
(2.2.3) design of Federal Filter Main Filter
The federal filter is a two-stage filter structure, and the output X of a common reference subsystem (SINS)kOn the one hand, the main filter and on the other hand, each sub-filter is used as a measurement value; the outputs of the sub-systems being supplied only to the respective filters, the local estimated values X of the sub-filtersiAnd its covariance matrix PiInto the main filter and the mainFusing the estimated values of the filters together to obtain a global estimated value;
global optimum estimation synthesized by main filter and sub-filter
Figure BDA0002925871360000081
And its corresponding covariance matrix PgIs amplified into
Figure BDA0002925871360000082
And then feeding back to the sub-filter to reset the estimation value of the sub-filter, namely:
Figure BDA0002925871360000083
the main filter has a covariance matrix of
Figure BDA0002925871360000084
βiDetermining 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 covariance matrix of the system and the observability of the system, and the method is described in detail in claim 4.
Further, the step 2 designs a method for detecting and isolating faults through vector distribution, and detects and isolates information of fault dimensions of each sensor, specifically as follows:
(3.1) sub-filter time update:
Figure BDA0002925871360000085
wherein i represents the ith sub-filter;
(3.2) fault diagnosis:
the following fault diagnosis functions are first constructed:
Λi,k＝ri,k(ri,k)T[Hi,kPi,k|k-1(Hi,k)T+Ri,k]-1 (33)
Figure BDA0002925871360000086
wherein r isi,kRepresenting the residual of system i at time k, Λi,kIs a matrix of m rows and m columns, which can be expressed as:
Figure BDA0002925871360000091
when no fault occurs in the sub-filter, Λi,kEach element on the diagonal in the array should obey x with degree of freedom of 12Distribution, when a sensor in the system fails, the fault is not satisfied any more, a proper threshold value is set at the moment, and the following judgment rule is established:
Figure BDA0002925871360000092
defining the measured noise coefficient B of the ith sub-filteri,kComprises the following steps:
Figure BDA0002925871360000093
wherein
Figure BDA0002925871360000094
By obtaining a measured noise figure Bi,kReconstructing the measured noise matrix
Figure BDA0002925871360000095
Figure BDA0002925871360000096
In equation (37), when a dimension of the measurement information is determined to be normal, Bi,kCorresponding opposite angleThe line element is set to 1, otherwise to 0, thus reconstructing the metric noise matrix in equation (39)
Figure BDA0002925871360000097
For normal measurement variables, the corresponding noise variance after adjustment is unchanged; for the fault measurement variable, the adjusted corresponding noise variance tends to be infinite, so that the dimension information of the sensor fault is dynamically isolated;
(3.3) sub-filter measurement update
Figure BDA0002925871360000101
And after the sub-filters perform measurement updating, transmitting the filtering result of the fault dimension information of the isolation sensor to the main filter for the next step of information fusion.
Further, in step 3, vector distribution coefficients are constructed for each dimension of information of each sub-filter by using output results of each sub-filter, and information fusion is performed in the main filter to obtain a global optimal estimation result, which is specifically as follows:
covariance matrix P of sub-filtersi,k|kThe estimation precision of the sub-filters can be reflected, and the structural performance of the system can be reflected by the observability of the system; the conventional adaptive information allocation method uses trace (P)i,k|k) Calculating information distribution coefficients, but in the actual federal filtering model, each sub-filter generally contains more than one measured variable, and even in the same filter, each measured variable has different estimation precision; the invention designs a self-adaptive information distribution coefficient algorithm based on vector distribution based on the covariance matrix of the sub-filters and the observability of the system;
first, a sub-filter covariance matrix Pi,k|kAnd (3) carrying out characteristic value decomposition:
Pi,k|k＝Di,kΛi,k(Di,k)T (41)
in the formula
Figure BDA0002925871360000102
Wherein λn,i,kIs the ith sub-filter covariance matrix Pi,k|kN characteristic value of (D)i,kIs an orthogonal matrix resulting from eigenvalue decomposition; defining a distribution coefficient matrix Ai,kComprises the following steps:
Figure BDA0002925871360000103
in the formula
Figure BDA0002925871360000111
Ai,kSatisfy the theorem of information conservation
Figure BDA0002925871360000112
The partition coefficient matrix C is constructed by the observability of the sub-filtersi,kLet us assume that the observability matrix of the sub-filter i is Qi,kTo Q, pairi,kPerforming singular value decomposition
Qi,k＝Ui,kSi,k(Vi,k)T (46)
Wherein U isi,kAnd Vi,kIs an orthogonal matrix, Si,kThe method specifically comprises the following steps:
Figure BDA0002925871360000113
wherein Λr×r＝diag{σ1,i,k,σ2,i,k…σri,i,k}，σn,i,k(n＝1,2,…ri)，riAre respectively Qi,kSingular value and rank of;
then measure the coefficient Ci,kIs defined as:
Figure BDA0002925871360000114
wherein
Figure BDA0002925871360000115
Ci,kSatisfy the theorem of information conservation
Figure BDA0002925871360000116
Then the vector-based information assigns coefficient Bi,kComprises the following steps:
Figure BDA0002925871360000117
at the moment, the information distribution coefficient still meets the information conservation principle:
Figure BDA0002925871360000121
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:
Figure BDA0002925871360000122
the invention is described in further detail below with reference to the figures and the embodiments.
Examples
With reference to fig. 1, the present invention is a vector distribution-based adaptive multi-source fusion navigation method, which includes the following steps:
step 1: selecting a northeast coordinate system as a navigation system, selecting 18-dimensional system errors as state quantities, establishing a federal filtering combined navigation model according to the output characteristics of each sensor, and designing a federal filter;
with reference to fig. 2, in the federation kalman filter of the present invention, 3 navigation information sources are used, so an SINS/GNSS, an SINS/odometer sub-filter, and a main filter for information fusion are adopted, information is distributed between each sub-filter and the main filter by using the information distribution principle, each sub-filter processes the respective measurement information and obtains a local estimate, and then information fusion is performed in the main filter to obtain an optimal estimate.
(1.1) firstly, establishing a federal filtering integrated navigation system model under a navigation coordinate system; the error model of the inertial navigation system adopts a universal error model, the public 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
Figure BDA0002925871360000123
Wherein
Figure BDA0002925871360000124
The attitude angle error in the northeast direction; delta VE、δVN、δVUIs the speed error in the northeast direction; δ L, δ λ, δ H are position errors in the weft height direction; epsilonbx、εby、εbzRandom drift of the gyroscope in three axial directions; epsilonrx、εry、εrzRandom noise is generated in a first-order Markov process of the gyroscope in three axial directions;
Figure BDA0002925871360000125
Figure BDA0002925871360000126
is a constant deviation of the accelerometer in three axial directions;
equation of state of system
Figure BDA0002925871360000127
Comprises the following steps:
Figure BDA0002925871360000128
wherein F (t) is a state transition matrix of the system, G (t) is an error coefficient matrix, and W (t) is a white noise random error vector, and the specific form is as follows:
state transition matrix f (t):
Figure BDA0002925871360000131
in the formula FNIs a systematic error matrix, FsError transformation matrix for inertial devices, FMThe noise matrix of the inertial device is as follows:
Figure BDA0002925871360000132
Figure BDA0002925871360000133
wherein
Figure BDA0002925871360000134
An attitude transformation matrix;
Figure BDA0002925871360000135
wherein, TgRepresenting the relevant time of the gyro, TaThe relevant time of the accelerometer is shown, and x, y and z respectively show the three-axis directions of the carrier system.
The error coefficient matrix g (t) is:
Figure BDA0002925871360000136
the white noise random error vector W (t) is:
W(t)＝[wgx wgy wgz wrx wry wrz wax way waz]T (1.8)
wherein, wgRepresenting white noise of the gyro, wrRepresenting March white noise, waRepresenting 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) ═ NE NN NU]TFor measuring noise, NE、NN、NUThe measurement noise in the direction, H (t), is the measurement matrix of the system, and is selected differently according to different sub-filters; since a continuous system model is not easily realized in a computer, it is necessary to discretize the system model and discretize the state equation (2) and the measurement equation (9) to obtain a system model
Figure BDA0002925871360000141
Wherein, XkIs the state vector at time k, phik|k-1For the system one-step transfer matrix, Γ, from time k-1 to time kk-1Is a noise matrix of the system, which characterizes that each system noise from k-1 to k time respectively influences the brightness of each state at k time, Wk-1System noise at time k-1, ZkIs the measurement vector at time k, HkIs a measurement matrix at time k, VkMeasurement noise at time k
In the formula
Figure BDA0002925871360000142
Figure BDA0002925871360000143
Where T is the iteration period, TkIs the k moment;
(1.2) design of a federal filter:
each sub-filter adopts a Kalman filtering mode, and the method specifically comprises the following steps:
one-step prediction equation of state:
Figure BDA0002925871360000144
in the formula (I), the compound is shown in the specification,
Figure BDA0002925871360000145
is to utilize
Figure BDA0002925871360000146
Calculating to obtain XkThe one-step prediction is carried out;
the state estimation equation:
Figure BDA0002925871360000147
Figure BDA0002925871360000151
is predicted in one step
Figure BDA0002925871360000152
Based on the measured value, the true value X is measuredkIs estimated, where KkIs the filter gain; kalman gain equation:
Figure BDA0002925871360000153
in the formula, Pk|k-1Predicting the mean square error for one step; rkA variance matrix for the measured noise;
one-step prediction mean square error equation:
Figure BDA0002925871360000154
mean square error estimation equation:
Figure BDA0002925871360000155
in the formula, Pk|kTo estimate the value
Figure BDA0002925871360000156
The estimated mean square error equation of (2).
The position information representing the inertial navigation system is
Figure BDA0002925871360000157
In the formula ofI、LI、HIAs a measure of latitude, longitude, altitude, λ, of the inertial navigation systemt、Lt、HtThe latitude, longitude and altitude of the vehicle-mounted device are true values, and the delta lambda, delta L and delta H are measurement error values of the latitude, longitude and altitude of the inertial navigation system;
the velocity information representing the inertial navigation system is
Figure BDA0002925871360000158
In the formula vIN、vIE、vIUIs a measure of the velocity of the inertial navigation system in the northeast direction, vN、vE、vUIs the true value of the speed of the vehicle-mounted device in the northeast direction, delta vN、δvE、δvUMeasuring error value of the velocity of the inertial navigation system in the northeast direction;
the position information of the satellite navigation system is
Figure BDA0002925871360000159
In the formula ofG、LG、HGAs a measure of the satellite navigation system latitude, longitude, altitude, lambdat、Lt、HtIs the true value of latitude, longitude and altitude of the vehicle-mounted device, NE、NN、NUMeasuring error values of the satellite navigation system in the northeast direction;
the velocity information representing the satellite navigation system is
Figure BDA0002925871360000161
In the formula vGE、vGN、vGUAs a measure of the velocity of the satellite navigation system in the northeast direction, vN、vE、vUIs the true value of the speed of the vehicle-mounted device in the northeast direction, MN、ME、MUMeasuring error value of the velocity of the inertial navigation system in the northeast direction; the position measurement value N and the speed measurement value M are converted in order to be matched with the longitude and latitude dimensions of the inertial navigation system;
the speed information indicating the odometer is
Figure BDA0002925871360000162
In the formula vOE、vON、vOUAs a measure of the velocity of the odometer in the northeast direction, vN、vE、vUIs the true value of the speed of the vehicle-mounted device in the northeast direction, ON、OE、OUThe measurement error value of the speed of the odometer in the northeast direction is shown;
the altitude information indicating the altimeter is
Ha＝HU-A (1.23)
In the formula HaIs a measure of the height of the altimeter,HUthe altitude measurement error value A is a true value of the position of the vehicle-mounted device in the vertical direction, and A is a measurement error value of the altimeter in the altitude;
(1.2.1) design of SINS/BDS sub-filter
From (2.1), the equation of state of the SINS/BDS sub-filter is known as
Figure BDA0002925871360000163
Measuring method of SINS/BDS sub-filter
Figure BDA0002925871360000171
Wherein
Figure BDA0002925871360000172
VG(t)＝[NN NE NU ME MN MU]T (1.27)
The measured noise is treated as white noise, and its variance is respectively
Figure BDA0002925871360000173
RM、RNThe long radius and the short radius of the earth, respectively;
(1.2.2) design of SINS/odometer sub-filter
According to (1.1), the state equation of the SINS/BDS sub-filter is
Figure BDA0002925871360000174
The measurement equation of the SINS/odometer sub-filter is as follows
Figure BDA0002925871360000175
Wherein
HO(t)＝[03×3 diag[1 1 1]03×12] (1.30)
VG(t)＝[OE ON OU]T (1.31)
Measuring the white noise with the average value of 0;
(1.2.3) design of Federal Filter Main Filter
The federal filter is a two-stage filter structure, and the output X of a common reference subsystem (SINS)kThe main filter on the one hand and the individual sub-filters on the other hand are provided as measured values. The output of each subsystem is only fed to the respective filter. Local estimated value X of each sub-filteriAnd its covariance matrix PiThe estimated values sent into the main filter and the main filter are fused together to obtain a global estimated value;
global optimum estimation synthesized by main filter and sub-filter
Figure BDA0002925871360000181
And its corresponding covariance matrix PgIs amplified into
Figure BDA0002925871360000182
And then feeding back to the sub-filter to reset the estimation value of the sub-filter, namely:
Figure BDA0002925871360000183
the main filter has a covariance matrix of
Figure BDA0002925871360000184
βiDetermined 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 covariance matrix of the system and the observability of the system, and the method is described in detail in claim 4.
Step 2: after the output results of the sub-filters in the step 1 are obtained, fault detection is carried out in a vector distribution mode
And isolation, the specific method is as follows:
(2.1) sub-filter time update:
Figure BDA0002925871360000185
where i denotes the ith sub-filter.
And (2.2) fault diagnosis. The following fault diagnosis functions are first constructed:
Figure BDA0002925871360000186
Figure BDA0002925871360000187
wherein r isi,kRepresenting the residual of system i at time k, Λi,kIs a matrix of m rows and m columns, which can be expressed as:
Figure BDA0002925871360000188
when no fault occurs in the sub-filter, Λi,kEach element on the diagonal in the array should obey x with degree of freedom of 12And when a sensor in the system fails, the distribution is not satisfied. At this time, a proper threshold value is set, and the following judgment rule is established:
Figure BDA0002925871360000189
defining the measured noise coefficient B of the ith sub-filteri,kComprises the following steps:
Figure BDA0002925871360000191
wherein
Figure BDA0002925871360000192
By obtaining a measured noise figure Bi,kReconstructing the measured noise matrix
Figure BDA0002925871360000193
Figure BDA0002925871360000194
In equation (37), when a dimension of the measurement information is determined to be normal, Bi,kThe corresponding diagonal element is set to 1, otherwise to 0, thus reconstructing the metric noise matrix in equation (39)
Figure BDA0002925871360000195
For normal measurement variables, the corresponding noise variance after adjustment is unchanged; for the fault measurement variable, the corresponding noise variance after adjustment tends to be infinite, and dynamic isolation of the dimension information of the sensor fault is realized.
(2.3) sub-filter measurement update
Figure BDA0002925871360000196
And after the sub-filters perform measurement updating, transmitting the filtering result of the fault dimension information of the isolation sensor to the main filter for the next step of information fusion.
And step 3: and (3) constructing a vector distribution coefficient for each dimension of information of each sub-filter by using the information obtained in the step (2) fault detection, and carrying out information fusion in the main filter to obtain a global optimal estimation result. The method comprises the following specific steps:
covariance matrix P of sub-filtersi,k|kThe estimation precision of the sub-filters can be reflected, and the structural performance of the system can be reflected by the observability of the system. Conventional adaptive information distribution method makesUsing trace (P)i,k|k) The information distribution coefficients are calculated, but in the actual federal filter model, each sub-filter generally contains more than one measured variable, and each measured variable has different estimation accuracy even in the same filter. The invention designs a self-adaptive information distribution coefficient algorithm based on vector distribution based on the covariance matrix of the sub-filters and the observability of the system.
First, a sub-filter covariance matrix Pi,k|kAnd (3) carrying out characteristic value decomposition:
Pi,k|k＝Di,kΛi,k(Di,k)T (1.41)
in the formula
Figure BDA0002925871360000201
Wherein λn,i,kIs the ith sub-filter covariance matrix Pi,k|kN characteristic value of (D)i,kIs an orthogonal matrix resulting from eigenvalue decomposition. Defining a distribution coefficient matrix Ai,kComprises the following steps:
Figure BDA0002925871360000202
Figure BDA0002925871360000203
Ai,ksatisfy the theorem of information conservation
Figure BDA0002925871360000204
The partition coefficient matrix C is constructed by the observability of the sub-filtersi,kLet us assume that the observability matrix of the sub-filter i is Qi,kTo Q, pairi,kPerforming singular value decomposition
Qi,k＝Ui,kSi,k(Vi,k)T (1.46)
Wherein U isi,kAnd Vi,kIs an orthogonal matrix, Si,kThe method specifically comprises the following steps:
Figure BDA0002925871360000205
wherein Λr×r＝diag{σ1,i,k,σ2,i,k…σri,i,k}，σn,i,k(n＝1,2,…ri)，riAre respectively Qi,kSingular value and rank.
Then measure the coefficient Ci,kIs defined as:
Figure BDA0002925871360000211
Figure BDA0002925871360000212
Ci,ksatisfy the theorem of information conservation
Figure BDA0002925871360000213
Then the vector-based information assigns coefficient Bi,kComprises the following steps:
Figure BDA0002925871360000214
at the moment, the information distribution coefficient still meets the information conservation principle:
Figure BDA0002925871360000215
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:
Figure BDA0002925871360000216
in summary, on the basis of a conventional GNSS/SINS integrated navigation algorithm, the invention designs a multi-source navigation system based on the Federal Kalman filtering algorithm, taking the SINS as a reference system and fusing the SINS/GNSS and the SINS/mileometer, thereby improving the navigation positioning precision of the integrated navigation system; aiming at the difference of estimation precision among sensors and among observation components 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 a system to navigation information is improved, and the precision and the reliability of a multi-source navigation system are enhanced.

Claims (4)

1. A self-adaptive multi-source fusion navigation method based on vector distribution is characterized by comprising the following steps:
step 1: selecting a northeast coordinate system as a navigation system, selecting 18-dimensional system errors as state quantities, 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 fault detection and isolation through vector distribution, and detecting and isolating information of fault dimensions of each sensor;
and 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 performing information fusion in the main filter to obtain a global optimal estimation result.
2. The vector distribution-based self-adaptive multi-source fusion navigation method according to claim 1, wherein the northeast coordinate system is selected as a navigation system in the step 1, 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, specifically as follows:
(2.1) firstly, establishing a federal filtering integrated navigation system model under a navigation coordinate system; the error model of the inertial navigation system adopts a universal error model, the public 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
Figure FDA0002925871350000011
Wherein
Figure FDA0002925871350000012
The attitude angle error in the northeast direction; delta VE、δVN、δVUIs the speed error in the northeast direction; δ L, δ λ, δ H are position errors in the weft height direction; epsilonbx、εby、εbzRandom drift of the gyroscope in three axial directions; epsilonrx、εry、εrzRandom noise is generated in a first-order Markov process of the gyroscope in three axial directions;
Figure FDA0002925871350000013
Figure FDA0002925871350000014
is a constant deviation of the accelerometer in three axial directions;
equation of state of system
Figure FDA0002925871350000015
Comprises the following steps:
Figure FDA0002925871350000016
wherein F (t) is a state transition matrix of the system, G (t) is an error coefficient matrix, and W (t) is a white noise random error vector, and the specific form is as follows:
state transition matrix f (t):
Figure FDA0002925871350000017
in the formula FNIs a systematic error matrix, FsError transformation matrix for inertial devices, FMThe noise matrix of the inertial device is as follows:
Figure FDA0002925871350000021
Figure FDA0002925871350000022
wherein
Figure FDA0002925871350000023
An attitude transformation matrix;
Figure FDA0002925871350000024
wherein, TgRepresenting the relevant time of the gyro, TaRepresenting the relevant time of the accelerometer, and x, y and z respectively representing the three-axis directions of the carrier system;
the error coefficient matrix g (t) is:
Figure FDA0002925871350000025
the white noise random error vector W (t) is:
W(t)＝[wgx wgy wgz wrx wry wrz wax way waz]T (8)
wherein, wgRepresenting the white noise of the gyro,wrrepresenting March white noise, waRepresenting 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) ═ NE NN NU]TFor measuring noise, NE、NN、NUThe measurement noise in the direction, H (t), is the measurement matrix of the system, and is selected differently according to different sub-filters;
discretizing the system model, and discretizing the state equation (2) and the measurement equation (9) to obtain
Figure FDA0002925871350000031
Wherein, XkIs the state vector at time k, phik|k-1For the system one-step transfer matrix, Γ, from time k-1 to time kk-1Is a noise matrix of the system, which characterizes that each system noise from k-1 to k time respectively influences the brightness of each state at k time, Wk-1System noise at time k-1, ZkIs the measurement vector at time k, HkIs a measurement matrix at time k, VkMeasurement noise at time k
In the formula
Figure FDA0002925871350000032
Figure FDA0002925871350000033
Where T is the iteration period, TkIs the k moment;
(2.2) design of a federal filter:
each sub-filter adopts a Kalman filtering mode, and the method specifically comprises the following steps:
one-step prediction equation of state:
Figure FDA0002925871350000034
in the formula (I), the compound is shown in the specification,
Figure FDA0002925871350000035
is to utilize
Figure FDA0002925871350000036
Calculating to obtain XkThe one-step prediction is carried out;
the state estimation equation:
Figure FDA0002925871350000037
Figure FDA0002925871350000038
is predicted in one step
Figure FDA0002925871350000039
Based on the measured value, the true value X is measuredkIs estimated, where KkIs the filter gain;
kalman gain equation:
Figure FDA00029258713500000310
in the formula, Pk|k-1Predicting the mean square error for one step; rkA variance matrix for the measured noise;
one-step prediction mean square error equation:
Figure FDA0002925871350000041
mean square error estimation equation:
Figure FDA0002925871350000042
in the formula, Pk|kTo estimate the value
Figure FDA0002925871350000043
The estimated mean square error equation of (a);
the position information representing the inertial navigation system is
Figure FDA0002925871350000044
In the formula ofI、LI、HIAs a measure of latitude, longitude, altitude, λ, of the inertial navigation systemt、Lt、HtThe latitude, longitude and altitude of the vehicle-mounted device are true values, and the delta lambda, delta L and delta H are measurement error values of the latitude, longitude and altitude of the inertial navigation system;
the velocity information representing the inertial navigation system is
Figure FDA0002925871350000045
In the formula vIN、vIE、vIUIs a measure of the velocity of the inertial navigation system in the northeast direction, vN、vE、vUIs the true value of the speed of the vehicle-mounted device in the northeast direction, delta vN、δvE、δvUMeasuring error value of the velocity of the inertial navigation system in the northeast direction;
the position information of the satellite navigation system is
Figure FDA0002925871350000046
In the formula ofG、LG、HGAs a measure of the satellite navigation system latitude, longitude, altitude, lambdat、Lt、HtIs the true value of latitude, longitude and altitude of the vehicle-mounted device, NE、NN、NUMeasuring error values of the satellite navigation system in the northeast direction;
the velocity information representing the satellite navigation system is
Figure FDA0002925871350000051
In the formula vGE、vGN、vGUAs a measure of the velocity of the satellite navigation system in the northeast direction, vN、vE、vUIs the true value of the speed of the vehicle-mounted device in the northeast direction, MN、ME、MUMeasuring error value of the velocity of the inertial navigation system in the northeast direction; the position measurement value N and the speed measurement value M are converted in order to be matched with the longitude and latitude dimensions of the inertial navigation system;
the speed information indicating the odometer is
Figure FDA0002925871350000052
In the formula vOE、vON、vOUAs a measure of the velocity of the odometer in the northeast direction, vN、vE、vUIs the true value of the speed of the vehicle-mounted device in the northeast direction, ON、OE、OUThe measurement error value of the speed of the odometer in the northeast direction is shown;
the altitude information indicating the altimeter is
Ha＝HU-A (23)
In the formula HaAs a measure of the height of the altimeter, HUThe altitude measurement error value A is a true value of the position of the vehicle-mounted device in the vertical direction, and A is a measurement error value of the altimeter in the altitude;
(2.2.1) design of SINS/BDS sub-filter
According to the equation of state of the known SINS/BDS sub-filter of (2.1) is
Figure FDA0002925871350000053
Measuring method of SINS/BDS sub-filter
Figure FDA0002925871350000054
Wherein
Figure FDA0002925871350000061
VG(t)＝[NN NE NU ME MN MU]T (27)
The measured noise is treated as white noise, and its variance is respectively
Figure FDA0002925871350000062
RM、RNThe long radius and the short radius of the earth, respectively;
(2.2.2) design of SINS/odometer sub-filter
According to (2.1), the state equation of the SINS/BDS sub-filter is
Figure FDA0002925871350000063
The measurement equation of the SINS/odometer sub-filter is as follows
Figure FDA0002925871350000064
Wherein
HO(t)＝[03×3 diag[1 1 1] 03×12] (30)
VG(t)＝[OE ON OU]T (31)
Measuring the white noise with the average value of 0;
(2.2.3) design of Federal Filter Main Filter
The federal filter is a two-stage filter structure, and the output X of a common reference subsystem (SINS)kOn the one hand, the main filter and on the other hand, each sub-filter is used as a measurement value; the outputs of the sub-systems being supplied only to the respective filters, the local estimated values X of the sub-filtersiAnd its covariance matrix PiThe estimated values sent into the main filter and the main filter are fused together to obtain a global estimated value;
global optimum estimation synthesized by main filter and sub-filter
Figure FDA0002925871350000065
And corresponding covariance matrix PgIs amplified into
Figure FDA0002925871350000066
And then feeding back to the sub-filter to reset the estimation value of the sub-filter, namely:
Figure FDA0002925871350000067
the main filter has a covariance matrix of
Figure FDA0002925871350000068
βiDetermined according to the information distribution principle.
3. The vector distribution-based adaptive multi-source fusion navigation method according to claim 2, wherein the method for detecting and isolating faults by vector distribution in step 2 is designed to detect and isolate information of fault dimensions of each sensor, and specifically comprises the following steps:
(3.1) sub-filter time update:
Figure FDA0002925871350000071
wherein i represents the ith sub-filter;
(3.2) fault diagnosis:
the following fault diagnosis functions are first constructed:
Λi,k＝ri,k(ri,k)T[Hi,kPi,k|k-1(Hi,k)T+Ri,k]-1 (33)
Figure FDA0002925871350000072
wherein r isi,kRepresenting the residual of system i at time k, Λi,kIs a matrix of m rows and m columns, represented as:
Figure FDA0002925871350000073
when no fault occurs in the sub-filter, Λi,kEach element on the diagonal in the array should obey x with degree of freedom of 12Distribution, when a sensor in the system fails, the sensor no longer meets the requirement, at the moment, a threshold value is set, and the following judgment rule is established:
Figure FDA0002925871350000074
defining the measured noise coefficient B of the ith sub-filteri,kComprises the following steps:
Figure FDA0002925871350000075
wherein
Figure FDA0002925871350000076
By obtaining a measured noise figure Bi,kReconstructing the measured noise matrix
Figure FDA0002925871350000077
Figure FDA0002925871350000081
In equation (37), when a dimension of the measurement information is determined to be normal, Bi,kThe corresponding diagonal element is set to 1, otherwise to 0, thus reconstructing the metric noise matrix in equation (39)
Figure FDA0002925871350000082
For normal measurement variables, the corresponding noise variance after adjustment is unchanged; for the fault measurement variable, the corresponding noise variance after adjustment tends to be infinite, and the dynamic isolation of the dimension information of the sensor fault is realized;
(3.3) sub-filter measurement update
Figure FDA0002925871350000083
And after the sub-filters perform measurement updating, transmitting the filtering result of the fault dimension information of the isolation sensor to the main filter for the next step of information fusion.
4. The vector distribution-based adaptive multi-source fusion navigation method according to claim 3, wherein in step 3, vector distribution coefficients are constructed for each dimension of information of each sub-filter by using output results of each sub-filter, and information fusion is performed in a main filter to obtain a global optimal estimation result, specifically as follows:
first, a sub-filter covariance matrix Pi,k|kAnd (3) carrying out characteristic value decomposition:
Pi,k|k＝Di,kΛi,k(Di,k)T (41)
in the formula
Figure FDA0002925871350000084
Wherein λn,i,kIs the ith sub-filter covariance matrix Pi,k|kN characteristic value of (D)i,kIs an orthogonal matrix resulting from eigenvalue decomposition; defining a distribution coefficient matrix Ai,kComprises the following steps:
Figure FDA0002925871350000091
in the formula
Figure FDA0002925871350000092
Ai,kSatisfy the theorem of information conservation
Figure FDA0002925871350000093
Constructing an allocation coefficient matrix C by the observability of sub-filtersi,kLet us assume that the observability matrix of the sub-filter i is Qi,kTo Q, pairi,kPerforming singular value decomposition
Qi,k＝Ui,kSi,k(Vi,k)T (46)
Wherein U isi,kAnd Vi,kIs an orthogonal matrix, Si,kThe method specifically comprises the following steps:
Figure FDA0002925871350000094
wherein
Figure FDA0002925871350000097
σn,i,k(n＝1,2,…ri)，riAre respectively Qi,kSingular value and rank of;
then measure the coefficient Ci,kIs defined as:
Figure FDA0002925871350000095
wherein
Figure FDA0002925871350000096
Ci,kSatisfy the theorem of information conservation
Figure FDA0002925871350000101
Then the vector-based information assigns coefficient Bi,kComprises the following steps:
Figure FDA0002925871350000102
at the moment, the information distribution coefficient still meets the information conservation principle:
Figure FDA0002925871350000103
in order to ensure the symmetry of the error covariance matrix, the information distribution mode is as follows:
Figure FDA0002925871350000104
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