CN103344260A  Initial alignment method of large azimuth misalignment angle of strapdown inertial navigation system based on RBCKF (raoblackwellised cubature kalman filter)  Google Patents
Initial alignment method of large azimuth misalignment angle of strapdown inertial navigation system based on RBCKF (raoblackwellised cubature kalman filter) Download PDFInfo
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 CN103344260A CN103344260A CN2013103027603A CN201310302760A CN103344260A CN 103344260 A CN103344260 A CN 103344260A CN 2013103027603 A CN2013103027603 A CN 2013103027603A CN 201310302760 A CN201310302760 A CN 201310302760A CN 103344260 A CN103344260 A CN 103344260A
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Abstract
Description
Technical field
The present invention relates to strapdown inertial navitation system (SINS) Initial Alignment of Large Azimuth Misalignment On method.
Background technology
The purpose of filtering (being state estimation) is according to certain method and criterion, goes a process of estimated state vector by the measurement amount that contains noise.Classic card Kalman Filtering from the beginning is various forms of nonlinear filterings till now, and through the development of nearly decades, filtering technique has become the focus of all trades and professions research.For filtering, stability, precision and speed of convergence are the problems that people generally are concerned about.
Strapdown inertial navitation system (SINS) (English full name: Strapdown inertial navigation system, be called for short SINS), inertial navigation mainly is by utilizing inertial sensor spare (comprising gyroscope and accelerometer) to measure carrier with respect to angular motion and the line motion of inertial space, and according to known starting condition, utilize machine solution to calculate navigational parameters such as the current velocity information of carrier, positional information and attitude information, further realize the navigational duty of carrier expection.
And for strapdown inertial navigation system, all inertial measurement component all directly are fixed on the carrier, the output data of inertial measurement component are angular velocity and the acceleration in carrier relative inertness space, be transformed under the navigation coordinate system by computing machine again and carry out navigation calculation, this process is equivalent to virtual platform in computing machine, to be used as the reference of navigation calculation.Stable platform in the effect of this virtual platform and the platform inertial navigation system is similar, and we are referred to as " mathematical platform ".For SINS itself, the precision of initial alignment and speed play a part very important for the SINS navigation procedure.Because the model of SINS initial alignment itself has nonlinear feature, therefore, adopt rational nonlinear filtering method according to concrete requirement.
Use on the engineering the earliest and the most widely nonlinear filtering method surely belong to EKF (Extend Kalman Filter, EKF).Its core concept is carried out linearization to nonlinear model at point of fixity exactly.But when system nonlinear strong, this filtering method precision is lower, and disperses easily.Even when system was discontinuous, EKF filtering just can't be used.Based on the viewpoint of " be similar to probability distribution will to compare nonlinear function approximate a lot of easily ", Julier and Uhlmann proposed Unscented kalman filtering (Unscented Kalman Filter, UKF).It approaches through obeying average and the variance of gauss' condition distribution variable by deterministic Sigma point.(Cubature Kalman Filter CKF) is at first put forward by Ienkaran Arasaratnam and Simon Haykin the volume Kalman filtering.Its core concept is the Cubature conversion, namely waits the Cubature point of weights the variable of the Gaussian distributed after the nonlinear transformation to be carried out the calculating of average and variance by choosing 2n.CKF filtering is to derive according to SphericalRadical Cubature criterion, compare with UKF have better stability, higher precision.From filtering method, CKF is a kind of special circumstances of UKF.But adopting of CKF counted less, calculated amount is little, and filtering accuracy also is better than UKF.The Cubature conversion that head and the tail are linked to each other in turn is applied to and has just produced CKF filtering on the Gaussian filter, and CKF filtering is all to have at state equation and measurement equation to propose when nonlinear at first.
Summary of the invention
The present invention is when wanting resolution system nonlinear strong, the filtering method precision is lower, and disperses easily, even when system is discontinuous, the problem that EKF filtering just can't be used, and strapdown inertial navitation system (SINS) Initial Alignment of Large Azimuth Misalignment On method based on RBCKF is provided.
Strapdown inertial navitation system (SINS) Initial Alignment of Large Azimuth Misalignment On method based on RBCKF realizes according to the following steps:
Step 1, according to the error characteristics of strapdown inertial navitation system (SINS), set up the error model of Initial Alignment of Large Azimuth Misalignment On, i.e. state equation and measurement equation;
Step 2, choose the filtering initial value:
Order With Wherein, x _{0}Be the initial value of state variable, P _{0}Initial error covariance matrix for state variable;
Step 3, according to the average of the state variable of current time
With state error covariance matrix P
_{Kk1}Calculate the Cubature point set:
Wherein, Be the onestep prediction of the k1 moment to k moment state variable average, P _{Kk1}Be the onestep prediction of the k1 moment to k moment state error covariance matrix; And P _{Kk1}Calculating all add up through state equation nonlinear propagation rear weight by k1 Cubature point constantly and obtain, the weights of each point are 1/2n, n is the dimension of system state variables;
Step 4, under state equation is nonlinear, that measurement equation is linear condition, the time of carrying out state variable and measuring variable upgrades;
Step 5, renewal error covariance matrix
Make k=k+1, continue to carry out from step 3, namely finished the strapdown inertial navitation system (SINS) Initial Alignment of Large Azimuth Misalignment On method based on RBCKF.
The invention effect:
Concrete error model at the big misalignment initial alignment of SINS has proposed a kind of filtering method, namely marginalisation volume Kalman filtering (RaoBlackwellised Cubature Kalman Filter, RBCKF).When state equation and measurement equation all have when nonlinear, traditional CKF is a kind of very outstanding nonlinear filtering method.But the state equation of the big misalignment initial alignment of SINS has nonlinear, and measurement equation has linear characteristics, therefore can CKF be improved, and namely state equation is adopted the Cubature conversion, and measurement equation is taked linear the renewal.Owing to no matter carry out Cubature conversion or linear transformation for linear model, the precision after the conversion is identical.Therefore, RBCKF can reduce the time of SINS initial alignment when not losing filtering accuracy.
The basis of CKF filtering is the Cubature conversion, and this conversion can be regarded the Nonlinear Mapping of different dimension linear space as.It approaches average and the variance of variable after the conversion by taking some fixed points.Because SINS is when Initial Alignment of Large Azimuth Misalignment On, state equation has nonlinear and measurement equation has linear characteristics.Therefore, can carry out certain improvement to CKF, make under the constant condition of filtering accuracy, shorten the time of aiming at.
One, the present invention compares traditional CKF and does not lose precision of filtering;
Two, technology of the present invention is compared the time that CKF can shorten SINS initial alignment under big orientation misalignment;
Three, to go for any state equation be nonlinear to technology of the present invention and measurement equation is linear Filtering Model.
Description of drawings
Fig. 1 is process flow diagram of the present invention;
Fig. 2 is the schematic diagram of RBCKF in the embodiment one;
Fig. 3 is the schematic diagram of SINS initial alignment in the embodiment one;
Fig. 4 is the rolling misalignment graph of errors in the lG simulation test; Wherein,expression CKF estimates thatexpression RBCKF estimates;
Fig. 5 is the pitching misalignment graph of errors in the lG simulation test; Wherein,expression CKF estimates thatexpression RBCKF estimates;
Fig. 6 is the course misalignment graph of errors in the lG simulation test; Wherein,expression CKF estimates thatexpression RBCKF estimates;
Fig. 7 is the course misalignment steadystate error curve in the lG simulation test; Wherein,expression CKF estimates thatexpression RBCKF estimates.
Embodiment
Embodiment one: the strapdown inertial navitation system (SINS) Initial Alignment of Large Azimuth Misalignment On method based on RBCKF of present embodiment realizes according to the following steps:
Step 1, according to the error characteristics of strapdown inertial navitation system (SINS), set up the error model of Initial Alignment of Large Azimuth Misalignment On, i.e. state equation and measurement equation;
Step 2, choose the filtering initial value:
Order With Wherein, x _{0}Be the initial value of state variable, P _{0}Initial error covariance matrix for state variable;
Step 3, according to the average of the state variable of current time
With state error covariance matrix P
_{Kk1}Calculate the Cubature point set:
Wherein, Be the onestep prediction of the k1 moment to k moment state variable average, P _{Kk1}Be the onestep prediction of the k1 moment to k moment state error covariance matrix; And P _{Kk1}Calculating all add up through state equation nonlinear propagation rear weight by k1 Cubature point constantly and obtain, the weights of each point are 1/2n, n is the dimension of system state variables;
Step 4, under state equation is nonlinear, that measurement equation is linear condition, the time of carrying out state variable and measuring variable upgrades;
Step 5, renewal error covariance matrix
Make k=k+1, continue to carry out from step 3, namely finished the strapdown inertial navitation system (SINS) Initial Alignment of Large Azimuth Misalignment On method based on RBCKF.
In the present embodiment, in the described step 2, because the statespace expression of SINS Initial Alignment of Large Azimuth Misalignment On is fully controlled and observable, and system can regard uniformly stable as, therefore, choosing of filtering starting condition generally can not influence the precision that filtering restrains;
In the step 5, owing to for linear equation, no matter be Cubature conversion or linear transformation, the precision after the conversion is identical.Therefore, RBCKF is identical with the filtering accuracy of CKF.But on calculated amount, when calculating measurement average, variance and simple crosscorrelation covariance, RBCKF does not but adopt 2n Cubature point again and carries out computings such as nonlinear transformation and square root decomposition, thereby has saved running time of algorithm.Simultaneously, from
As seen, the RBCKF filtering algorithm is applied in the SINS Initial Alignment of Large Azimuth Misalignment On, can when not losing filtering accuracy, shortens the time of aiming at greatly.
The present embodiment effect:
Concrete error model at the big misalignment initial alignment of SINS has proposed a kind of filtering method, namely marginalisation volume Kalman filtering (RaoBlackwellised Cubature Kalman Filter, RBCKF).When state equation and measurement equation all have when nonlinear, traditional CKF is a kind of very outstanding nonlinear filtering method.But the state equation of the big misalignment initial alignment of SINS has nonlinear, and measurement equation has linear characteristics, therefore can CKF be improved, and namely state equation is adopted the Cubature conversion, and measurement equation is taked linear the renewal.Owing to no matter carry out Cubature conversion or linear transformation for linear model, the precision after the conversion is identical.Therefore, RBCKF can reduce the time of SINS initial alignment when not losing filtering accuracy.
The basis of CKF filtering is the Cubature conversion, and this conversion can be regarded the Nonlinear Mapping of different dimension linear space as.It approaches average and the variance of variable after the conversion by taking some fixed points.Because SINS is when Initial Alignment of Large Azimuth Misalignment On, state equation has nonlinear and measurement equation has linear characteristics.Therefore, can carry out certain improvement to CKF, make under the constant condition of filtering accuracy, shorten the time of aiming at.
One, present embodiment is compared traditional CKF and is not lost precision of filtering;
Two, the technology of present embodiment is compared the time that CKF can shorten SINS initial alignment under big orientation misalignment;
Three, to go for any state equation be nonlinear to the technology of present embodiment and measurement equation is linear Filtering Model.
Embodiment two: what present embodiment and embodiment one were different is: the error model of setting up Initial Alignment of Large Azimuth Misalignment On in the step 1 is specially:
Choose the velocity error of east orientation, north orientation in the general quiet pedestal Initial Alignment of Large Azimuth Misalignment On And the misalignment φ in three orientation _{x}, φ _{y}And φ _{z}Be state variable, namely Therefore, the state equation of its quiet pedestal initial alignment is as follows:
Wherein, Be local latitude; ω _{Ie}Be rotationalangular velocity of the earth; With Be three axial gyroscopic drifts; With Be that three axial acceleration zero are inclined to one side; f _{x}, f _{y}And f _{z}For the ratio output valve of accelerometer is being calculated projection in the Department of Geography; C _{Ij}Be that carrier is tied to the element in the direction matrix of Department of Geography; C ' _{Ij}Be that carrier is tied to the element that calculates in Department of Geography's matrix;
Choose east orientation and north orientation velocity error Be semblance measure, the measurement equation of strapdown inertial navitation system (SINS) initial alignment is: Z=HX+V
Wherein, H gets H=[I _{2 * 2}0 _{2 * 3}]; V is measurement noise.Other step and parameter are identical with embodiment one.
Embodiment three: what present embodiment was different with embodiment one or two is: calculate the Cubature point set in the step 3 and be specially:
The error covariance matrix is carried out square root decompose, choose the Cubature point set then, namely
Embodiment four: what present embodiment was different with one of embodiment one to three is: the time renewal of carrying out state variable and measurement variable in the step 4 is specially: in the strapdown inertial navitation system (SINS) Initial Alignment of Large Azimuth Misalignment On, state equation is nonlinear and measurement equation is linear, and concrete mathematic(al) representation is as follows:
Time for state variable upgrades, and will calculate the onestep prediction average of state variable after the process of the Cubature point set in the step 3 nonlinear transformation of state equation , and the time of measurement amount upgrades not through the Cubature conversion but directly carries out the onestep prediction average that the linear transformation calculated amount is measured , detailed process is as shown in the formula calculating:
Embodiment five: what present embodiment was different with one of embodiment one to four is: step 5 is upgraded the error covariance matrix and is specially:
When the measurement of carrying out filtering is upgraded, need the error covariance matrix P of computing mode variable _{Kk1}, the error covariance matrix of measurement variable And simple crosscorrelation covariance matrix Then these variablees are applied on the Gaussian filter, have just formed the RBCKF filtering algorithm;
Step May Day: in RBCKF, the error covariance matrix P of state variable _{Kk1}Calculating identical with the computing method of traditional CKF, still need to calculate by the Cubature point set, and will include the influence of statenoise in, concrete meter
Calculate formula as
Measure the error covariance matrix of variable And simple crosscorrelation covariance matrix Calculating different with traditional CKF, Be directly to upgrade by linear equation, Need carry out the fusion of nonlinear equation and linear equation, it is as follows specifically to derive:
Step 5 two: will And Be reapplied under the Gaussian filter, just produced RBCKF, the general type of Gaussian filter is as follows:
Step 5 three: compare CKF, RBCKF can shorten the convergence time of filtering greatly when not losing filtering accuracy, specifically be compared as follows:
Suppose that measurement equation is: Z _{k}=H _{k}X _{k}+ V _{k}(wherein, H _{k}Matrix for m * n) from whole filtering algorithm, RBCKF and CKF are just calculating the measurement average Measure variance And simple crosscorrelation covariance matrix The time exist difference, in traditional C KF, this computing formula of three is as follows:
Other step and parameter are identical with one of embodiment one to four.
Verify by following lG simulation test:
Before the SINS initial alignment, choose the initial value x (0)=0 of state variable; Initial east orientation, north orientation and sky are set at respectively to misalignment: first group: φ _{E}=φ _{N}=0.5 ^{0}, φ _{U}=10 ^{0}Second group: φ _{E}=φ _{N}=0.5 ^{0}, φ _{U}=15 ^{0}The 3rd group: φ _{E}=φ _{N}=0.5 ^{0}, φ _{U}=20 ^{0}Calculate according to the medium accuracy gyro, the constant value drift of supposing gyro is 0.1 ^{0}/ h, random drift is 0.05 ^{0}/ h; The zero drift of accelerometer is 1.0 * 10 ^{4}M/s ^{2}, random deviation is 0.5 * 10 ^{4}G;
Filtering parameter is set as follows:
The initial error covariance matrix of state variable x is P _{0}=diag{ (0.1m/s) ^{2}(0.1m/s) ^{2}(0.5 ^{0}) ^{2}(0.5 ^{0}) ^{2}(10 ^{0}) ^{2}; The random drift of degree of will speed up meter random deviation and gyro is designated as process noise, and then the noise error covariance matrix of state equation is Q=diag{ (50ug) ^{2}(50ug) ^{2}(0.05 ^{0}/ h) ^{2}(0.05 ^{0}/ h) ^{2}(0.05 ^{0}/ h) ^{2}; Simultaneously, the noise error covariance matrix of measurement equation is designated as R=diag{ (0.1m/s) ^{2}(0.1m/s) ^{2}.The filtering algorithm of CKF and RBCKF is as shown in table 1 working time under the different azimuth misalignment:
The operation time of CKF and RBCKF under the different initial orientation misalignments of table 1
Provided the working time of two kinds of filtering algorithms under the different big orientation misalignment in the table 1.Because measurement equation is linear, RBCKF has adopted the mode of linear renewal when upgrading in the time, compares the mode that 2n point adopted in traditional C KF filtering, and the calculated amount of RBCKF is little.Therefore, under identical orientation misalignment, the working time of RBCKF is always less than working time of traditional CKF filtering.That is to say that RBCKF can improve the alignment speed of inertial navigation initial alignment.
Fig. 4～7 have provided at φ _{x}=φ _{y}=0.5 ^{0}, φ _{z}=10 ^{0}The estimation misalignment graph of errors in following rolling, pitching and course.
Because it is wideangle that initial misalignment has only the orientation misalignment, and horizontal misalignment is lowangle.Therefore, Fig. 7 has provided the steadystate error curve map of orientation misalignment error.
As can be seen from Figure 7 CKF is identical for course misalignment steadystate error value with RBCKF, is3.588'.Therefore, the filtering accuracy of two kinds of filtering methods is identical.
To sum up, the RBCKF filtering algorithm is than traditional C KF filtering algorithm, and precision of filtering is identical, but from algorithm on working time, and the working time of RBCKF is always less than working time of traditional C KF under identical big orientation misalignment.Therefore, RBCKF can help to shorten the time that strapdown inertial navitation system (SINS) is aimed at when not losing filtering accuracy.
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Cited By (12)
Publication number  Priority date  Publication date  Assignee  Title 

CN103575298A (en) *  20131114  20140212  哈尔滨工程大学  Selfregulationbased unscented Kalman filter (UKF) misalignment angle initialalignment method 
CN103727940A (en) *  20140115  20140416  东南大学  Gravity acceleration vector fittingbased nonlinear initial alignment method 
CN103727941A (en) *  20140106  20140416  东南大学  Volume kalman nonlinear integrated navigation method based on carrier system speed matching 
CN103791918A (en) *  20140210  20140514  哈尔滨工程大学  Polar region moving base alignment method for naval vessel strapdown inertial navigation system 
CN104374401A (en) *  20141015  20150225  哈尔滨工程大学  Compensating method of gravity disturbance in strapdown inertial navigation initial alignment 
CN104374405A (en) *  20141106  20150225  哈尔滨工程大学  MEMS strapdown inertial navigation initial alignment method based on adaptive central difference Kalman filtering 
CN104567871A (en) *  20150112  20150429  哈尔滨工程大学  Quaternion Kalman filtering attitude estimation method based on geomagnetic gradient tensor 
CN105004351A (en) *  20150514  20151028  东南大学  SINS largeazimuth misalignment angle initial alignment method based on selfadaptation UPF 
CN105180968A (en) *  20150902  20151223  北京天航华创科技股份有限公司  IMU/magnetometer installation misalignment angle online filter calibration method 
CN105806363A (en) *  20151116  20160727  东南大学  Alignment method of an underwater large misalignment angle based on SINS (Strapdown Inertial Navigation System)/DVL (Doppler Velocity Log) of SRQKF (Squareroot Quadrature Kalman Filter) 
CN106123921A (en) *  20160710  20161116  北京工业大学  Latitude the unknown Alignment Method of SINS under the conditions of dynamic disturbance 
CN106840194A (en) *  20160920  20170613  南京喂啊游通信科技有限公司  A kind of Large azimuth angle linear alignment method 
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Cited By (18)
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CN103575298A (en) *  20131114  20140212  哈尔滨工程大学  Selfregulationbased unscented Kalman filter (UKF) misalignment angle initialalignment method 
CN103727941A (en) *  20140106  20140416  东南大学  Volume kalman nonlinear integrated navigation method based on carrier system speed matching 
CN103727940A (en) *  20140115  20140416  东南大学  Gravity acceleration vector fittingbased nonlinear initial alignment method 
CN103727940B (en) *  20140115  20160504  东南大学  Nonlinear initial alignment method based on acceleration of gravity vector matching 
CN103791918A (en) *  20140210  20140514  哈尔滨工程大学  Polar region moving base alignment method for naval vessel strapdown inertial navigation system 
CN104374401A (en) *  20141015  20150225  哈尔滨工程大学  Compensating method of gravity disturbance in strapdown inertial navigation initial alignment 
CN104374405A (en) *  20141106  20150225  哈尔滨工程大学  MEMS strapdown inertial navigation initial alignment method based on adaptive central difference Kalman filtering 
CN104567871B (en) *  20150112  20180724  哈尔滨工程大学  A kind of quaternary number Kalman filtering Attitude estimation method based on earth magnetism gradient tensor 
CN104567871A (en) *  20150112  20150429  哈尔滨工程大学  Quaternion Kalman filtering attitude estimation method based on geomagnetic gradient tensor 
CN105004351A (en) *  20150514  20151028  东南大学  SINS largeazimuth misalignment angle initial alignment method based on selfadaptation UPF 
CN105180968A (en) *  20150902  20151223  北京天航华创科技股份有限公司  IMU/magnetometer installation misalignment angle online filter calibration method 
CN105180968B (en) *  20150902  20180601  北京天航华创科技股份有限公司  A kind of IMU/ magnetometers installation misalignment filters scaling method online 
CN105806363A (en) *  20151116  20160727  东南大学  Alignment method of an underwater large misalignment angle based on SINS (Strapdown Inertial Navigation System)/DVL (Doppler Velocity Log) of SRQKF (Squareroot Quadrature Kalman Filter) 
CN105806363B (en) *  20151116  20180821  东南大学  The underwater large misalignment angle alignment methods of SINS/DVL based on SRQKF 
CN106123921A (en) *  20160710  20161116  北京工业大学  Latitude the unknown Alignment Method of SINS under the conditions of dynamic disturbance 
CN106123921B (en) *  20160710  20190524  北京工业大学  The unknown Alignment Method of the latitude of Strapdown Inertial Navigation System under the conditions of dynamic disturbance 
CN106840194A (en) *  20160920  20170613  南京喂啊游通信科技有限公司  A kind of Large azimuth angle linear alignment method 
CN106840194B (en) *  20160920  20190927  南京喂啊游通信科技有限公司  A kind of Large azimuth angle linear alignment method 
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