《Improved Kalman Filter Algorithm of GPS》由会员分享，可在线阅读，更多相关《Improved Kalman Filter Algorithm of GPS（8页珍藏版）》请在金锄头文库上搜索。
1、Improved Kalman Filter Algorithm of GPS/INS Integrated Navigation without GPS SignalZHU Lixin1, MENG Yan2(1.Electronic Engineering Institute of PLA, Anhui 230037,China)(2.No.72671 Unit of PLA, Jinan 250022,China)Abstract: To solve the problems that the navigation accuracy of GPS/INS(Global Positioni
2、ng System/Inertial Navigation System) tightly integrated navigation system is lower under GPS signal invalidation circumstances, and the model error and calculation error exists in the application of CKF(Cubature Kalman Filter), a strong tracking SRCKF(Square-Root CKF) is proposed under the backgrou
3、nd. By stressing the function of new data artificially, the algorithm improves the robustness when the model is uncertain, and the square-root strategy ensures the positive definiteness and symmetry of covariance matrix. Simulation results show that the improved algorithm can improve the navigation
4、accuracy and the ability of adapting to the complex environment, and have better efficiency under GPS signal invalidation circumstances.Key words: GPS/INS tightly integrated navigation, CKF, strong tracking filter, square-root strategy, navigation accuracy1. IntroductionThe navigation accuracy of GP
5、S/INS integrated navigation system overcoming the respective defects is higher than the accuracy of the two systems working separately. When the receiver is under the great angle motion and the complex circumstances of the city and the valley, satellite signals are disturbed and shielded easily. On
6、the situation, observations provided by GPS/INS tightly integration utilizing less than 4 satellites in the measurement of pseudorange and pseudorange rate leads to integrated model working well.Considering the nonlinear characteristic of GPS/INS tightly integrated navigation model, a hybrid linear/
7、nonlinear model based on linear state equation and nonlinear measurement equation is proposed. EKF(Extend Kalman filter) and UKF(Unscented Kalman filter) are classical nonlinear filters. EKF expanding the nonlinear equation by the Taylor series up to the first order approximates the original equatio
8、n. To some extent, although EKF can solve the problem of nonlinear state estimation, it has some disadvantages obviously. First, due to the lack of high order terms, it can induce truncation error having a bad influence on the estimation accuracy. Second, its difficult to compute the Jacobian matrix
9、 when the nonlinear degree is high. The computation of UKF is similar to EKFs and the property of UKF is better than that of EKF. Additionally, UKF dont need to compute the Jacobian matrix, which is expanded continuously in the field of application. However, in the process of recursive filtering, UK
10、F needs to do the matrix decomposition and the inverse matrix, which is difficult to ensure the positive definiteness of covariance matrix.From the above problems, This paper proposes the CKF algorithm based on the strong tracking filter theory and the square-root strategy under GPS/INS tightly inte
11、grated navigation signal invalidation circumstances.2. GPS/INS tightly integrated modelUnder normal circumstances, the characteristic of tightly integration which is integrated in depth is that the GPS receiver and the inertial navigation system work together. We calculate the pseudorange and pseudo
12、range rate by utilizing the data of satellite ephemeris given by the GPS receiver and the position and velocity given by the inertial navigation system. Compared and with and given by the GPS receiver, the results are observations. Two system is adjusted by the error of the GPS receiver and the iner
13、tial navigation system estimated by the integrated Kalman filter. Work diagram is shown as Fig.1.2.1 State equationThe error state variable of GPS is 2-dimensional . The error of INS consisting of platform error angles(3D), velocity errors(3D), position errors(3D), INS component errors(9D) is 18 dim
14、ension. The state equation of GPS/INS integrated navigation system can be written as (1)i.e. (2)where (3)are attitude errors, velocity errors, position errors, gyro drift errors(constant offset and random offset ), accelerometer errors, GPS clock correction equivalent distance and equivalent distanc
15、e rates respectively. are state transition matrices, noise coefficient matrices and noise vectors respectively. Specifically, its shown in literature 6.2.2 Measurement equationAssume that the position given by INS in the geodetic coordinate system denotes longitude , latitude and altitude , then the
16、 actual position of carrier,which is transformed into ECEF(earth-centered earth-fixed) coordinate system as follows (4)then the actual distance between the satellite and the carrier is (5)the pseudorange of between the GPS receiver and the satellite is (6)i.e. (7)Substituting x,y,z into the above equation yields(8)Similarly, the pseudorange is (9)Substituting into (9) yields (1
