Kalman Filtering Method for GNSS / INS Integrated Navigation

Transcription

1 2016 nternational Conference on Electrical Engineering and Automation (CEEA 2016) SBN: Kalman Filtering Method for GNSS / NS ntegrated Navigation Qiang J * and Hao-guang ZHAO College of Aerospace Science and Engineering, National University of Defense echnology, Changsha , China *Corresponding author Keywords: nertial navigation system, Global navigation satellite system, Filter, Error model. Abstract. According to the GPS positioning principle and the main sources of error, the GNSS error model is analyzed and established. he positioning principle of the inertial navigation system is introduced. he solving process of strap down inertial navigation system using quaternion method is described in detail. he error model of inertial navigation system is deduced. Based on the inertial navigation error model, the state equation and observation equation of the combined system are analyzed and analyzed, and the selection of the observation equation is analyzed. Finally, the alternating observation equations of the position and velocity are determined. he traditional Kalman filter is compared with the Kalman filter which introduces the outlier processing. he normal observation is not affected, and there is an excellent detection and suppression for the single outliers and the outliers. Effect, greatly enhanced the stability of the integrated navigation system, significantly improve the anti-poor results. ntroduction With the navigation and positioning accuracy requirements continue to improve, a single navigation method has been unable to meet the demand. nertial navigation system (NS) / GNSS (ntegrated Navigation Systems) (GNSS) integrated navigation system combines the advantages of different systems, more than a single way it will become a better choice. By applying the optimal estimation theory and combining the multiple navigation methods to realize the information fusion of subsystems, a more accurate navigation system can be obtained. Especially in the past two decades, GNSS / NS integrated navigation system has become popular, has become an important direction of navigation research. n the combined system, GPS can provide a long time to stabilize the signal to compensate for the cumulative error NS shortcomings, and NS can provide low-noise, short-term accurate continuous navigation data. t is the key to the design and implementation of the integrated navigation system to synthesize the data of the navigation subsystem by choosing the optimal optimal filtering method. Kalman filter (KF) is the most mature information fusion and filtering method in navigation field at present. Kalman filtering is optimal in the sense of unbiased, consistent and asymptotically efficient for linear systems where the process noise and the observed noise are white noise sequences. ntegrated Navigation Model of GNSS/NS ntegrated navigation system consists of three parts: GNSS receiver module, NS module and the combination of filtering module. ntegrated navigation system block diagram is as follows

2 nertial Sensors NS Navigation Calculation NS Parameters + + Navigation information Adjust Kalman Filter F Siganl Processing racking Loop GNSS Kalman filter Position, Velocity GPS eceiver Feedback Figure 1. Block diagram of integrated navigation system. he difference between the position and velocity estimation information of the output of NS and GNSS is obtained, and input to the navigation filter (usually Kalman filter). After filtering, the error estimation value is obtained and fed back to the NS, so that each measurement After updating the NS to carry out feedback correction or output correction, through the GNSS data to improve the accuracy of NS. According to the principle of position and velocity combination, the error of GPS can be taken as measurement noise. herefore, the equation of state of the combined system is the same as the error equation of NS system. x Fx W (1) Let, L, h are the true longitude, latitude and altitude of the carrier; is the longitude of the NS with error, L is the latitude of the NS output with L errors, and h is the height of the NS with error h. he location information obtained by the NS can be expressed as L L L h h h Let G, L G, and h G be the GNSS output position information; N, N and N Gy Gz are the error distances measured by the GNSS in the east, GPS location information can be expressed as NGy G M h N LG L (3) ( N h)cosl hg h Nh aking the difference between the NS and the GPS output as the observed quantity, we can get the observation equation (2) ( L )( ) ( ) LG M h M h LNGy yp ( G)( N h)cos L ( Nh)cos LN h h G hn Gz Can also be expressed as y H xv p p p (4) (5)

3 where, V is treated as white noise, and p p 36 M N 36 H [ O diag ( h) ( h)cosl 1 O ] (6) Vp N NGy N Gz (7) Suppose that v x, v and v y z are the velocity of the carrier in east, north and sky respectively. v x, v, and v y z are the speed values of the NS output with errors vx, v, and v y z, respectively vx vx v x vy vy vy vz vz vz (8) v Suppose vgy, v and Gz are the velocity information obtained by GNSS in east, north and sky respectively. N vx N, vy and Nvz are the velocity errors of the east, north, and sky upward GNSS measurements, respectively. he GPS velocity information can be expressed as v vx N vx vgy vy Nvy (9) vgz vz Nvz aking the error of the velocity of the NS and GPS output in each direction as the observation, the following observation equation can be obtained vx v v x Nvy yv vy vgy vy Nvy v v v N z Gz z vz y HxV v v v (10) (11) Hv diag O (12) Vv N NGy N Gz (13) V where v is treatted as white noise. Using any of the observed equations, the output of the final combined navigation system will outperform the results of pure NS or pure GNSS. Using the position observation equation alone will improve the position output accuracy of the system, but not much for the speed part. A separate speed observation equation will improve the speed of the output accuracy, but does not improve the accuracy of the location. n order to improve the overall accuracy of the system at the same time, choose the combination of the location of the speed of observation. Alternating combinations of position and velocity observations are those of alternating observations of position and velocity. Since the position estimation time constant is usually much larger than the velocity estimation time constant, it is possible to use the position observations again after using the position observations once, and again when updating the position estimation values. Which not only improves the speed precision and the position precision of the integrated navigation system.

4 Kalman Filtering Algorithm Due to the uncertainty of noise in practical application [9], the Kalman filter algorithm combines the state equation and the observation equation of the system by using the idea of first prediction and correction [10], and finally obtains the equations which can realize the state optimal estimation. Suppose there is a dynamic system model Xk k, k1xk1k1w k1 Yk HkXk Vk (14) W where k and Vk areunrelated Gaussian white noise, he mean and variance of the system initial X vector 0 X are known, the residual initial vector 0 V of k W and k is uncorrelated. hen there are Kalman filter equations as follows (1)State one step prediction equation Xˆ Xˆ kk 1 kk 1 k1 (2)One Step Prediction of Mean Square Error Equation (15) Pkk 1 k, k1pk 1 k, k1+ k 1Qk1 k1 (16) (3)nnovation vector i ˆ k Yk HkXk 1 (17) (4)Filter gain equation 1 Kk Pk k 1 Hk ( HkPk k 1Hk k) (18) (5)Equation of state estimation Xˆ ˆ k Xk k1 Kkik (19) (6)Estimate the mean square error equation Pk ( KkHk) Pkk 1( KkHk) KkkKk (20) X Xˆ is the predicted state vector obtained by estimating the optimal state k 1 at time k-1 to k, ˆ 1 where kk kk 1 k1 Pkk 1 is the state transition matrix k-1 to k, is the prediction error variance matrix at time k-1 to k, Q are the interference matrix and interference variance matrix of the system respectively, ik and k 1 K is the innovation vector, k is the gain matrix, k Xˆ is the observed noise covariance matrix, k is the P optimal estimated state vector, k is the estimated mean square error matrix at time k. Simulation Verification n the integrated navigation system simulation process, take the parameters as follows, GNSS receiver set the horizontal position deviation of 10m, random deviation of 32m, velocity deviation of 0.5m/s. he initial error of the navigation system is as following, the attitude error angle in the horizontal direction is 30 and the azimuth error angle is 60, irrespective of the initial position error and the initial velocity error. he initial latitudeis , the initial longitude of , height 14m, a total of 990s simulation is carried out. Comparison of Position, Velocity and Attitude

5 Error between the nertial Navigation System and the ntegrated Navigation System after Kalman Filtering. Figure 2. Comparison of position error between pure inertial navigation and integrated navigation. Figure 3. Comparison of the error between pure inertial navigation and integrated navigation. Figure 4. Comparison of posture error between pure inertial navigation and integrated navigation. From Figure 2. to Figure 4., we can make conclusions as following, under the pure inertial output, the error of the system will accumulate continuously, and the error will no longer accumulate after the filtering and fusion of the combinatorial system, the error in the long time will be improved obviously, Better than 10m, the speed error is better than 0.5m / s, the heading angle error is better than 0.5 / s after stabilization and the error has no accumulation tendency. Conclusions NS / GNSS / GNSS combines NS and GNSS through information filtering fusion, but GNSS is susceptible to anomalous observations to conventional Kalman filtering accuracy. n this paper, the GNSS error model and the calculation procedure of strapdown inertial navigation system are established, and the error model of the inertial navigation system is deduced. Based on the inertial

6 navigation error model, the combination equation of state and position and velocity are established. he results show that after using the Kalman method proposed in this paper, the normal observations are not affected, and for the single outliers and the outliers, Excellent detection and suppression effect, greatly enhanced the stability of the integrated navigation system, significantly improve the anti-poor results. eferences [1] Hu Gao-Ge, Liu Yi-Han, Gao She-Sheng, Yang Yi. mproved strong tracking UKF and its application in NS/GPS integrated navigation [J]. Journal of Chinese nertial echnology, 2015, 22 (05): [2] Li Ke, Jin Jihang, Chang Guobin. Detection and esistance of the Outlying Observation in GNSS /NS ntegrated Navigation System [J]. Hydrographic Surveying and Charting, 2015, 35(1): [3] Liu Shuai, Sun Fuping, Chen Po et al. A Survey of ime Synchronization Solutions in GPS/NS ntegrated Systems [J]. GNSS world of China, 2012, 37(1): [4] Miao Yuewang, Zhou Wei, ian Liang, Cui Zhiwei. Extended obust Kalman Filter Based on nnovation Chi-Square est Algorithm and ts Application [J]. Geomatics and nformation Science of Wuhan University, 2016, 41(2): [5] Godha S. Performance Evaluation of Low Cost MEMS-Based MU ntegrated with GNSS for Land Vehicle Navigation Application [D]. Calgary: he University of Calgary, [6] Woodman, O.J. An ntroduction to nertial Navigation. University of Cambridge, Computer Laboratory, ech. ep. UCAMCL [7] A. Angrisano, M. Petovello, G. Pagliano. GNSS/NS ntegration in Vehicular Urban Navigation[C]. Proceedings of ON GNSS 2010, Sep, Portland. [8] Luo Jianjun, Ma Weihua, Yuan Jianping, Yue Xiaokui. Principle and Application of ntegrated Navigation [M]. Xi an: Northwestern Polytechnic University Press, [9] Chang G. Loosely Coupled NS/GPS ntegration with Constant Lever Arm using Marginal Unscented Kalman Filter [J]. he Journal of Navigation, 2014, 67 (3): [10] Koch K. obust estimations for the nonlinear Gauss Helmert model by the expectation maximization algorithm [J]. Journal of Geodesy, 2014, 88 (3): [11] Quan Wei, Liu Baiqi, Gong Xiaolin, et al. NS/CNS/GNSS ntegrated Navigation echnology [M]. Beijing: National Defense ndustry Press, 2011 [12] Simon D. Optimal state estimation: Kalman, H, and nonlinear approach [M]. New Jersey: Wiley-nterscience, [13] Chang G. obust Kalman filtering based on Mahalanobis distance as outlier judging criterion [J]. Journal of Geodesy, 2014, 88(4): [14] Chang G. Kalman filter with both adaptivity and robustness [J]. Journal of Process Control, 2014, 24: [15] Xue Li, Gao She-sheng, HU Gao-ge. Adaptive Sage-Husa particle filtering and its application in integrated navigation [J]. Journal of Chinese nertial echnology, 2013, 21(1): [16] Yedukondalu K., Sarma A.D., Ashwani K., et al. Spectral analysis and mitigation of GPS multipath error using digital filtering for static applications [J]. EE Journal of esearch, 2013, 59(2):