Comparison of robust H_∞ filter and Kalman filter for initial alignment of inertial navigation system

Abstract

There are many filtering methods that can be used for the initial alignment of an integrated inertial navigation system. This paper discussed the use of GPS, but focused on two kinds of filters for the initial alignment of an integrated strapdown inertial navigation system (SINS). One method is based on the Kalman filter (KF), and the other is based on the robust filter. Simulation results showed that the filter provides a quick transient response and a little more accurate estimate than KF, given substantial process noise or unknown noise statistics. So the robust filter is an effective and useful method for initial alignment of SINS. This research should make the use of SINS more popular, and is also a step for further research.

Keywords

H_∞ filter / Kalman filter / initial alignment / integrated navigation system / SINS

References

[1] Widrow B., Hoff M. E. Jr.. Adaptive switching circuits[J]. IRE WESCON Convention Record, 1960, 4: 96-104

[2] WIDROW B, STEARNS S D. Adaptive signal processing[M]. Upper Saddle River: Prentice Hall Inc, 1885.

[3] Haykin S. Adaptive filter theory[M]. 1991, 2nd ed, Prentice Hall: Upper Saddle River

[4] Hassibi B., Sayed A. H., Kailath T. H_∞ optimality of the LMS algorithm[R]. 1995, Palo Alto: Stanford University Information Systems Laboratory

[5] Kwakernaak H. A polynomial approach to miminax frequency domain optimization of multivariable feedback systems[J]. Int J of Control, 1986, 44: 117-156

[6] Doyle J. C., Glover K., Khargonekar P., Francis B. State-space solutions to standard H₂ and H_∞ control problems[J]. IEEE Transactions on Automatic Control, 1989, 34: 831-847

[7] Khargonekar P. P., Nagpal K. M. Filtering and smoothing in an H_∞ setting[J]. IEEE Trans on Automatic Control, 1991, AC-36: 151-166

[8] Basar T. Optimum performance levels for minimax filters, predictors and smoothers[J]. Systems and Control Letters, 1991, 16: 309-317

[9] LIMEBEER D J, SHAKED U. New results in H_∞ filtering[C]// Proc Int Symp On MTNS. New York, 1991: 317–322.

[10] SHAKED U, THEODOR Y. H_∞ optimal estimation: a tutorial[C]// Proc IEEE Conference on Decision and Control. Tucson, AZ, 1992: 2278–2286.

[11] YAESH I, SHAKED U. H_∞ optimal estimation: the discrete time case [C]// Proc Int Symp On MTNS. New York, 1991: 261–267.

[12] Grimble M. J. Polynomial matrix solution of the H_∞ filtering problem and the relationship to Riccati equation state-space results[J]. IEEE Trans on Signal Processing, 1993, 41: 61-81

[13] Hassibi B., Sayed A. H., Kailath T. Linear estimation in Krein spaces-part II: application[J]. IEEE Transactions on Automatic Control, 1996, 41: 24-49

[14] HASSIBI B, SAYED A H, KAILATH T. H_∞ optimality of the LMS algorithm[C]// The Proceeding of 32^nd IEEE Conf on Dec and Cont. [S.l.], 1993: 74–80.