Abstract
This paper proposes a new FIR (finite impulse response) filter under a least squares criterion using a forgetting factor. The proposed FIR filter does not require information of the noise covariances as well as the initial state, and has some inherent properties such as time-invariance, unbiasedness and deadbeat. The proposed FIR filter is represented in a batch form and then a recursive form as an alternative form. From discussions about the choice of a forgetting factor and a window length, it is shown that they can be considered as useful parameters to make the estimation performance of the proposed FIR filter as good as possible. It is shown that the proposed FIR filter can outperform the existing FIR filter with incorrect noise covariances via computer simulations. Finally, as a useful application, an image sequence stabilization problem is considered. Through this application, the FIR filtering based approach is shown to be superior to the Kalman filtering based approach.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Kalman R E, Bucy R S. A new approach to linear filtering and prediction problems. Trans. ASME J. Basic Eng., 1960, 82(D): 35–45.
Kalman R E, Bucy R S. New results in linear filtering and prediction theory. Trans. ASME J. Basic Eng., 1961, 83(D): 95–108.
Zadrozny P A, Mittnik S. Kalman filtering methods for computing information matrices for timeinvariant, periodic, and generally time-varying models and samples. Computers & Mathematics with Applications, 1994, 28(4): 107–119.
Kirubarajan T, Bar-Shalom Y. Kalman filter versus imm estimator: When do we need the latter? IEEE Trans. Aerosp. Electron. Syst., 2003, 39(4): 1452–1457.
Kwon W H, Kim P S, Han S H. A receding horizon unbiased FIR filter for discrete-time state space models. Automatica, 2002, 38(3): 545–551.
Kim P S. Maximum likelihood FIR filter for state space signal models. IEICE Trans. Commun., 2002, E85-B(8): 1604–1607.
Kim P S. Separate-bias estimation scheme with diversely behaved biases. IEEE Trans. Aerosp. Electron. Syst., 2002, 38(1): 333–339.
Kim P S. FIR filtering based image stabilization mechanism for mobile video appliances. Lecture Notes in Computer Science, 2004, 3314: 1106–1113.
Fitzgerald R J. Divergence of the Kalman filter. IEEE Trans. Automat. Contr., 1971, 16(6): 736–747.
Bruckstein A M, Kailath T. Recursive limited memory filtering and scattering theory. IEEE Trans. Inform. Theory, 1985, 31(3): 440–443.
L Xie, Y C Soh, C E de Souza. Robust Kalman filtering for uncertain discrete-time systems. IEEE Trans. Automat. Contr., 1994, 39(6): 1310–1313.
Erturk S, Dennis T J. Image sequence stabilisation based on Kalman filtering of frame positions. Electronics Letters, 2001, 37(20): 1217–1219.
Park S H, Kwon W H, Kwon O K et al. Short-time Fourier analysis using optimal harmonic FIR filters. IEEE Trans. Signal Processing, 1997, 45(6): 1535–1542.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kim, PS., Lee, ME. A New FIR Filter for State Estimation and Its Application. J Comput Sci Technol 22, 779–784 (2007). https://doi.org/10.1007/s11390-007-9085-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11390-007-9085-8