Filters, theory

The vector nk describes the unknown additive measurement noise, which is assumed in accordance with Kalman filter theory to be a Gaussian random variable with zero mean and covariance matrix R. Instead of the additive noise term nj( in equation (20), the errors of the different measurement values are assumed to be statistically independent and identically Gaussian distributed, so... 

Jang, S. S., Josepth, B and Mukai, H. (1986). Comparison of two approaches to on-line parameter and state estimation problem of non-linear systems. Ind. Eng. Chem. Process Des. Dev. 25, 809-814. Jazwinski, A. H. (1970). Stochastic Processes and Filtering Theory. Academic Press, New York. Liebman, M. J., Edgar, T. F., and Lasdon, L. S. (1992). Efficient data reconciliation and estimation for dynamic process using non-linear programming techniques. Comput. Chem. Eng. 16, 963-986. McBrayer, K. F., and Edgar, T. F. (1995). Bias detection and estimation on dynamic data reconciliation. J Proc. Control 15, 285-289. 

Haykin, 1991] Haykin, S. (1991). Adaptive Filter Theory, Second Edition. Prentice-Hall, Englewood Cliffs, NJ. 

Fettweis, 1986] Fettweis, A. (1986). Wave digital filters Theory and practice. Proc. IEEE, 74(2) 270-327. 

Jazwinski, A.H. "Stochastic Processes and Filtering Theory" Academic Press New York, 1970. 

Bose, N.K., Digital Filters Theory and Applications, Elsevier Science, New York, 1985. 

Haykin, S., Adaptive Filter Theory, 2nd ed., Prentice Hall, Upper Saddle River, NJ, 1991. Haykin, S., Ed., Advances in Spectrum Analysis and Array Processing, Vol. 2, Prentice Hall, Upper Saddle River, NJ, 1991. 

S. G. Mohinder, P. A. Angus, Kalman Filtering Theory and Practice Using MATLAB, 2th Edn., Wiley-VCH, Wein-heim, 2001. 

This fast and effective digital algorithm is based on a linear stochastic model that is equivalent to Eq. (1). The theoretical background is beyond the scope of the present article unfortunately, some knowledge of the basic Kalman filtering theory [5,7] is necessary for an adequate algorithm adjustment. The adjustment requires estimating the variances of the measurement noise and of the expected solution. 

L. M. Gugliotta, D. Alba, and G. R. Meira, Correction for instrumental broadening in SEC through a stochastic matrix approach based on Wiener filtering theory, ACSSymp. Ser. 352 287 (1987). 

A.H. Jazwinski, Stochastic processes and filtering theory. Academic Press, New York, (1970). 

Jazwinski, A.H. (1970) Stochastic Processes and Filtering Theory. Academic Press, San Diego, California. 

Ma6klewicz, Jolanta, "The Development of Flocculation Effects in Filter Theory," Chem. Eng. Commun.. 23, 1983, pp 305-314. 

The design procedures suggested here are based on what is sometimes called modern filter theory. Modern filter theory (as contrasted with classical filter theory relies more on ad hoc design calculations and less on the use of tabulated parameters. In brief, the design procedure is as follows ... 

The textbook by D.E. Johnson, Introduction to Filter Theory, mentioned in the references, is recommended as a compact but thorough seminal reference for the design of lumped-parameter passive filters. In addition, this subject has been the primary focus of a number of other textbooks and is included in virtually every basic circuit theory textbook. 

Sedra, A.C. and Brackett, P.0.1978. Filter Theory and Design Active and Passive. Matrix, Portland, OR. Seidman, A. 1983. Integrated Circuits Applications Handbook. Wiley, New Yorlc. 

Haykin, S.S. 1991. Adaptive Filter Theory. Prentice-HaU, Engelwood CUfFs, NJ. 

Mansoudi M, Heibel A, Then P M (2000) Predicting pressure drop of wall-flow diesel particulate filters - Theory and experiment. SAE Technical Paper 2000-01-0184... 

BG Bovard. Rugate filter theory—An overview. Appl Optics 32 5427-5442, 1993. 

Grewal M, Andrews A (2001) Kalman filtering, theory and practice using MATLAB, 2nd edn. Wiley, New York... 

Buttkus B (2000) Spectral analysis and filter theory in applied geophysics. Springer, Berlin, xv + 667 pp. ISBN 3-540-62674-3... 

The purpose of this paper is to show the application of Kalman Filter theory to the problem of extracting the motion parameters from a sequence of images of a rigid body which is moving in a three dimensional space. The objective is to apply the Kalman Filter equations to the system of a moving object using the state variable approach. The system is described by a set of equations that specify the position and orientation of the body in space and how these coordinates are changing in time. 

The paper is divided into four sections. Section I shows a review of related papers. Section II deals with the set of equations that describes the system of the body in three dimensional motion. Section III develops the application of the Kalman Filter theory to this problem and Section IV describes the experiment and some results. Conclusions are shown at the end of the paper. 

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