Finite difference implementation of distributed parameter filters

The numerical problems associated with the full three-dimensional (spatial) distributed parameter filters demand a novel technique that maintains accuracy and efficiency for the complex partial differential Riccati equation governing the filter variance. The filters can be successfully implemented by using numerical operators that can, in various ways, be factored. Use of the finite difference method having this property increases the accuracy and efficiency of the implementation. This paper outlines a time-splitting technique for the numerical implementation of distributed parameter filters. The paper provides rationales to the square root and U-D factorizations of the distributed parameter filter by means of the time-splitting finite difference method.

[1]  Robert W. MacCormack,et al.  Numerical solution of the interaction of a shock wave with a laminar boundary layer , 1971 .

[2]  J. Seinfeld,et al.  Numerical implementation of distributed parameter filters with application to problems in air pollution , 1978 .

[3]  A. C. Hindmarsh,et al.  Applications of EPISODE: an experimental package for the integration of systems of ordinary differential equations. [In FORTRAN for CDC 7600] , 1975 .

[4]  M. B Ajinkya,et al.  The experimental implementation of a distributed parameter filter , 1975, Autom..

[5]  B. Leden,et al.  Different methods for estimating thermal diffusivity of a heat process , 1976, Autom..

[6]  A. Bryson,et al.  Discrete square root filtering: A survey of current techniques , 1971 .

[7]  N. N. Yanenko,et al.  The Method of Fractional Steps , 1971 .

[8]  B. Finlayson.  The method of weighted residuals and variational principles : with application in fluid mechanics, heat and mass transfer , 1972 .

[9]  S. Prabhu,et al.  Optimal control of linear diffusion processes with quadratic error criteria , 1972 .

[10]  R. F. Warming,et al.  Upwind Second-Order Difference Schemes and Applications in Aerodynamic Flows , 1976 .

[11]  Gerald J. Bierman,et al.  Measurement updating using the U-D factorization , 1975, 1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes.

[12]  W. Harmon Ray,et al.  Real time distributed parameter state estimation applied to a two dimensional heated ingot , 1978, Autom..

[13]  W. Harmon Ray,et al.  Distributed parameter systems: Identification, estimation, and control , 1978 .

[14]  M. Wozny,et al.  On parameter identification for distributed systems using Galerkin's criterion , 1973 .

[15]  D. Gilai,et al.  An alternative formulation of a distributed-parameter optimal cotrol problem applied to nuclear shielding , 1976 .

[16]  G. Bierman.  Factorization methods for discrete sequential estimation , 1977 .

[17]  Masato Koda,et al.  Estimation of urban air pollution , 1978, Autom..