Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31105
On Adaptive Optimization of Filter Performance Based on Markov Representation for Output Prediction Error

Authors: Hong Son Hoang, Remy Baraille


This paper addresses the problem of how one can improve the performance of a non-optimal filter. First the theoretical question on dynamical representation for a given time correlated random process is studied. It will be demonstrated that for a wide class of random processes, having a canonical form, there exists a dynamical system equivalent in the sense that its output has the same covariance function. It is shown that the dynamical approach is more effective for simulating and estimating a Markov and non- Markovian random processes, computationally is less demanding, especially with increasing of the dimension of simulated processes. Numerical examples and estimation problems in low dimensional systems are given to illustrate the advantages of the approach. A very useful application of the proposed approach is shown for the problem of state estimation in very high dimensional systems. Here a modified filter for data assimilation in an oceanic numerical model is presented which is proved to be very efficient due to introducing a simple Markovian structure for the output prediction error process and adaptive tuning some parameters of the Markov equation.

Keywords: Dynamical System, Data Assimilation, statistical simulation, Canonical form, Markov and non-Markovian processes

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1037


[1] Bryson A.E. and Henrikson L.J. (1968) Estimation Using Sampled Data Containing Sequentially Correlated Noise. Journal of Spacecraft, Vol. 5, No. 6, pp. 662-665.
[2] T. Kailath (1968) An Innovations Approach to Least-Squares Estimation, Pt. I: Linear Filtering in Additive Noise, IEEE Trans. Autom. Contr., 13(6), pp. 646-655.
[3] Hoang H.S. and Baraille R. (2011) Approximation Approach to Linear Filtering Problem with Correlated Noise. Engineering and Technology, 59, pp. 298-305.
[4] Hoang H.S. and Baraille R. (2012) On Gain Initialization and Optimization of Reduced-Order Adaptive Filter. Journal IAENG IJAM, 42:1, pp. 19-33.
[5] Lo`eve, M. (1978) Probability theory. Vol. II, 4th ed. Graduate Texts in Mathematics. 46. Springer-Verlag
[6] Nguyen T.L. and Hoang H.S. (1982) On one model of non-Markovian random process and its application to optimal estimation theory. Automat. Remote Contr., 43 (1982), 8 (1), pp. 1021-1032.
[7] Pugachev V.S. and Sinitsyn I.N. (1987). Stochastic systems : theory and applications, John Wiley and Sons.
[8] Golub G.H. and van Loan C.F. (1996). Matrix Computations, Cambridge University Press.