Time-varying matrix estimation in stochastic continuous-time models under coloured noise using LSM with forgetting factor

Abstract

In this article, we deal with time-varying matrix estimation in continuous-time stochastic models under a coloured noise. The suggested estimation algorithm is based on the least squares method (LSM) with forgetting factor. The forming filter generating this ‘coloured‘ noise from a standard ‘white noise’ is assumed to be partially known. An analysis of the convergence zone is presented. A numerical example illustrates the effectiveness of the proposed algorithm.

Keywords:

• parameter estimation
• stochastic systems
• least squares method
• forgetting factor
• coloured noise

Notes

Notes

1. As for a matrix forgetting factor, see Poznyak and Medel (1999a).

2. If, H is Hurwitz, σ_θ = σ = const, then ℐ_0,∞ satisfies the Lyapunov equation