Particle Filtering for Enhanced Parameter Estimation in Bilinear Systems Under Colored Noise

This paper addresses the challenging problem of parameter estimation in bilinear systems under colored noise. A novel approach, termed B-PF-RLS, is proposed, combining a particle filter (PF) with a recursive least squares (RLS) estimator. The B-PF-RLS algorithm tackles the complexities arising from system nonlinearities and colored noise by effectively estimating unknown system states using the particle filter, which are then integrated into the RLS parameter estimation process. Furthermore, the paper introduces an enhanced particle filter that eliminates the need for explicit knowledge of the measurement noise variance, enhancing the method's practicality for real-world applications. Numerical examples demonstrate the B-PF-RLS algorithm's superior performance in accurately estimating both system parameters and states, even under uncertain noise conditions. This work offers a robust and effective solution for system identification in various engineering applications involving bilinear models subject to complex noise environments.