Adaptive Filter Synthesis for Speed Tracking Based on a Two-Dimensional Markov Model with Unknown Parameters
Luong Van Huy1*
Abstract
This paper presents a method for synthesizing an adaptive filter for speed-tracking systems operating in noisy environments, based on a two-dimensional Markov model of the velocity–acceleration process when the damping coefficient of the process is unknown. The model is described by a continuous-state system with Gaussian white noise. The characteristic ratio ρ between the process noise and measurement noise is defined based on the noise spectral density and the damping coefficient. On that basis, the paper constructs a two-dimensional adaptive filter to estimate velocity and acceleration, and establishes adaptive Riccati equations for computing the steady-state error covariance matrix. Analytical solutions for variance, covariance, and sensitivity with respect to parameter ρ are derived from the corresponding differential equations. Finally, the paper evaluates the accuracy gain of the filter when the damping coefficient is estimated, and analyzes the impact of model mismatch on filtering quality. Results indicate that the adaptive filter significantly improves tracking accuracy in cases where model parameters are unknown.
Keywords:
Adaptive filter, two-dimensional Markov model, Riccati equation, parameter estimation, damping coefficient, velocity tracking, error variance.
