Order Tracking using Kalman Estimator and Taylor Series Approximation

摘要

Order tracking using the state space approach is one of the tool dedicated for non-stationary signal processing. The well-known Kalman estimator is the most found in the literature to estimate order's parameters. One of the current problem is the appropriate modeling of the state variable which contains order's parameters. The classical manner to do so is to impose the Vold_Kalman constraint. It generally consists in assuming the second derivative of the state variable to be a white Gaussian noise. In this paper, the authors propose to model the state variable using a Taylor series approximation of the order's parameters. This new approach suppose that the coefficients of Taylor series are a Gauss-Markov process. The mixture of the Taylor series and the Gauss-Markov process can be seen as a local polynomial approximation which helps fitting very well the signal to be estimated. The limitations and capabilities of this new method are discussed using a gear signal with respect to the classical Vold_Kalman estimator. Considering the signal to noise ratio, this new approach is a good alternative compared to currently used techniques.