New insights into derivative estimation via least squares approximation - theory and application

In this article, we revise a well-known derivative estimation scheme which is based on a least squared error polynomial approximation of a noisy measurement signal. Our contribution is to determine the influence of the estimation parameters onto the covariance matrix and the temporal delay of the estimation result. Also, it is shown that the least squares estimator is statistically optimal in the presence of white Gaussian measurement noise. Our ideas are applied to the estimation of derivatives of the first state of Chen's chaotic oscillator and to the fault tolerant swing up of the inverted pendulum on a cart.