Determining parameters of dynamic systems from noisy measurements

Abstract

This paper uses the method of least-squares k-spline approximation to generate time derivatives of sampled- data measurements required to determine values for parameters in models of linear and nonlinear dynamic systems. When identifying the parameter values in a nonlinear system in which signals are corrupted with measurement noise, the method developed in this paper provides more accurate values than does an approximate time-delay filter. In generating the required deriva tives in the presence of noise, the least-squares k- spline approximation yielded higher-order derivatives which were substantially more accurate than the same derivatives obtained from a low-pass filter. In a nonlinear case used as an illustrative example, the technique described in this paper resulted in as much as a 32% improvement in the accuracy of one of the identified model parameter values, and its largest error in any of the six parameters identified was 3.5 percent. The method was particularly effective in counteracting impulse noise caused by bad data points.