A method of speed observation based on least-squares linear-fitting with weight factor

In industry application, the speed usually has to be observed with the position signal. But the position signal noises have been analyzed and modeled rarely. In this paper, by analyzing the characteristics of the position noises, white noise of uniform distribution model and the triangle wave noise model are proposed. The two models can be used to evaluate the influence of position measurement noises on the observed speed. Among the speed observation methods, the methods based on model predicted error can be used to observe the speed faster, due to the use of some priori knowledge. But these methods cannot be suitable for the case when the accurate model parameters cannot be obtained. Though the IIR filter has better low-pass filtering characteristic, it does not have linear phase and the stability is also a potential problem. There are not such drawbacks mentioned above for the FIR filter. The least-squares linear-fitting with weight factor speed observer based on position signal, which is a FIR filter essentially, is proposed in this paper. Compared with the direct differentiator, the wider bandwidth and smaller the maximum amplitude of speed fluctuation are validated by simulation results and experimental results.