عنوان مقاله [English]
Calculation the rate of change or differentiation of digital signal has always been one of the most important challenges in Digital Signal Processing field. Differentiating digital signals is essential in various applications. In many applications, even well-known methods aren’t useful and cause sharp increase in error and noise up to 10 times. One of the applications that is focused on in this paper is determining velocity from noisy and discrete data. Various aspects of this issue is investigated and the best derivation algorithm for the aforementioned application is designed and proposed. It was seen that Kalman filter method is the best approach for minimizing least square error for determining derivative from GPS data. It was also seen that Kalman filter method has not good transient response. This problem is somewhat improved with modification Kalman filter and using adaptive Kalman filter with appropriate weighting of old data. Another important aspect, which is also discussed in this paper, is adequate classification of various differentiation algorithms that is designed and referring the practical application of each algorithms. In order to depict the advantages of the methods, some practical results are given based on real GPS data for extracting instantaneous velocity vector.