In this paper, the general model of the Gaussian regression filter, including both the linear and nonlinear filter of zeroth, second order, has been reviewed. A fast algorithm based on the FFT algorithm has been proposed and tested for its speed and accuracy. Both simulated and practical engineering data have been used in the testing of the proposed algorithm. Results show that with the same accuracy, the processing times of the second order linear and nonlinear regression filters for a typical 40,000 points dataset have been reduced to under 0.5second from the several hours of the traditional convolution algorithm
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