Abstract: A general form of the optimal algorithm of the Terrain Contour Ma-tching（TERCOM） is derived. By simplifying the general form, several realizable algorithms for different models are obtained. Simulation of them has been done and the results show the following Peculiarities;（1） The measurements are processed recursively. The algorithms begin to be executed as soon as the vehicle receives the first measurement. So they can save more computation time than the algorithms with batch processing.（2） There is no limitation on the flight trace of the vehicle. The vehicle can maneuvre while the algorithms are being carried on.（3） The algorithms can work at lower signal-to-noise ratio.（4） The convolution-multiplication algorithm can work under serious random disturbance and has good robustness to the existing course and speed deviations.These algorithms may also be applied to pattern recognition, image recognition and some filter problems.