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Adaptive filtering for radar pulse compression has been shown to improve sidelobe suppression through the estimation of an appropriate pulse compression filter for each individual range cell of interest. However, the relatively high computational cost of full-dimension, adaptive range processing may limit practical implementation in many current real-time systems. Dimensionality reduction techniques are here employed to approximate the framework for pulse compression filter estimation. Within this approximate framework, two new minimum mean square error (MMSE) based adaptive algorithms are derived. The two algorithms are denoted as specific embodiments of the fast adaptive pulse compression (FAPC) method and are shown to maintain performance close to that of full-dimension adaptive processing, while reducing computation cost by nearly an order of magnitude (in terms of the discretized waveform length N).