Topological Matched Filtering Algorithm for Chaotic Echo of Active Sonar

We present a topological matched filtering algorithm to reduce noise of chaotic echo, which applies embedding theory that reconstruction trace of embedded phase is in topological equivalence with original time series.According to the predefined phase trace of clean chaotic data,we correct the observed noisy chaotic signal in an incremental mode to match this filter as close as possible to the original phase trace.So chaotic signal can be extracted from noisy signal by using the topological matched filter.We optimize the search algorithm with grid search to find nearest neighbors. Simulation results show that this algorithm has a good signal filtering effect even when the signal to noise ratio decreases to 0 dB, and is suitable for white noise, Lorenz chaotic signal and ocean ambient noise. With this algorithm two types of broadband signals can be separated to effectively, recover the original clean chaotic echo.