An improved wavelet based shock wave detector

In this paper, the detection of shock wave that generated by supersonic bullet is considered. A wavelet based multi-scale products method has been widely used for detection. However, the performance of method decreased at low signal-to-noise ratio (SNR). It is noted that the method does not consider the distribution of the signal and noise. Thus we analyze the method under the standard likelihood ratio test in this paper. It is found that the multi-scale product method is made in an assumption that is extremely restricted, just hold for a special noise condition. Based on the analysis, a general condition is considered for the detection. An improved detector under the standard likelihood ratio test is proposed. Monte Carlo simulations is conducted with simulated shock waves under additive white Gaussian noise. The result shows that this new detection algorithm outperforms the conventional detection algorithm.