Detection and Extraction of Weak Pulse Signals in Chaotic Noise with PTAR and DLTAR Models

With the development in communications, the weak pulse signal is submerged in chaotic noise, which is very common in seismic monitoring and detection of ocean clutter targets, and is very difficult to detect and extract. Based on the threshold autoregressive model, pulse linear form, Markov chain Monte Carlo (MCMC), and profile least squares (PrLS) algorithm, phase threshold autoregressive (PTAR) model and double layer threshold autoregressive (DLTAR) model are proposed for detection and extraction of weak pulse signals in chaotic noise, respectively. Firstly, based on noisy chaotic observation, phase space is reconstructed according to Takens’s delay embedding theorem, and the phase threshold autoregressive (PTAR) model is presented to detect weak pulse signals, and then the MCMC algorithm is applied to estimate parameters in the PTAR model; lastly, we obtain one-step prediction error, which is used to realize adaptively detection of weak signals with the hypothesis test. Secondly, a linear form for the pulse signal and PTAR model is fused to build a DLTAR model to extract weak pulse signals. The DLTAR model owns two kinds of parameters, which are affected mutually. Here, the PrLS algorithm is applied to estimate parameters of the DLTAR model and ultimately extract weak pulse signals. Finally, accurate rate (Acc), receiver operating characteristic (ROC) curve, and area under ROC curve (AUC) are used as the detector performance index; mean square error (MSE), mean absolute percent error (MAPE), and relative error (Re) are used as the extraction accuracy index. The presented scheme does not need prior knowledge of chaotic noise and weak pulse signals, and simulation results show that the proposed PTAR-DLTAR model is significantly effective for detection and extraction of weak pulse signals under chaotic interference. Specifically, in very low signal-to-interference ratio (SIR), weak pulse signals can be detected and extracted compared with support vector machine (SVM) class and neural network model.