Detection and estimation of weak pulse signal in chaotic background noise

As is well known, people has been suffering noise interference for a long time, and more and more researches show that a lot of weak signals such as pulse signal are embedded in the strong chaotic noise. The purpose of weak signal detection and recovery is to retrieve useful signal from strong noise. It is very difficult to detect and estimate the weak pulse signal which is mixed in the chaotic background interference. Therefore, the detection and recovery of weak signal are significant and have application value in signal processing area, especially for the weak pulse signal detection and recovery. By studying various methods of detecting and estimating the weak pulse signal in strong chaotic background noise, in this paper, we propose an efficient hybrid processing technique. First, based on the short-term predictability and sensitivity to the tiny disturbance, a new method is proposed, which can be used for detecting and estimating the weak pulse signals in chaotic background that the nonlinear mapping is unknown. We reconstruct a phase space according to Takens delay embedding theorem; then we establish the local linear autoregressive model to predict the short-term chaotic signal and obtain the fitting error, and judge whether there are weak pulse signals. Second, we establish a single-jump model for pulse signals, and combine the local linear autoregressive model with it to build a double local linear (DLL) model for estimating the weak pulse signal. DLL model contains two parameters, and the two parameters affect each other. We use the back-fitting algorithm to estimate model parameters and ultimately recover the weak pulse signals. Detecting and estimating the pulse signals in chaotic background turns into estimating the parameters of DLL model. The minimum fitting error criterion is used as the objective function to estimate the parameters of the DLL model. To make the estimation more exact, we can use the formula of mean square error. The new algorithm presented here in this paper does not need to know the prior knowledge of the chaotic background nor weak pulse signal, and this algorithm is also simple and effective. Finally, the simulation results show that the method is effective for detecting and estimating the weak pulse signals based on the chaotic background noise. Specifically, the weak pulse signal can be extracted well with low SNR and the minimum mean square error or the minimum normalized mean squared error is very low.