Group of  Nonlinear Dynamics & Complex Systems

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Research Fields —Nonlinear time series analysis

 

Weak signal detection in a nonstationary environment

The detection of a target signal in a background of noise is basic to signal processing. The classical solution to the problem of detection is to use a matched filter receiver, which maximize the signal-to-noise ratio (SNR) at the receiver output, and is optimal in some sense when the interference is modeled as additive white Gaussian noise (AWGN). When the statistics of the noise are unknown, and signals that we have to deal with are generated by dynamic process that are simultaneously nonlinear, nonstationary, and non-Gaussian. The end result of designing a signal-processing system along traditional lines is a suboptimal solution.

We proposed a novel cascading strategy for weak signal detection in a non-stationary environment. The method combines the nonlinear singular spectrum analysis (SSA), time-frequency analysis and the neural network. Such a system can detect an unknown signal from the unknown nonstationary environment with high performance, providing that we can also observe the inteference alone.

The flow chart of the whole detection algorithm is illustrated in the left figure.For weak signal, prefiltering by SSA filter is crucial. The effect of the filter is depicted in the following figures.

 

Figure: STFT images of target signal (left panel) and background noise (right panel) before and after SSA filter. For different segment of signal, the filtered TF distributions of noise will be quite different, while for target signal, the filtered TF distributions are similar.

Related publications:

Gong Xiaofeng, etc. "weak signal detection by neural networks based cascading classifier", Technique Report, 2001.

 

 

Prediction and predictability of chaotic time series

Although Long term unpredictability is the hallmark of a chaotic system, short term prediction is always quite reliable even without the knowledge of the underlying system. One of the interesting questions is how to predict into the future as far as possible based on the available finite length history data. This problem essentially is to seek a better model from the data. We found however, that by iterating the simple local prediction process, the prediction performance will systematically increase. That is, if we use very long predicted values to build a new, enlarged database (although these predicted values are not corresponding to the true trajectory), we can achieve much better prediction than use only the original database.

Related publications:

Gong Xiaofeng and C. H. Lai, " Improvement of the local prediction of chaotic time series", Phys. Rev. E60, p5463--5468, 1999.

Gong Xiaofeng and C. H. Lai, "Iterating prediction of chaotic time series", (preparing).