M. R. Cowper

False detection of chaotic behaviour in the stochastic compound k-distribution model of radar sea clutter

There is current debate in the radar community whether sea clutter is stochastic or chaotic. In this paper, a stochastic k-distributed surrogate is generated for a typical sea clutter data set. The k-distributed set was then analysed using the methods recently applied to sea clutter by Haykin et al. (Haykin and Li, Proc. IEEE, vol.83, pp.95-122, 1995; Haykin and Puthusserypady, Proc. IEE Radar, pp.75-9, 1997). The k-distributed set is shown to have DML (maximum likelihood estimation of the correlation dimension) and FNN (false nearest neighbours) values in the same range as reported by Haykin et al. (1995; 1997) and with positive and negative Lyapunov exponents. In addition, various white and correlated noise distributed sets are analysed in the same way and found to produce a similar artefact. It is concluded that these chaotic invariants cannot be used to distinguish between chaotic and stochastic time series and are redundant in an application, such as radar sea clutter, where the time series is unknown and could be of a stochastic nature.

Nonlinear processing of high resolution radar sea clutter

This work deals with investigating whether or not nonlinear predictor networks can be used to improve the performance of high resolution surveillance radars which are used to detect targets on, or near the sea surface. Prediction and detection results are presented for new sea clutter data sets.

A new method to detect nonlinearity in a time-series: synthesizing surrogate data using a Kolmogorov-Smirnoff tested, hidden Markov model

Abstract A way of statistically testing for nonlinearity in a time-series is to employ the method of surrogate data. This method often makes use of the Fourier transform (FT) in order to generate the surrogate. As various authors have shown, this can lead to artefacts in the surrogates and spurious detection of nonlinearity can result. This paper documents a new method to synthesize surrogate data using a 1st order hidden Markov model (HMM) combined with a Kolmogorov–Smirnoff test (KS-test) to determine the required resolution of the HMM. Significance test results for a sinewave, Henon map and Gaussian noise time-series are presented. It is demonstrated that KS-tested HMM surrogates can be successfully used to distinguish between a deterministic and stochastic time-series. Then by applying a simple test for linearity, using linear and nonlinear predictors, it is possible to determine the nature of the deterministic class and hence conclude whether the system is linear deterministic or nonlinear deterministic. Furthermore, it is demonstrated that the method works for periodic functions too, where FT surrogates break down.

The application of a nonlinear inverse noise cancellation technique to maritime surveillance radar

A method, referred to as Broomheads filter method, is reviewed. This method uses a nonlinear inverse to a linear bandstop filter to obtain better noise reduction results, in terms of signal to noise ratio, than linear noise reduction techniques, for the cancellation of wideband chaotic noise from a sinusoid. A novel and unorthodox approach is suggested for the linear bandstop filtering aspect of Broomheads filter method, which allows it to be applied in situations where the signal of interest has a broader spectrum than that of a sinusoid. This unorthodox approach, referred to as the modified Broomhead filter method, is used to cancel chaotic noise and sea clutter from narrowband Gaussian signals of interest.