A method for extracting range and Doppler information from a Doppler-spread active sonar echo is proposed. The Doppler spreading is based on Van Trees' model, and the method is based on the fourth-order cumulant spectrum. Specifically, from the envelope of an amplitude modulated coded pulse train the spectrum and fourth-order cumulant spectrum are derived. It is demonstrated by analysis and simulation that, due to Doppler-spreading, the conventional method cannot extract range and Doppler shift frequencies of the return pulse without degradation. However, under the same conditions the method based on the fourth-order cumulant spectrum can. It is also shown that a special case of this method is independent of the covariance of the Doppler spreading function.>

The hypothesis for non-Gaussian processes higher-order spectra contain information that usually is not contained in second-order spectra is proved for a special case of the trispectrum using mixture processes. Specifically, the fourth-order cumulant spectrum is shown to differentiate between a Gaussian process and a non-Gaussian mixture process. Mixture processes often represent physical phenomena arising in sonar and radar applications. For example, the reflected components of an active transmission can be composed of a mixture of two sinusoids due to target resonances. It is demonstrated that the fourth-order cumulant spectrum can differentiate between a sum of sinusoids and a mixture of sinusoids.>

The author formulates the multiple transmission application in terms of a sequential detection problem based on the likelihood ratio. The first application is for a Rayleigh fluctuating target. The likelihood ratio is constructed based on probability density functions. This gives the optimum receiver for the assumed conditions. A more general model based on Markov process is considered next. In this case the current return is correlated with past returns. It is shown that correlated returns improve detection performance. Extending this model further, correlated returns with non-Gaussian statistics are formulated using mixture densities.>

Multisensor data from sonar arrays are usually temporally and spatially dependent. In addition, in some environments the noise field in which the sonar system must operate is contaminated by impulsive and non-Gaussian interference. A natural way to include these effects is to formulate a statistic based upon the likelihood ratio. However, implementing a multisensor likelihood ratio statistic in its full generality is a formidable task. Our approach to solving the implementation complexity problem is to partition the amplitude of each sensor output intomintervals and model the resulting data as a finite Markov chain. Certain performance measures for fixed-sample-size and sequential detection statistics based on Markov chains are considered.

The use of sensors configured into various geometrical shapes called arrays are of fundamental importance in extracting temporal, spatial, frequency, and probability distribution information in underwater acoustic and other applications. This paper explores the effectiveness of a two-dimensional or planar array in extracting spatial and frequency information. The method utilizes a receiver which converts digitized data at the output of each element, which may be nonlinear, into its frequency components using a discrete-Fourier transform. The frequency components are then weighted and summed over all spatial elements. The objective of the optimum receiver is to choose the weights so that a performance measure is maximized. To combat non-Gaussian interference an ideal nonlinearity is introduced. Several examples are given comparing the performance of a receiver with and without an ideal nonlinearity in an impulsive or non-Gaussian noise environment.

A method to remove narrowband interference in the frequency domain is considered. It consists of first transforming the data into the frequency domain by an FFT, passing the transformed data through an ideal non-linearity, and then transforming the data back into the time domain by an IFFT. The essential mathematical details of the method are given and an error criterion is defined which measures the effectiveness of the technique.

The detection of signals by power spectrum density (PSD) estimation is a well known and often employed method. The PSD estimate is essentially a second order measure which is not sensitive to the statistical nature of the signals. For non-Gaussian signals, a frequency domain Kurtosis (FDK) estimate supplements the PSD estimate and in some cases of practical importance is superior as a detection statistic. Non-Gaussian signals occur in underwater acoustics due to multipath and frequency modulation effects. Specifically, we have considered sinusoidal and narrowband Gaussian signals which, when propagated through fading or multipath environments, are received as non-Gaussian in terms of a frequency domain Kurtosis estimate. The environment is modeled by introducing amplitude probability density distributions which are due to the fading or multipath conditions. Several distributions were considered previously which included Rayleigh and log-normal, both of which have been experimentally verified to exist in the ocean. The asymptotic probability of detection for a randomly occurring signal is derived for the PSD and FDK. A simulation comparing the probability of detection for the FDK and PSD is also included.

It is known that the sequential probability ratio test (SPRT) minimizes the average detection time among all tests for fixed type I and type II errors under the hypothesis and alternative. Often, in practical detection problems, the signal level is unknown during the decision interval. In this paper, the relative efficiency of a sequential detector is compared with its fixed sample size detector counterpart for signal levels which may be inconsistent with the assumed alternative. The results are applicable to detectors called partition detectors which are designed based on knowledge of a set of quantiles and related functions from the unknown noise field, and guarantee distribution-free performance under the hypothesis. For the class of sequential detectors that have boundaries which are linear functions of the sample size, the operating characteristic function and average sample number ASN are derived.

Partitioning of the observation space using quantiles of the underlying noise distribution is a useful technique to achieve distribution-free performance. A set of quantiles and related functions essentially determine a nonlinearity which depends on the underlying noise and precedes the standard detector. In this paper, the received data in each channel of the array is first partitioned by a set of quantiles and then transformed by a discrete Fourier transform into discrete frequency estimates which are then multiplied by complex weights. The cross-spectrum for each frequency is then obtained by the direct segment method. The results show, based on a modified version of the asymptotic relative efficiency measure, that performance gains can be achieved in non-Gaussian noise compared with detectors designed assuming Gaussian noise.

In this paper, the theory of sequential partition detectors with dependent sampling is introduced. A new formulation is given which predicts the thresholds under q-dependent sampling in order to maintain the same error probabilities as in the independent sampling case. A comparison is made between independent and dependent sequential partition detectors based on the average time to detection. Under stated conditions dependent sequential partition detectors show improved efficiency for both Lehmann and shift of the mean alternatives.

Given only the outputs from a discrete Fourier transform (DFT) a robust sequential detector (RSD) for weak signals is derived based on m-interval partitioning. A loglikelihood ratio at the output of the DFT is formulated assuming knowledge of a set of quantiles and scores of the unknown and possible changing noise distribution. The quantiles and scores are chosen to minimize the average time to a decision under practical implementation constraints.