Isabel M. G. Lourtie

L/sup 2/(R) nonstationary processes and the sampling theorem

In a previous paper W. Gardner (see IEEE Trans. Inform. Theory, vol.IT-18, p.808-9, 1972) developed a sampling theorem for nonstationary random processes, under the condition that the two-dimensional (2-D) power spectrum (2DPS) of the process has compact support. In this letter, it is shown that, for L/sup 2/(R) processes, only a one-dimensional (1-D) restriction on the marginal along time of the time-frequency distribution is necessary to guarantee the compactness of the 2DPS in the 2-D plane. As a direct consequence, it is observed that under mild conditions, a nonstationary autocorrelation function of a bandpass L/sup 2/(R) process is nearly stationary in small time intervals, The influence of this result in real-time detection of nonstationary stochastic signals is discussed.

Hybrid navigation system for long range operation

Describes a navigation system that allows long range navigation by combining two distinct modes: local positioning with respect to a long baseline array of known localization (reference points) and autonomous mode in-between reference points, relying only on sonar/Doppler and depth information. The areas of transponder-based navigation are defined by the maximum range of transponder operation. In both modes, a Kalman based design approach was chosen, using, when necessary, the available position estimates to characterize the errors associated with the filter inputs. The authors present simulation results that illustrate the systems behavior for a typical maneuvering operation.

Signal detectors for random ocean media

This paper reports on acoustic signal detection in a stationary random multipath environment. The multipath transmission channel is modeled considering that both multipath time delay and attenuation coefficients characterizing the emitter/receiver transfer function are random variables with an a priori given distribution. Under the above condition, and assuming the signal‐to‐noise ratio (SNR) is either low or high, the likelihood ratio (LR) detector structure is developed, analyzed, and interpreted. A Monte Carlo study is also carried out. For low SNR conditions, the statistical behavior of the achieved processor is evaluated and compared to that of two classical detectors: (i) the standard detector derived based on a presumed known multipath channel structure, and (ii) the ad hoc detector developed for inaccurate multipath time delay modeling assumptions.

Signal detection in the presence of inaccurate multipath time delay modeling

In this paper, a new class of signal detectors is considered whose structure is similar to the log‐likelihood detector developed under low signal‐to‐noise ratio conditions, but with different choices to the sensor filters. In the presence of incorrect delay assumptions, the performance of the log‐likelihood processor is analyzed and interpreted. Based on this study, ad hoc detectors are proposed, and their performance compared to that of the log‐likelihood structure. It is shown that, for increasing misadjustment in the delay assumptions, the performance of the proposed ad hoc detectors is superior.

A wavelet transform frequency classifier for stochastic transient signals

The paper presents a wavelet transform based frequency classifier for stochastic bandpass transient signals. Using compactly supported bases of wavelets, continuous nonstationary bandpass processes can be described by reduced dimension discrete time signal representations. We develop an optimization procedure to adapt both the sampling frequency and the discrete time wavelet filters to the continuous classes of signals involved. When compared to the classical Bayesian structures, the proposed receiver strongly reduces the required computational load. The receiver performance is accessed by Monte Carlo simulation, the probabilities of detection for each signal class, and the probability of false alarm, being computed.

Multisource delay estimation: nonstationary signals (underwater acoustics)

The authors study delay estimation in a very general framework: multiple sources, correlated noises, nonstationary random signals, and varying delays. The optimal maximum likelihood (ML) delay estimator is derived; its performance via the Cramer-Rao inequality is analyzed; and it is tested by experimentation with synthetic data. The present time-varying delay estimator extends to the nonstationary/multisource environment the estimators of L.C. Ng and Y. Bar-Shalom (1986), L.R. Kirlin and L.A. Dewey (1985), and C.H. Knapp and G.C. Carter (1976). However, the present receiver significantly departs from the correlator structures of those authors. >

Signal detection in a multiple time delay environment

A signal detection method is presented for a multipath stationary environment. The multipath transmission channel is modeled assuming a different transfer function from the source to each hydrophone of the receiving array and a low signal-to-noise ratio (SNR). Under the above framework a log-likelihood detector is developed and interpreted. The structure is conceptually equivalent to the cascade of a generalized beamformer and an energy detector. The decision about the presence or absence of an object is accomplished by comparing the output signal energy with a threshold.<<ETX>>

Efficiency of real-time Gaussian transient detectors: comparing the Karhunen-Loeve and the wavelet decompositions

In general, finite-dimensional discrete-time representations of continuous-time Gaussian transients is not complete. Such representations typically lead to suboptimal detectors, where the compromise between computational complexity and processor performance requires optimization, specially when real-time processing is mandatory. This paper proposes a procedure for the optimization of the processor parameters, using the Bhattacharyya distance to evaluate the resemblance between the original continuous-time signal and its finite dimensional discrete representation. Two different decompositions are analyzed and compared, namely the Karhunen-Loeve decomposition (KLD) and the discrete wavelet transform (DWT). It is shown that the DWT presents serious advantages when the signals to detect have a large number of important eigenvalues, which is often the case in some applications such as passive sonar.

Time delay determination: Maximum likelihood and Kalman-Bucy type structures

Time delay determination is an important problem in numerous applications. The approach taken here models the signals via linear differential equations driven by white noise. The time delays are unknown parameters modulating the received signals. The maximum likelihood estimation of the delays requires the filtering in the minimum mean square error (MMSE) sense of the signals. The problem becomes that of the joint estimation of the signals with the identification of the delays. Due to the structure of the signal model, the signal MMSE estimate is obtained via a recursive structure of the Kalman-Bucy type. The class of signals considered includes the stationary signals, to which the cross-correlation receivers are restricted. In fact, it can be shown that the receiver studied in this paper is a generalization of the cross-correlation receiver. The paper presents the general receiver structure, discussing it in the context of a specific example. The Cramer-Rao bound associated with the delay estimation is also discussed.

Detection of transient signals with unknown localization

In the context of real-time detection of transient signals, a likelihood ratio (LR) test is evaluated at every sampling interval. Performing the LR tests at a lower rate reduces significantly the computational complexity of the detection algorithm. However, in general, this simplification also leads to a strong degradation of the detector performance. For example, with a small shift error, an arriving transient may be in quadrature with its model. This degradation is particularly noticeable when the signals to detect are deterministic and sampled at a frequency close to the Nyquist rate. This letter proposes a method to overcome this limitation by using locally stationary models of the signals to detect. The resulting detectors are robust to shift errors and computationally efficient.