Cramer-Rao bound for location systems in multipath environments

The Cramer-Rao lower bound for source localization is studied in the context of multipath stochastic sources, multipath propagation, and observations, in an array of sensors. A general expression is derived and then specialized to simpler configurations and related to results previously reported in the literature. The special case of a single stochastic source in a multipath environment is treated. The relative importance for source localization of the temporal (multipath) and spatial (array baseline) structures of the incoming wavefield is assessed. It is shown that for an array of K sensors the multipath contribution to the Fisher information matrix can be interpreted as the contribution of K independent arrays whose size depends on the number of spatially resolved replicas. The degradation due to unknown source spectra is analyzed. When the source spectrum is completely arbitrary, source location is not possible with a single sensor. If a parametric form of the source spectrum is available, the multipath structure can be used to locate the acoustic source     

Bayesian Local Kriging

We consider the problem of constructing metamodels for computationally expensive simulation codes; that is, we construct interpolators/predictors of functions values (responses) from a finite collection of evaluations (observations). We use Gaussian process (GP) modeling and kriging, and combine a Bayesian approach, based on a finite set GP models, with the use of localized covariances indexed by the point where the prediction is made. Our approach is not based on postulating a generative model for the unknown function, but by letting the covariance functions depend on the prediction site, it provides enough flexibility to accommodate arbitrary nonstationary observations. Contrary to kriging prediction with plug-in parameter estimates, the resulting Bayesian predictor is constructed explicitly, without requiring any numerical optimization, and locally adjusts the weights given to the different models according to the data variability in each neighborhood. The predictor inherits the smoothness properties of the covariance functions that are used and its superiority over plug-in kriging, sometimes also called empirical-best-linear-unbiased predictor, is illustrated on various examples, including the reconstruction of an oceanographic field over a large region from a small number of observations. Supplementary materials for this article are available online.     

Ambiguity in radar and sonar

We introduce a new ambiguity function for general parameter estimation problems in curved exponential families. We focus the presentation on passive and active radar and sonar location mechanisms. The new definition is based on the Kullback (1978) directed divergence and reflects intrinsic properties of the model. It is independent of any specific algorithms used in the processing of the signals. For the active single target problem, we show that our definition is equivalent to Woodward's (1953) radar narrow-band ambiguity function. However, the new ambiguity is much broader, handling radar/sonar problems when there are unknown parameters (e.g., unknown power level in active systems), when the signals are random (e.g., passive systems), when the signals are wideband, or when there are model mismatches. We illustrate the new ambiguity in localization problems in multipath channels