This paper describes the coupling of Bayesian learning methods with realistic statistical models for randomly scattered signals. Such a formulation enables efficient learning of signal properties observed at sensors in urban and other complex environments. It also provides a realistic assessment of the uncertainties in the sensed signal characteristics, which is useful for calculating target class probabilities in automated target recognition. In the Bayesian formulation, the physics-based model for the random signal corresponds to the likelihood function, whereas the distribution for the uncertain signal parameters corresponds to the prior. Single and multivariate distributions for randomly scattered signals (as appropriate to single- and multiple-receiver problems, respectively) are reviewed, and it is suggested that the log-normal and gamma distributions are the most useful due to their physical applicability and the availability of Bayesian conjugate priors, which enable efficient refinement of the signal hyperparameters. Realistic simulations for sound propagation are employed to illustrate the Bayesian processing. The processing is found to be robust to mismatches between the simulated signal distributions and the assumed forms of the likelihood functions.
KEYWORDS: Atmospheric propagation, Acoustics, Data modeling, Radio propagation, 3D modeling, Java, Atmospheric modeling, Sensors, Refraction, Systems modeling
A computational framework is described for modeling acoustic and radio-frequency (RF) signal propagation in complex environments, such as urban, mountainous, and forested terrain. In such environments, the influences of three-dimensional atmospheric fields and terrain variations must be addressed. The approach described here involves creation of a full environmental data representation (abstraction layer), which can be initialized with many different environmental data resources, including weather forecasts, digital terrain elevations, landcover types, and soil properties. The environmental representation is then converted into the parameters needed for particular signal modalities and classes of propagation algorithms. In this manner, execution of the signal propagation calculations is isolated from the sources of environmental data, so that all models will function with all types of environmental data. The formulation of the acoustic (infrasound and audible) and RF (VHF/UHF/SHF) feature spaces is also described. Example calculations involving infrasound propagation with 3D weather fields and RF propagation in mountainous terrain are provided.
KEYWORDS: Signal processing, Signal to noise ratio, Atmospheric propagation, Turbulence, Probability theory, Receivers, Scattering, Sensor performance, Sensors, Statistical analysis, Interference (communication), Environmental sensing, Signal detection
The receiver operating characteristic (ROC curve), which is a plot of the probability of detection as a function of the probability of false alarm, plays a key role in the classical analysis of detector performance. However, meaningful characterization of the ROC curve is challenging when practically important complications such as variations in source emissions, environmental impacts on the signal propagation, uncertainties in the sensor response, and multiple sources of interference are considered. In this paper, a relatively simple but realistic model for scattered signals is employed to explore how parametric uncertainties impact the ROC curve. In particular, we show that parametric uncertainties in the mean signal and noise power substantially raise the tails of the distributions; since receiver operation with a very low probability of false alarm and a high probability of detection is normally desired, these tails lead to severely degraded performance. Because full a priori knowledge of such parametric uncertainties is rarely available in practice, analyses must typically be based on a finite sample of environmental states, which only partially characterize the range of parameter variations. We show how this effect can lead to misleading assessments of system performance. For the cases considered, approximately 64 or more statistically independent samples of the uncertain parameters are needed to accurately predict the probabilities of detection and false alarm. A connection is also described between selection of suitable distributions for the uncertain parameters, and Bayesian adaptive methods for inferring the parameters.
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