The authors discuss the aspects of the radar target/identification problem which have made progress slow and difficult. They summarize their research program and discuss the mathematical foundations for solving the problem. To simplify the discussion, only aircraft-type targets are considered, and clutter is ignored. Target-library problems, are examined in some detail, including the proposed use of scattering-center models to mitigate problems and related electromagnetic-modeling considerations.

This paper gives an algorithm for calculating posterior probabilities using thermodynamic integration. The thermodynamic integration calculations are accomplished by annealing an ensemble of Markov chains with an adaptive schedule. The algorithm includes a method for determining “good” starting positions for the chains at each new value of the annealing parameter.

Due to recent developments in concert hall design, there is an increasing interest in the analysis of sound energy decays consisting of multiple exponential decay rates. It has been considered challenging to estimate parameters associated with double-rate (slope) decay characteristics, and even more challenging when the coupled-volume systems contain more than two decay processes. To meet the need of characterizing energy decays of multiple decay processes, this work investigates coupled-volume systems using acoustic scale-models of three coupled rooms. Two Bayesian formulations are compared using the experimentally measured sound energy decay data. A fully parameterized Bayesian formulation has been found to be capable of characterization of multiple-slope decays beyond the single-slope and double-slope energy decays. Within the Bayesian framework using this fully parameterized formulation, an in-depth analysis of likelihood distributions over multiple-dimensional decay parameter space motivates the use of Bayesian information criterion, an efficient approach to solving Bayesian model selection problems that are suitable for estimating the number of exponential decays. The analysis methods are then applied to a geometric-acoustics simulation of a conceptual concert hall. Sound energy decays more complicated than single-slope and double-slope nature, such as triple-slope decays have been identified and characterized.

The complex-envelope representation of bandpass-limited signals is used to formulate a bandpass-limited vector wave equation and a new finite-difference time-domain (FDTD) scheme that solves the bandpass-limited vector wave equation is presented. For narrow-band electromagnetic systems, this new method allows the time step to be several orders of magnitude larger than current FDTD formulations while maintaining an amplification factor equal to one. Example results obtained by this method are presented and compared with analytic solutions.

Determination of sound decay times in coupled spaces often demands considerable effort. Based on Schroeder’s backward integration of room impulse responses, it is often difficult to distinguish different portions of multirate sound energy decay functions. A model-based parameter estimation method, using Bayesian probabilistic inference, proves to be a powerful tool for evaluating decay times. A decay model due to one of the authors [N. Xiang, J. Acoust. Soc. Am. 98, 2112–2121 (1995)] is extended to multirate decay functions. Following a summary of Bayesian model-based parameter estimation, the present paper discusses estimates in terms of both synthesized and measured decay functions. No careful estimation of initial values is required, in contrast to gradient-based approaches. The resulting robust algorithmic estimation of more than one decay time, from experimentally measured decay functions, is clearly superior to the existing nonlinear regression approach.

This paper applies Bayesian probability theory to determination of the decay times in coupled spaces. A previous paper [N. Xiang and P. M. Goggans, J. Acoust. Soc. Am. 110, 1415–1424 (2001)] discussed determination of the decay times in coupled spaces from Schroeder’s decay functions using Bayesian parameter estimation. To this end, the previous paper described the extension of an existing decay model [N. Xiang, J. Acoust. Soc. Am. 98, 2112–2121 (1995)] to incorporate one or more decay modes for use with Bayesian inference. Bayesian decay time estimation will obtain reasonable results only when it employs an appropriate decay model with the correct number of decay modes. However, in architectural acoustics practice, the number of decay modes may not be known when evaluating Schroeder’s decay functions. The present paper continues the endeavor of the previous paper to apply Bayesian probability inference for comparison and selection of an appropriate decay model based upon measured data. Following a summary of Bayesian model comparison and selection, it discusses selection of a decay model in terms of experimentally measured Schroeder’s decay functions. The present paper, along with the Bayesian decay time estimation described previously, suggests that Bayesian probability inference presents a suitable approach to the evaluation of decay times in coupled spaces.