No abstract

For an ocean sound channel whose environmental parameters depend not only on depth, but in a gradual fashion also on range, the wave equation may be separated by the adiabatic range variation method of Pierce [J. Acoust. Soc. Am. 37, 19 (1965)]. This method is used here to calculate underwater sound propagation in a channel with arbitrary (but gradual) range dependence, and also with arbitrary depth dependence of the sound velocity profile, by employing Airy function solutions of segmentwise linearized problems. Our results are illustrated for a realistic deep-water propagation case with profile data collected in the western North Atlantic, as well as a shallow-water example from the Norwegian Sea, and compared against the experimental transmission loss data, and the results of calculations using other methods for the same cases.

We present a new set of Kalman filters that posit near constant-velocity motion in spherical coordinates. Since the filter operates in spherical coordinates, a new nonlinear dynamic motion equation is developed along with a linear observation equation. Specific filter implementations include a spherical extended Kalman filter (KF) and a spherical sigma point Kalman filter structure that includes the unscented, spherical simplex and Gauss-Hermite KF's. The performance of the filters are demonstrated for a target that maneuvers in three dimensions and compared to similar results from their Cartesian filter counterparts.

This is the first part of a three‐part article examining methods for Bayesian estimation and tracking. This first part presents the general theory of Bayesian estimation where we show that Bayesian estimation methods can be divided into two very general classes: the first class where the observation conditioned posterior densities are propagated in time through a predictor/corrector method; and the second class where the first two moments are propagated in time, with state and observation moment prediction steps followed by state moment update steps that use the latest observations. We show how the moment propagation method leads to very general linear and extended Kalman filters that are applicable to non‐Gaussian densities that meet several restrictions. In Part 2 of this article we will show that for Gaussian densities, with the expansion of all nonlinear functions in polynomials, the moment propagation method leads to several well‐known Kalman filter methods. In Part 3, we will show that approximating a density by a set of Monte Carlo samples leads to particle filter methods, where the posterior density is propagated in time and moment integrals are approximated by sample moments. WIREs Comput Stat 2012 doi: 10.1002/wics.1211 This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory

This is the second part of a three part article examining methods for Bayesian estimation and tracking. In the first part we presented the general theory of Bayesian estimation where we showed that Bayesian estimation methods can be divided into two very general classes: a class where the observation conditioned posterior densities are propagated in time through a predictor/corrector method; and a second class where the first two moments are propagated in time, with state and observation moment prediction steps followed by state moment update steps that use the latest observations. In this second part, we make the assumption that all densities are Gaussian and, after applying an affine transformation and approximating all nonlinear functions by interpolating polynomials, we recover the sigma‐point class of Kalman filters, including the unscented, spherical simplex, and Gauss‐Hermite Kalman filters. In part 3, we will show that approximating a density by a set of Monte Carlo samples leads to particle filter methods, where the posterior density is propagated in time and moment integrals are approximated by sample moments. WIREs Comput Stat 2012 doi: 10.1002/wics.1215 This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory