3D Reflectivity Reconstruction by Means of Spatially Distributed Kalman Filters

Abstract

Abstract-In seismic, radar, and sonar imaging the exact determination of the reflectivity distribution is usually intractable so that approximations have to be applied. A method called synthetic aperture focusing technique (SAFT) is typically used for such applications as it provides a fast and simple method to reconstruct (3D) images. Nevertheless, this approach has several drawbacks such as causing image artifacts as well as offering no possibility to model system-specific uncertainties.In this paper, a statistical approach is derived, which models the region of interest as a probability density function (PDF) representing spatial reflectivity occurrences. To process the nonlinear measurements, the exact PDF is approximated by well-placed Extended Kalman Filters allowing for efficient and robust data processing.The performance of the proposed method is demonstrated for a 3D ultrasound computer tomograph and comparisons are carried out with the SAFT image reconstruction.

Distributed Kalman filtering: a bibliographic review

“…In [36, 37], distributed recursive mean‐square error optimal quantiser‐estimator based on the quantised observations is presented. Other DKF applications can be seen in [1, 38–65].…”

Distributed Kalman Filtering

“…Other DKF applications can be seen in [335], [336], [338], [339] . [38], [39], [40], [41], [42], [43], [44], [105], [106], [109], [114], [119], [156], [179], [191], [197], [213], [214], [215], [216], [221], [233], [237] , [238] and [242]. [151] • Distributed Kalman-type processing scheme essentially makes use of the fact that the sensor measurements do not enter into the update equation for the estimation error covariance matrices [152] • DKF fusion with weighted covariance approach [158] • DKF fusion with passive packet loss or initiative intermittent communications from local estimators to a fusion center while the process noise does exist [162] • For each Kalman update, an infinite number of consensus steps to restricted to one [202] [203] • For each Kalman update, state estimates are additionally exchanged [204] • Only the estimates at each Kalman update over-head are exchanged [205] • Analyzes the number of messages to exchange between successive updates in DKF [206] • Global Optimality of DKF fusion exactly equal to the corresponding centralized optimal Kalman filtering fusion [276] • A parallel and distributed state estimation structure developed from an hierarchical estimation structu...…”