Bayesian state estimation in the presence of slow-rate integrated measurement

Abstract

This paper presents parallel-in-time state estimation methods for systems with Slow-Rate inTegrated Measurements (SRTM). Integrated measurements are common in various applications, and they appear in analysis of data resulting from processes that require material collection or integration over the sampling period. Current state estimation methods for SRTM are inherently sequential, preventing temporal parallelization in their standard form. This paper proposes parallel Bayesian filters and smoothers for linear Gaussian SRTM models. For that purpose, we develop a novel smoother for SRTM models and develop parallel-in-time filters and smoother for them using an associative scan-based parallel formulation. Empirical experiments ran on a GPU demonstrate the superior time complexity of the proposed methods over traditional sequential approaches.

Parameter estimation for nonlinear systems with multirate measurements and random delays

“…Guo and Huang 4 proposed a variable dimension unscented Kalman filter to estimate the states with infrequent, delayed, and integral measurements for a nonlinear system. Also, the problem of fast‐rate instantaneous state estimation for linear and nonlinear systems were addressed in Reference 5 and 6, respectively. Both Salehi et al 5 and Yaghoobi et al 6 formulated the problem when the only available measurements are in integrated form with no delay.…”

“…Also, the problem of fast‐rate instantaneous state estimation for linear and nonlinear systems were addressed in Reference 5 and 6, respectively. Both Salehi et al 5 and Yaghoobi et al 6 formulated the problem when the only available measurements are in integrated form with no delay. We also note that nonlinear observers have been explored for state estimation in multirate systems 7–10 .…”