Parallel state estimation for systems with integrated measurements

TL;DR

This work tackles state estimation for systems with Slow-Rate Integrated Measurements by developing parallel-in-time Bayesian filtering and smoothing methods tailored to SRTMs. It introduces a novel smoothing approach for SRTMs and a parallel-in-time formulation based on associative scans, achieving a theoretical time complexity of $O(\log N)$. The methods separate slow-rate and fast-rate dynamics, deriving parallel IMKF and IMS that leverage interval batching and cross-interval couplings, with closed-form expressions for linear Gaussian models. GPU experiments on a CSTR benchmark demonstrate speedups over sequential methods and competitive accuracy, highlighting the practical viability of real-time estimation in integrated-measurement systems.

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.

Figures (2)

• Figure 1: Graphical representation of one interval of SSM in a SRTM system.
• Figure 2: GPU run time comparison. The average RMSE over $100$ runs for $N=200$ is $1.689$ for IMKF and $1.597$ for IMS, respectively.

Theorems & Definitions (6)

• Definition 1
• Definition 2
• Remark 1
• Remark 2
• Remark 3
• Remark 4