Parallel-in-Time Kalman Smoothing Using Orthogonal Transformations

TL;DR

This paper introduces a numerically stable parallel Kalman smoother that leverages novel QR factorization and selective-inversion algorithms, achieving significant speedups and better scalability on multi-core systems.

Contribution

It presents a new parallel Kalman smoothing algorithm using orthogonal transformations, improving stability and scalability over previous methods.

Findings

Achieves up to 47x speedup on 64 cores.

Scales well on both Intel and ARM multi-core servers.

Performs more arithmetic but is faster overall than previous parallel smoothers.

Abstract

We present a numerically-stable parallel-in-time linear Kalman smoother. The smoother uses a novel highly-parallel QR factorization for a class of structured sparse matrices for state estimation, and an adaptation of the SelInv selective-inversion algorithm to evaluate the covariance matrices of estimated states. Our implementation of the new algorithm, using the Threading Building Blocks (TBB) library, scales well on both Intel and ARM multi-core servers, achieving speedups of up to 47x on 64 cores. The algorithm performs more arithmetic than sequential smoothers; consequently it is 1.8x to 2.5x slower on a single core. The new algorithm is faster and scales better than the parallel Kalman smoother proposed by S\"arkk\"a and Garc\'{\i}a-Fern\'andez in 2021.