A scalable Kalman filter algorithm: Trustworthy analysis on constrained least square model

Abstract

Summary Kalman filter (KF) is one of the most important and common estimation algorithms. We introduce an innovative designing of Kalman filter algorithm based on domain decomposition (we call it DD‐KF). DD‐KF involves decomposition of the whole computational problem, partitioning of the solution and a slight modification of KF algorithm allowing a correction at run‐time of local solutions. The resulted parallel algorithm consists of concurrent copies of KF algorithm, each one requiring the same amount of computations on each subdomain and an exchange of boundary conditions between adjacent subdomains. Main advantage of this approach is that it can be potentially applied in a moderately nonintrusive manner to existing codes for tracking and controlling systems in location, navigation, in computer graphics and in much more state estimation problems. To highlight the capability of DD‐KF of exploiting the computing power provided by future designs of microprocessors based on multi/many‐cores CPU/GPU technologies, we consider DD both at physical core level and at microprocessor level and we discuss scalability of DD‐KF algorithm at coarse and fine grained level. Throughout the present work, we derive and discuss DD‐KF algorithm for solving constrained least square model, which underlies any data sampling and estimation problem.