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.

中文翻译：

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一种可扩展的卡尔曼滤波器算法：约束最小二乘模型的可信分析

卡尔曼滤波器（KF）是最重要和最常见的估计算法之一。我们介绍了一种基于域分解的卡尔曼滤波器算法的创新设计（我们称之为 DD-KF）。DD-KF 涉及整个计算问题的分解、解的划分和 KF 算法的轻微修改，允许在运行时对局部解进行修正。生成的并行算法由 KF 算法的并发副本组成，每个副本都需要对每个子域进行相同数量的计算，并在相邻子域之间交换边界条件。这种方法的主要优点是它可以以适度非侵入性的方式潜在地应用于用于跟踪和控制位置、导航、计算机图形和更多状态估计问题中的系统的现有代码。为了突出 DD-KF 利用基于多核/多核 CPU/GPU 技术的微处理器未来设计提供的计算能力的能力，我们在物理核心级别和微处理器级别考虑了 DD，并讨论了 DD-的可扩展性粗粒度和细粒度的 KF 算法。在目前的工作中，我们推导出并讨论了用于求解约束最小二乘模型的 DD-KF 算法，这是任何数据采样和估计问题的基础。