In this paper, a new filter in the nonlinear Kalman filtering framework is proposed. The new filter is referred to as the lattice Kalman filter (LKF) and is based on a class of quasi-Monte Carlo (QMC) methods known as lattice rules. The proposed LKF method uses the Korobov type lattice rule to deterministically generate sample points that are randomly shifted based on the Cranley-Patterson shift method in order to approximate multi-dimensional integrals in the Gaussian filtering context. The mathematical formulation of the proposed LKF method as well as its error bound propagation are discussed. To evaluate the efficiency of the LKF, it is applied on a nonlinear aerospace system and compared with four other well-known methods presented in the literature. Simulation results demonstrate LKF uses significantly fewer sampling points yielding a significantly lower computational burden than another variant of QMC filter while maintaining the estimation accuracy. Furthermore, it provides asymptotically similar results to the unscented Kalman filter (UKF) but with less computational complexity, which is an important consideration in real applications.

中文翻译：

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 格子卡尔曼滤波器


本文提出了一种非线性卡尔曼滤波框架中的新滤波器。新滤波器称为格卡尔曼滤波器 (LKF)，基于一类称为格规则的准蒙特卡罗 (QMC) 方法。所提出的 LKF 方法使用 Korobov 型晶格规则来确定性地生成基于 Cranley-Patterson 移位方法随机移位的样本点，以便在高斯滤波上下文中逼近多维积分。讨论了所提出的 LKF 方法的数学公式及其误差界传播。为了评估 LKF 的效率，将其应用于非线性航空航天系统，并与文献中提出的其他四种众所周知的方法进行比较。仿真结果表明，LKF 使用明显更少的采样点，与 QMC 滤波器的另一种变体相比，计算负担显着降低，同时保持估计精度。此外，它提供了与无迹卡尔曼滤波器（UKF）渐近相似的结果，但计算复杂度较低，这是实际应用中的一个重要考虑因素。