This paper proposes a novel and efficient key conditional quotient filter (KCQF) for the estimation of state in the nonlinear system which can be either Gaussian or non-Gaussian, and either Markovian or non-Markovian. The core idea of the proposed KCQF is that only the key measurement conditions, rather than all measurement conditions, should be used to estimate the state. Based on key measurement conditions, the quotient-form analytical integral expressions for the conditional probability density function, mean, and variance of state are derived by using the principle of probability conservation, and are calculated by using the Monte Carlo method, which thereby constructs the KCQF. Two nonlinear numerical examples were given to demonstrate the superior estimation accuracy of KCQF, compared to seven existing filters.

翻译：本文提出了一种新颖高效的关键条件商滤波器，用于估计非线性系统的状态，该系统可以是高斯或非高斯的，也可以是马尔可夫或非马尔可夫的。所提出的KCQF的核心思想是，仅使用关键测量条件而非所有测量条件来估计状态。基于关键测量条件，利用概率守恒原理推导了状态的条件概率密度函数、均值与方差的商形式解析积分表达式，并通过蒙特卡洛方法进行计算，从而构建了KCQF。通过两个非线性数值算例，与七种现有滤波器进行比较，验证了KCQF在估计精度上的优越性。