A convergence analysis of the modified unscented Kalman filter (UKF), used as an observer for a class of nonlinear deterministic continuous time systems, is presented. Under certain conditions, the extended Kalman filter (EKF) is an exponential observer for non-linear systems, i.e., the dynamics of the estimation error is exponentially stable. It is shown that unlike the EKF, the UKF is not an exponentially converging observer. A modification of the UKF – the unscented Kalman observer – is proposed, which is a better candidate for an observer.

This paper is a first step towards a proof of the global convergence of the high-gain version of the UKO.

中文翻译：

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关于无味卡尔曼滤波器的收敛性

提出了针对一类非线性确定性连续时间系统的观测器的改进无味卡尔曼滤波器（UKF）的收敛性分析。在某些条件下，扩展卡尔曼滤波器（EKF）是非线性系统的指数观测器，即，估计误差的动力学呈指数稳定。结果表明，与EKF不同，UKF不是指数收敛的观察者。提议对UKF（无味的Kalman观察者）进行修改，这对于观察者而言是更好的选择。

本文是证明UKO高增益版本在全球趋同的第一步。