面向预测的卡尔曼滤波

Variational Bayesian Adaptation of Noise Covariances in Non-Linear Kalman Filtering

This paper is considered with joint estimation of state and time-varying noise covariance matrices in non-linear stochastic state space models. We present a variational Bayes and Gaussian filtering based algorithm for efficient computation of the approximate filtering posterior distributions. The Gaussian filtering based formulation of the non-linear state space model computation allows usage of efficient Gaussian integration methods such as unscented transform, cubature integration and Gauss-Hermite integration along with the classical Taylor series approximations. The performance of the algo…

Kalman Filtering With Censored Measurements

This paper concerns Kalman filtering when the measurements of the process are censored. The censored measurements are addressed by the Tobit model of Type I and are one-dimensional with two censoring limits, while the (hidden) state vectors are multidimensional. For this model, Bayesian estimates for the state vectors are provided through a recursive algorithm of Kalman filtering type. Experiments are presented to illustrate the effectiveness and applicability of the algorithm. The experiments show that the proposed method outperforms other filtering methodologies in minimizing the computation…

Numerical Gaussian process Kalman filtering

In this manuscript we introduce numerical Gaussian process Kalman filtering (GPKF). Numerical Gaussian processes have recently been developed to simulate spatiotemporal models. The contribution of this paper is to embed numerical Gaussian processes into the recursive Kalman filter equations. This embedding enables us to do Kalman filtering on infinite-dimensional systems using Gaussian processes. This is possible because i) we are obtaining a linear model from numerical Gaussian processes, and ii) the states of this model are by definition Gaussian distributed random variables. Convenient prop…

Kalman Filtering with Gaussian Processes Measurement Noise

Real-world measurement noise in applications like robotics is often correlated in time, but we typically assume i.i.d. Gaussian noise for filtering. We propose general Gaussian Processes as a non-parametric model for correlated measurement noise that is flexible enough to accurately reflect correlation in time, yet simple enough to enable efficient computation. We show that this model accurately reflects the measurement noise resulting from vision-based Simultaneous Localization and Mapping (SLAM), and argue that it provides a flexible means of modeling measurement noise for a wide variety of …

The discriminative Kalman filter for nonlinear and non-Gaussian sequential Bayesian filtering

The Kalman filter (KF) is used in a variety of applications for computing the posterior distribution of latent states in a state space model. The model requires a linear relationship between states and observations. Extensions to the Kalman filter have been proposed that incorporate linear approximations to nonlinear models, such as the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). However, we argue that in cases where the dimensionality of observed variables greatly exceeds the dimensionality of state variables, a model for $p(\text{state}|\text{observation})$ proves bot…

基于扩散分数匹配的观测噪声误设定下鲁棒集成卡尔曼滤波

Robust ensemble Kalman filtering under observation noise misspecification via diffusion score matching

针对动态系统贝叶斯滤波中观测噪声误设定问题，提出利用扩散分数匹配调整分析步信息处理的鲁棒卡尔曼滤波器，理论证明其在线性高斯状态空间中的共轭性、鲁棒性、协方差稳定性及高维一致性，并通过集成近似实现EnKF、ESRF和LETKF变体，在目标跟踪、Lorenz 63和Lorenz 96系统中验证了鲁棒性与稳定性的权衡。