Related papers: The Kalman Filter: a didactical overview
Filters, especially wide range of Kalman Filters have shown their impacts on predicting variables of stochastic models with higher accuracy then traditional statistic methods. Updating mean and covariance each time makes Bayesian inferences…
This letter shows that the following three classes of recursive state estimation filters: standard filters, such as the extended Kalman filter; iterated filters, such as the iterated unscented Kalman filter; and dynamically iterated…
Common filters are usually based on the linear approximation of the optimal minimum mean square error estimator. The Extended and Unscented Kalman Filters handle nonlinearity through linearization and unscented transformation, respectively,…
Kalman filtering is a classic state estimation technique used in application areas such as signal processing and autonomous control of vehicles. It is now being used to solve problems in computer systems such as controlling the voltage and…
The models of partially observed linear stochastic differential equations with unknown initial values of the non-observed component are considered in two situations. In the first problem, the initial value is deterministic, and in the…
Both constrained and unconstrained optimization problems regularly appear in recursive tracking problems engineers currently address -- however, constraints are rarely exploited for these applications. We define the Kalman Filter and…
Various methods have been proposed for the nonlinear filtering problem, including the extended Kalman filter (EKF), iterated extended Kalman filter (IEKF), unscented Kalman filter (UKF) and iterated unscented Kalman filter (IUKF). In this…
In this paper, we present the optimization formulation of the Kalman filtering and smoothing problems, and use this perspective to develop a variety of extensions and applications. We first formulate classic Kalman smoothing as a least…
The input-parameter-state estimation capabilities of a novel unscented Kalman filter is examined herein on both linear and nonlinear systems. The unknown input is estimated in two stages within each time step. Firstly, the predicted dynamic…
The unscented Kalman filter is a nonlinear estimation algorithm commonly used in navigation applications. The prediction of the mean and covariance matrix is crucial to the stable behavior of the filter. This prediction is done by…
The Kalman filter and its extensions are used in a vast number of aerospace and navigation applications for nonlinear state estimation of time series. In the literature, different approaches have been proposed to exploit the structure of…
Kalman filter is presumably one of the most important and extensively used filtering techniques in modern control systems. Yet, nearly all current variants of Kalman filters are formulated in the Euclidean space $\mathbb{R}^n$, while many…
This document contains a concise and unified reference for one of the existing mechanizations of the UD Kalman filter. The associated matrix algorithms are also included along with the corresponding references.
Many nonlinear extensions of the Kalman filter, e.g., the extended and the unscented Kalman filter, reduce the state densities to Gaussian densities. This approximation gives sufficient results in many cases. However, this filters only…
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…
The Kalman filter is a fundamental filtering algorithm that fuses noisy sensory data, a previous state estimate, and a dynamics model to produce a principled estimate of the current state. It assumes, and is optimal for, linear models and…
Filtering is concerned with online estimation of the state of a dynamical system from partial and noisy observations. In applications where the state of the system is high dimensional, ensemble Kalman filters are often the method of choice.…
This article develops a comprehensive framework for stability analysis of a broad class of commonly used continuous and discrete time-filters for stochastic dynamic systems with non-linear state dynamics and linear measurements under…
The well-known Kalman filters model dynamical systems by relying on state-space representations with the next state updated, and its uncertainty controlled, by fresh information associated with newly observed system outputs. This paper…
The possible methodologies to handle the uncertain parameter are reviewed. The core idea of the desensitized Kalman filter is introduced. A new cost function consisting of a posterior covariance trace and trace of a weighted norm of the…