Related papers: Limits of Kalman Filter application in heavy taile…

This paper studies the optimal state estimation for a dynamic system, whose transfer function can be nonlinear and the input noise can be of arbitrary distribution. Our algorithm differs from the conventional extended Kalman filter (EKF)…

We consider the problem of estimating the means $\mu_i$ of $n$ random variables $Y_i \sim N(\mu_i,1)$, $i=1,\ldots ,n$. Assuming some structure on the $\mu$ process, e.g., a state space model, one may use a summary statistics for the…

State-space models are pivotal for dynamic system analysis but often struggle with outlier data that deviates from Gaussian distributions, frequently exhibiting skewness and heavy tails. This paper introduces a robust extension utilizing…

In this paper, a new filter model called set-membership Kalman filter for nonlinear state estimation problems was designed, where both random and unknown but bounded uncertainties were considered simultaneously in the discrete-time system.…

Driven by the filtering challenges in linear systems disturbed by non-Gaussian heavy-tailed noise, the robust Kalman filters (RKFs) leveraging diverse heavy-tailed distributions have been introduced. However, the RKFs rely on precise noise…

Kalman filtering can provide an optimal estimation of the system state from noisy observation data. This algorithm's performance depends on the accuracy of system modeling and noise statistical characteristics, which are usually challenging…

In this paper, the problem of state estimation, in the context of both filtering and smoothing, for nonlinear state-space models is considered. Due to the nonlinear nature of the models, the state estimation problem is generally intractable…

The extended Kalman filter (EKF) is a cornerstone of nonlinear state estimation, yet its performance is fundamentally limited by noise-model mismatch and linearization errors. We develop a residual-aware distributionally robust EKF that…

In this paper we address the problem of estimating the posterior distribution of the static parameters of a continuous time state space model with discrete time observations by an algorithm that combines the Kalman filter and a particle…

We consider two nonlinear state estimation problems in a setting where an extended Kalman filter receives measurements from two sets of sensors via two channels (2C). In the stochastic-2C problem, the channels drop measurements…

Distributed state estimation strongly depends on collaborative signal processing, which often requires excessive communication and computation to be executed on resource-constrained sensor nodes. To address this problem, we propose an…

This article explores the estimation of parameters and states for linear stochastic systems with deterministic control inputs. It introduces a novel Kalman filtering approach called Kalman Filtering with Correlated Noises Recursive…

Reliable state estimation is essential for autonomous systems operating in complex, noisy environments. Classical filtering approaches, such as the Kalman filter, can struggle when facing nonlinear dynamics or non-Gaussian noise, and even…

We consider approximate maximum likelihood parameter estimation in nonlinear state-space models. We discuss both direct optimization of the likelihood and expectation--maximization (EM). For EM, we also give closed-form expressions for the…

In this paper, we propose an approach to address the problems with ambiguity in tuning the process and observation noises for a discrete-time linear Kalman filter. Conventional approaches to tuning (e.g. using normalized estimation error…

Stochastic models in biomolecular contexts can have a state-dependent process noise covariance. The choice of the process noise covariance is an important parameter in the design of a Kalman Filter for state estimation and the theoretical…

A new ensemble filter that allows for the uncertainty in the prior distribution is proposed and tested. The filter relies on the conditional Gaussian distribution of the state given the model-error and predictability-error covariance…

This report derives a generalized, converted measurement Kalman filter for the class of filtering problems with a linear state equation and nonlinear measurement equation, for which a bijective mapping exists between the state and…

In this letter, a new filtering technique to solve a nonlinear state estimation problem has been developed. It is well known that for a nonlinear system, the prior and posterior probability density functions (pdf) are non-Gaussian in…

Structural identification and damage detection can be generalized as the simultaneous estimation of input forces, physical parameters, and dynamical states. Although Kalman-type filters are efficient tools to address this problem, the…