Related papers: Hidden AR Process and Adaptive Kalman Filter

The model of partially observed linear stochastic differential equations depending on some unknown parameters is considered. An proximation of the unobserved component is proposed. This approximation is realized in three steps. First an…

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…

We consider the problem of parameter estimation for the partially observed linear stochastic differential equation. We assume that the unobserved Ornstein-Uhlenbeck process depends on some unknown parameter and estimate the unobserved…

We consider the problem of the construction of the estimator-process of the unknown finite-dimensional parameter in the case of the observations of nonlinear autoregressive process. The estimation is done in two or three steps. First we…

We present results on parameter estimation and non-parameter estimation of the linear partially observed Gaussian system of stochastic differential equations. We propose new one-step estimators which have the same asymptotic properties as…

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 partially observed linear Gaussian system of stochastic differential equations with low noise in observations is considered. A kernel-type estimators are used for estimation of the quadratic variation of the derivative of the limit of…

We use statistical learning methods to construct an adaptive state estimator for nonlinear stochastic systems. Optimal state estimation, in the form of a Kalman filter, requires knowledge of the system's process and measurement uncertainty.…

The unscented Kalman filter is an algorithm capable of handling nonlinear scenarios. Uncertainty in process noise covariance may decrease the filter estimation performance or even lead to its divergence. Therefore, it is important to adjust…

Kalman filtering has been traditionally applied in three application areas of estimation, state estimation, parameter estimation (a.k.a. model updating), and dual estimation. However, Kalman filter is often not sufficient when experimenting…

This paper presents an adaptive Kalman filter for a linear dynamic system perturbed by an additive disturbance. The objective is to estimate both of the state and the unknown disturbance concurrently, while learning the disturbance as a…

In this paper, we consider the task of designing a Kalman Filter (KF) for an unknown and partially observed autonomous linear time invariant system driven by process and sensor noise. To do so, we propose studying the following two step…

For many nonlinear Bayesian state estimation problems, the posterior recursion is not analytically tractable, leading to algorithms that are influenced by numerical approximation errors. These algorithms depend on parameters that affect the…

For linear time-invariant systems with uncertain parameters belonging to a finite set, we present a purely deterministic approach to multiple-model estimation and propose an algorithm based on the minimax criterion using constrained…

State estimation that combines observational data with mathematical models is central to many applications and is commonly addressed through filtering methods, such as ensemble Kalman filters. In this article, we examine the signal-tracking…

Semiparametric forecasting and filtering are introduced as a method of addressing model errors arising from unresolved physical phenomena. While traditional parametric models are able to learn high-dimensional systems from small data sets,…

The problem of parameter estimation by the observations of the two-state telegraph process in the presence of white Gaussian noise is considered. The properties of estimator of the method of moments are described in the asymptotics of large…

We consider a problem of parameter estimation for the state space model described by linear stochastic differential equations. We assume that an unobservable Ornstein-Uhlenbeck process drives another observable process by the linear…

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…

The objective of this article is to study the asymptotic behavior of a new particle filtering approach in the context of hidden Markov models (HMMs). In particular, we develop an algorithm where the latent-state sequence is segmented into…