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This work introduces an algorithm for state estimation on manifolds within the framework of the Kalman filter. Its primary objective is to provide a methodology enabling the evaluation of the precision of existing Kalman filter variants…

A recursive state estimation procedure is derived for a linear time varying system with both parametric uncertainties and stochastic measurement droppings. This estimator has a similar form as that of the Kalman filter with intermittent…

State estimation in stochastic dynamical systems with noisy measurements is a challenge. While the Kalman filter is optimal for linear systems with independent Gaussian white noise, real-world conditions often deviate from these…

State estimation is a fundamental problem in control and signal processing, for which the Kalman Filter provides an optimal solution under linear dynamics, Gaussian noise, and known noise covariances. However, these assumptions often fail…

This paper considers the Linear Minimum Variance recursive state estimation for the linear discrete time dynamic system with random state transition and measurement matrices, i.e., random parameter matrices Kalman filtering. It is shown…

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…

In this paper we are concerned with the error-covariance lower-bounding problem in Kalman filtering: a sensor releases a set of measurements to the data fusion/estimation center, which has a perfect knowledge of the dynamic model, to allow…

Since the innovation of the ubiquitous Kalman filter more than five decades back it is well known that to obtain the best possible estimates the tuning of its statistics $X_0$, $P_0$, $\Theta$, $R$ and $Q$ namely initial state and…

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…

In this paper, we present a novel optimization algorithm designed specifically for estimating state-space models to deal with heavy-tailed measurement noise and constraints. Our algorithm addresses two significant limitations found in…

Contemporary data assimilation often involves millions of prediction variables. The classical Kalman filter is no longer computationally feasible in such a high dimensional context. This problem can often be resolved by exploiting the…

This paper develops a robust extended Kalman filter to estimate the rotor angles and the rotor speeds of synchronous generators of a multimachine power system. Using a batch-mode regression form, the filter processes together predicted…

State estimation in the presence of uncertain or data-driven noise distributions remains a critical challenge in control and robotics. Although the Kalman filter is the most popular choice, its performance degrades significantly when…

Here we revisit the classic problem of linear quadratic estimation, i.e. estimating the trajectory of a linear dynamical system from noisy measurements. The celebrated Kalman filter gives an optimal estimator when the measurement noise is…

Recently, it has been demonstrated experimentally that adaptive estimation of a continuously varying optical phase provides superior accuracy in the phase estimate compared to static estimation. Here, we show that the mean-square error in…

The Derivative-free nonlinear Kalman Filter is proposed for state estimation and fault diagnosis in distributed parameter systems and particularly in dynamical systems described by partial differential equations of the nonlinear wave type.…

This paper presents a novel Wasserstein distributionally robust control and state estimation algorithm for partially observable linear stochastic systems, where the probability distributions of disturbances and measurement noises are…

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…

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…

In this paper, we study the problem of estimating the state of a dynamic state-space system where the output is subject to quantization. We compare some classical approaches and a new development in the literature to obtain the filtering…