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In many physical applications, the system's state varies with spatial variables as well as time. The state of such systems is modelled by partial differential equations and evolves on an infinite-dimensional space. Systems modelled by…

Accurate state estimates are required for increasingly complex systems, to enable, for example, feedback control. However, available state estimation schemes are not necessarily real-time feasible for certain large-scale systems. Therefore,…

In this article, we consider the implications of unobservable subspaces in the construction of a Kalman filter. In particular, we consider dynamical systems which are invariant with respect to a group action, and which are therefore…

Uncertain parameters of state-space models have always been a considerable problem. Consider Kalman filter (CKF) and desensitized Kalman filter (DKF) are two methods to solve this problem. Based on the sensitivity matrix respected to the…

Conventional Bayesian estimation requires an accurate stochastic model of a system. However, this requirement is not always met in many practical cases where the system is not completely known or may differ from the assumed model. For such…

The Extended Kalman Filter (EKF) is a well established technique for position and velocity estimation. However, the performance of the EKF degrades considerably in highly non-linear system applications as it requires local linearisation in…

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…

A Schmidt filter is a modification of the Kalman filter that allows to append system parameters as states and considers their uncertainty effect in the filtering process without attempting to estimate such parameters. The states that are…

In this work, we consider a sensor selection drawn at random by a sampling with replacement policy for a linear time-invariant dynamical system subject to process and measurement noise. We employ the Kalman filter to estimate the state of…

This paper proposes a simple, accurate and computationally efficient method to apply the ordinary unscented Kalman filter developed in Euclidean space to systems whose dynamics evolve on manifolds.We use the mathematical theory called…

This article presents an up-to-date tutorial review of nonlinear Bayesian estimation. State estimation for nonlinear systems has been a challenge encountered in a wide range of engineering fields, attracting decades of research effort. To…

Accurate estimation of power system dynamics is very important for the enhancement of power system reliability, resilience, security, and stability of power system. With the increasing integration of inverter-based distributed energy…

The Kalman filter (KF) provides optimal recursive state estimates for linear-Gaussian systems and underpins applications in control, signal processing, and others. However, it is vulnerable to outliers in the measurements and process noise.…

This paper revisits the problem of orientation estimation for rigid bodies through a novel framework based on scalar measurements. Unlike traditional vector-based methods, the proposed approach enables selective utilization of only the…

This paper presents an approach for simultaneous estimation of the state and unknown parameters in a sequential data assimilation framework. The state augmentation technique, in which the state vector is augmented by the model parameters,…

Knowledge of remaining battery charge is fundamental to electric vehicle deployment. Accurate measurements of state-of-charge (SOC) cannot be directly obtained, and estimation methods must be used instead. This requires both a good model of…

Global Positioning System (GPS) and inertial measurement unit (IMU) sensors are commonly integrated using the extended Kalman filter (EKF), for achieving better navigation performance. However, because of nonlinearity, the performance of…

Existing state estimation algorithms for legged robots that rely on proprioceptive sensors often overlook foot slippage and leg deformation in the physical world, leading to large estimation errors. To address this limitation, we propose a…

Switching Kalman Filters (SKF) are well known for their ability to solve the piecewise linear dynamic system estimation problem using the standard Kalman Filter (KF). Practical SKFs are heuristic, approximate filters that are not guaranteed…

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…