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Kalman filters provide a straightforward and interpretable means to estimate hidden or latent variables, and have found numerous applications in control, robotics, signal processing, and machine learning. One such application is neural…

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…

This document presents the study of the problem of location and trajectory that a robot must follow. It focuses on applying the Kalman filter to achieve location and trajectory estimation in an autonomous mobile differential robot. The…

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 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…

This study considers the object localization problem and proposes a novel multiparticle Kalman filter to solve it in complex and symmetric environments. Two well-known classes of filtering algorithms to solve the localization problem are…

A Kalman filter can be used to determine material parameters using uncertain experimental data. However, starting with inappropriate initial values for material parameters might include false local attractors or even divergence. Also,…

Large-scale distributed systems such as sensor networks, often need to achieve filtering and consensus on an estimated parameter from high-dimensional measurements. Running a Kalman filter on every node in such a network is computationally…

Kalman filtering is a widely used framework for Bayesian estimation. The partitioned update Kalman filter applies a Kalman filter update in parts so that the most linear parts of measurements are applied first. In this paper, we generalize…

In an age of exponentially increasing data generation, performing inference tasks by utilizing the available information in its entirety is not always an affordable option. The present paper puts forth approaches to render tracking of…

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…

Recent researches in data assimilation lead to the introduction of the parametric Kalman filter (PKF): an implementation of the Kalman filter, where the covariance matrices are approximated by a parameterized covariance model. In the PKF,…

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…

We present a step by step mathematical derivation of the Kalman filter using two different approaches. First, we consider the orthogonal projection method by means of vector-space optimization. Second, we derive the Kalman filter using…

Most Kalman filter extensions assume Gaussian noise and when the noise is non-Gaussian, usually other types of filters are used. These filters, such as particle filter variants, are computationally more demanding than Kalman type filters.…

Quantum algorithms offer significant speed-ups over their classical counterparts in various applications. In this paper, we develop quantum algorithms for the Kalman filter widely used in classical control engineering using the block…

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…

Many interventional surgical procedures rely on medical imaging to visualise and track instruments. Such imaging methods not only need to be real-time capable, but also provide accurate and robust positional information. In ultrasound…

This paper presents a new optimal filter namely past observation-based extended Kalman filter for the problem of localization of Internet-based mobile robot in which the control input and the feedback measurement suffer from communication…

In this paper we present a new Kalman filter extension for state update called Partitioned Update Kalman Filter (PUKF). PUKF updates the state using multidimensional measurements in parts. PUKF evaluates the nonlinearity of the measurement…