Related papers: Geometric methods for optimal sensor design
The use of Kalman filtering, as well as its nonlinear extensions, for the estimation of system variables and parameters has played a pivotal role in many fields of scientific inquiry where observations of the system are restricted to a…
Two central problems in modern control theory are the controller design problem: which deals with designing a control law for the dynamical system, and the state estimation problem (observer design problem): which deals with computing an…
Observers are well known in control theory. Originally designed to estimate the hidden states of dynamical systems given some measurements, the observers scope has been recently extended to the estimation of some unknowns, for systems…
The increasing availability of sensing techniques provides a great opportunity for engineers to design state estimation methods, which are optimal for the system under observation and the observed noise patterns. However, these patterns…
We consider a sensor scheduling and remote estimation problem with one sensor and one estimator. At each time step, the sensor makes an observation on the state of a source, and then decides whether to transmit its observation to the…
The implementation of fringe tracking for optical interferometers is inevitable when optimal exploitation of the instrumental capacities is desired. Fringe tracking allows continuous fringe observation, considerably increasing the…
Track geometry monitoring is essential for maintaining the safety and efficiency of railway operations. While Track Recording Cars (TRCs) provide accurate measurements of track geometry indicators, their limited availability and high…
The Kalman filter is an established tool for the analysis of dynamic systems with normally distributed noise, and it has been successfully applied in numerous application areas. It provides sequentially calculated estimates of the system…
This paper considers the problem of fitting the parameters of a Kalman smoother to data. We formulate the Kalman smoothing problem with missing measurements as a constrained least squares problem and provide an efficient method to solve it…
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…
Ordinary Differential Equations are a simple but powerful framework for modeling complex systems. Parameter estimation from times series can be done by Nonlinear Least Squares (or other classical approaches), but this can give…
In this paper we revisit a non-linear filter for {\em non-Gaussian} noises that was introduced in [1]. Goggin proved that transforming the observations by the score function and then applying the Kalman Filter (KF) to the transformed…
State estimation refers to determining the states of a dynamical system that starts from a noisy initial condition and evolves under process noise, based on noisy measurements and a known system model. For linear dynamical systems with…
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…
Predicting the behavior of a dynamical system from noisy observations of its past outputs is a classical problem encountered across engineering and science. For linear systems with Gaussian inputs, the Kalman filter -- the best linear…
This report provides a brief historical evolution of the concepts in the Kalman filtering theory since ancient times to the present. A brief description of the filter equations its aesthetics, beauty, truth, fascinating perspectives and…
This article examines state estimation in discrete-time nonlinear stochastic systems with finite-dimensional states and infinite-dimensional measurements, motivated by real-world applications such as vision-based localization and tracking.…
Kalman filtering is a cornerstone of estimation theory, yet learning the optimal filter under unknown and potentially singular noise covariances remains a fundamental challenge. In this paper, we revisit this problem through the lens of…
The measurement precision of the static atomic gravimetry is limited by white Gaussian noise in short term, which costs previous works an inevitable integration to reach the precision demanded. Here, we propose a statistical model based on…
This paper introduces a novel Kalman filter framework designed to achieve robust state estimation under both process and measurement noise. Inspired by the Weighted Observation Likelihood Filter (WoLF), which provides robustness against…