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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,…
The measure timetable plays a critical role for the accuracy of the estimator. This article deals with the optimization of the schedule of measures for observing a random process in time using a Kalman filter, when the length of the process…
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…
The Kalman filter is the most powerful tool for estimation of the states of a linear Gaussian system. In addition, using this method, an expectation maximization algorithm can be used to estimate the parameters of the model. However, this…
Time-scale theory, due to its ability to unify the continuous and discrete cases, allows handling intractable non-uniform measurements, such as intermittent received signals. In this work, we address the state estimation problem of a…
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…
Filtering is a widely used methodology for the incorporation of observed data into time-evolving systems. It provides an online approach to state estimation inverse problems when data is acquired sequentially. The Kalman filter plays a…
We study causal waveform estimation (tracking) of time-varying signals in a paradigmatic atomic sensor, an alkali vapor monitored by Faraday rotation probing. We use Kalman filtering, which optimally tracks known linear Gaussian stochastic…
In this article, we present a structured Kalman filter associated with the transformation matrix for observable Kalman canonical decomposition from conventional Kalman filter (CKF) in order to generate a more accurate time scale. The…
This report derives a generalized, converted measurement Kalman filter for the class of filtering problems with a linear state equation and nonlinear measurement equation, for which a bijective mapping exists between the state and…
This paper focused on the design of an optimized object tracking technique which would minimize the processing time required in the object detection process while maintaining accuracy in detecting the desired moving object in a cluttered…
In this paper we propose a Kalman filter aided saliency detection model which is based on the conjecture that salient regions are considerably different from our "visual expectation" or they are "visually surprising" in nature. In this…
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…
This paper investigates waveform estimation (tracking) of the time-varying force in a two-level optomechanical system with backaction noise by Kalman filtering. It is assumed that the backaction and measurement noises are Gaussian and…
We present a method of using classical wavelet based multiresolution analysis to separate scales in model and observations during data assimilation with the ensemble Kalman filter. In many applications, the underlying physics of a phenomena…
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…
An important part of system modeling is determining parameter values, particularly for biomolecular systems, where direct measurements of individual parameters are typically hard. While Extended Kalman Filters have been used for this…
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…
In this paper, we present the optimization formulation of the Kalman filtering and smoothing problems, and use this perspective to develop a variety of extensions and applications. We first formulate classic Kalman smoothing as a least…
This paper aims to introduce an application to Kalman Filtering Theory, which is rather unconventional. Recent experiments have shown that many natural phenomena, especially from ecology or meteorology, could be monitored and predicted more…