Related papers: Robust Bayesian Filtering and Smoothing Using Stud…
Student's $t$ statistic is finding applications today that were never envisaged when it was introduced more than a century ago. Many of these applications rely on properties, for example robustness against heavy tailed sampling…
This work studies the state estimation problem of a stochastic nonlinear system with unknown sensor measurement losses. If the estimator knows the sensor measurement losses of a linear Gaussian system, the minimum variance estimate is…
Gaussian process priors are commonly used in aerospace design for performing Bayesian optimization. Nonetheless, Gaussian processes suffer two significant drawbacks: outliers are a priori assumed unlikely, and the posterior variance…
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…
Cubature Kalman Filter (CKF) has good performance when handling nonlinear dynamic state estimations. However, it cannot work well in non-Gaussian noise and bad data environment due to the lack of auto-adaptive ability to measure noise…
A robust estimator, namely M-smoother, for piecewise-constant smoothing is revisited in this paper. Starting from its generalized formulation, we propose a numerical scheme/framework for solving it via a series of weighted-average filtering…
We propose an approximation to the forward-filter-backward-sampler (FFBS) algorithm for large-scale spatio-temporal smoothing. FFBS is commonly used in Bayesian statistics when working with linear Gaussian state-space models, but it…
This paper presents a novel adaptive fading cubature Kalman filter (AFCKF) based on double transitive factors. The developed adaptive algorithm is explained in two stages; stage (i) a single transitive factor is used to update the predicted…
Kalman filtering and smoothing algorithms are used in many areas, including tracking and navigation, medical applications, and financial trend filtering. One of the basic assumptions required to apply the Kalman smoothing framework is that…
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…
We present optimality results for robust Kalman filtering where robustness is understood in a distributional sense, i.e.; we enlarge the distribution assumptions made in the ideal model by suitable neighborhoods. This allows for outliers…
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…
In this study, we address the challenges associated with accurately determining gaze location on a screen, which is often compromised by noise from factors such as eye tracker limitations, calibration drift, ambient lighting changes, and…
In this paper, a distributed Kalman filtering (DKF) algorithm is proposed based on a diffusion strategy, which is used to track an unknown signal process in sensor networks cooperatively. Unlike the centralized algorithms, no fusion center…
To estimate the smoothing distribution in a nonlinear state space model, we apply the conditional particle filter with ancestor sampling. This gives an iterative algorithm in a Markov chain Monte Carlo fashion, with asymptotic convergence…
Distributed sensor networks often include a multitude of sensors, each measuring parts of a process state space or observing the operations of a system. Communication of measurements between the sensor nodes and estimator(s) cannot…
Sequential Bayesian Filtering aims to estimate the current state distribution of a Hidden Markov Model, given the past observations. The problem is well-known to be intractable for most application domains, except in notable cases such as…
A Gaussian measurement error assumption, i.e., an assumption that the data are observed up to Gaussian noise, can bias any parameter estimation in the presence of outliers. A heavy tailed error assumption based on Student's t distribution…
Decoherence remains a major challenge in quantum computing hardware and a variety of physical-layer controls provide opportunities to mitigate the impact of this phenomenon through feedback and feedforward control. In this work, we compare…
We present a general nonlinear Bayesian filter for high-dimensional state estimation using the theory of reproducing kernel Hilbert space (RKHS). Applying kernel method and the representer theorem to perform linear quadratic estimation in a…