Related papers: Robust Bayesian Filtering and Smoothing Using Stud…
We present a Kalman smoothing framework based on modeling errors using the heavy tailed Student's t distribution, along with algorithms, convergence theory, open-source general implementation, and several important applications. The…
State filtering is a key problem in many signal processing applications. From a series of noisy measurement, one would like to estimate the state of some dynamic system. Existing techniques usually adopt a Gaussian noise assumption which…
Filtering and smoothing algorithms for linear discrete-time state-space models with skewed and heavy-tailed measurement noise are presented. The algorithms use a variational Bayes approximation of the posterior distribution of models that…
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.…
In the classical Kalman filter(KF), the estimated state is a linear combination of the one-step predicted state and measurement state, their confidence level change when the prediction mean square error matrix and covariance matrix of…
We propose two nonlinear Kalman smoothers that rely on Student's t distributions. The T-Robust smoother finds the maximum a posteriori likelihood (MAP) solution for Gaussian process noise and Student's t observation noise, and is extremely…
Filtering and smoothing algorithms for linear discrete-time state-space models with skew-t-distributed measurement noise are proposed. The algorithms use a variational Bayes based posterior approximation with coupled location and skewness…
A major stage of radio interferometric data processing is calibration or the estimation of systematic errors in the data and the correction for such errors. A stochastic error (noise) model is assumed, and in most cases, this underlying…
Robustness and adaptivity are two competing objectives in Kalman filters (KF). Robustness involves temporarily inflating prior estimates of noise covariances, while adaptivity updates prior beliefs by exploiting measurements. In practical…
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…
Using a perturbation technique, we derive a new approximate filtering and smoothing methodology generalizing along different directions several existing approaches to robust filtering based on the score and the Hessian matrix of the…
In this paper, state and noise covariance estimation problems for linear system with unknown multiplicative noise are considered. The measurement likelihood is modelled as a mixture of two Gaussian distributions and a Student's t…
Motivated by filtering tasks under a linear system with non-Gaussian heavy-tailed noise, various robust Kalman filters (RKFs) based on different heavy-tailed distributions have been proposed. Although the sub-Gaussian $\alpha$-stable…
Driven by the filtering challenges in linear systems disturbed by non-Gaussian heavy-tailed noise, the robust Kalman filters (RKFs) leveraging diverse heavy-tailed distributions have been introduced. However, the RKFs rely on precise noise…
The Kalman filter and Rauch-Tung-Striebel (RTS) smoother are optimal for state estimation in linear dynamic systems. With nonlinear systems, the challenge consists in how to propagate uncertainty through the state transitions and output…
Filtering and smoothing algorithms for linear discrete-time state-space models with skew-t distributed measurement noise are presented. The proposed algorithms improve upon our earlier proposed filter and smoother using the mean field…
State estimation in the presence of uncertain or data-driven noise distributions remains a critical challenge in control and robotics. Although the Kalman filter is the most popular choice, its performance degrades significantly when…
We present a general probabilistic perspective on Gaussian filtering and smoothing. This allows us to show that common approaches to Gaussian filtering/smoothing can be distinguished solely by their methods of computing/approximating the…
The analysis of high-dimensional dynamical systems generally requires the integration of simulation data with experimental measurements. Experimental data often has substantial amounts of measurement noise that compromises the ability to…
In this paper, a new robust Student's t based stochastic cubature filter (RSTSCF) is proposed for nonlinear state-space model with heavy-tailed process and measurement noises. The heart of the RSTSCF is a stochastic Student's t spherical…