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Safety-critical control is imperative for deploying autonomous systems in the real world. Control Barrier Functions (CBFs) offer strong safety guarantees when accurate system and sensor models are available. However, widely used additive,…

Navigation plays a vital role in the ability of autonomous surface and underwater platforms to complete their tasks. Most navigation systems apply a fusion between inertial sensors and other external sensors, such as global navigation…

In this manuscript we introduce numerical Gaussian process Kalman filtering (GPKF). Numerical Gaussian processes have recently been developed to simulate spatiotemporal models. The contribution of this paper is to embed numerical Gaussian…

We present a multisensor fusion framework for the onboard real-time navigation of a quadrotor in an indoor environment. The framework integrates sensor readings from an Inertial Measurement Unit (IMU), a camera-based object detection…

Extended Kalman filter (EKF) does not guarantee consistent mean and covariance under linearization, even though it is the main framework for robotic localization. While Lie group improves the modeling of the state space in localization, the…

In this paper, in order to enhance the numerical stability of the unscented Kalman filter (UKF) used for power system dynamic state estimation, a new UKF with guaranteed positive semidifinite estimation error covariance (UKF-GPS) is…

Data assimilation (DA) for compressible flows with shocks is challenging because many classical DA methods generate spurious oscillations and nonphysical features near uncertain shocks. We focus here on the ensemble Kalman filter (EnKF). We…

A new ensemble filter that allows for the uncertainty in the prior distribution is proposed and tested. The filter relies on the conditional Gaussian distribution of the state given the model-error and predictability-error covariance…

The widely-used Extended Kalman Filter (EKF) provides a straightforward recipe to estimate the mean and covariance of the state given all past measurements in a causal and recursive fashion. For a wide variety of applications, the EKF is…

This paper focuses on designing a consistent and efficient filter for map-based visual-inertial localization. First, we propose a new Lie group with its algebra, based on which a novel invariant extended Kalman filter (invariant EKF) is…

Consider a space object in an orbit about the earth. An uncertain initial state can be represented as a point cloud which can be propagated to later times by the laws of Newtonian motion. If the state of the object is represented in…

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…

Recent advances in counter-adversarial systems have garnered significant research attention to inverse filtering from a Bayesian perspective. For example, interest in estimating the adversary's Kalman filter tracked estimate with the…

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.…

The extended Kalman filter (EKF) has been the industry standard for state estimation problems over the past sixty years. The classical formulation of the EKF is posed for nonlinear systems defined on global Euclidean spaces. The design…

The most accurate version of the unscented Kalman filter (UKF) involves the construction of two ensembles. To reduce computational cost, however, UKF is often implemented without the second ensemble. This simplification comes at a price,…

Consistent state estimation is challenging, especially under the epistemic uncertainties arising from learned (nonlinear) dynamic and observation models. In this work, we propose a set-based estimation algorithm, named Gaussian…

Accurate estimation of noise parameters is critical for optimal filter performance, especially in systems where true noise parameter values are unknown or time-varying. This article presents a quaternion left-invariant extended Kalman…

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…

This paper continues our research devoted to an accurate nonlinear Bayesian filters' design. Our solution implies numerical methods for solving ordinary differential equations (ODE) when propagating the mean and error covariance of the…