Related papers: Observer Design for Nonlinear Systems with Equivar…

Equivariance is a nice property to have as it produces much more parameter efficient neural architectures and preserves the structure of the input through the feature mapping. Even though some combinations of transformations might never…

This paper proposes an $SE_2(3)$ based extended Kalman filtering (EKF) framework for the inertial-integrated state estimation problem. The error representation using the straight difference of two vectors in the inertial navigation system…

Incorporating symmetry as an inductive bias into neural network architecture has led to improvements in generalization, data efficiency, and physical consistency in dynamics modeling. Methods such as CNNs or equivariant neural networks use…

This work addresses the problem of designing an equivariant observer for a first order dynamical system on the unit-sphere. Building upon the established case of unit bearing vector dynamics with angular velocity inputs, we introduce an…

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.…

From early image processing to modern computational imaging, successful models and algorithms have relied on a fundamental property of natural signals: symmetry. Here symmetry refers to the invariance property of signal sets to…

The Koopman operator has become an essential tool for data-driven analysis, prediction and control of complex systems. The main reason is the enormous potential of identifying linear function space representations of nonlinear dynamics from…

Various methods have been proposed for the nonlinear filtering problem, including the extended Kalman filter (EKF), iterated extended Kalman filter (IEKF), unscented Kalman filter (UKF) and iterated unscented Kalman filter (IUKF). In this…

Understanding human motion is of critical importance for health monitoring and control of assistive robots, yet many human kinematic variables cannot be directly or accurately measured by wearable sensors. In recent years, invariant…

This paper presents a new observer design approach for linear time invariant multivariable systems subject to unknown inputs. The design is based on a transformation to the so-called special coordinate basis. This form reveals important…

A symmetry-preserving, reduced-order state observer is presented for the unmeasured part of a system's state, where the nonlinear system dynamics exhibit symmetry under the action of a Lie group. Leveraging this symmetry with a moving…

This paper addresses the problem of nonlinear state estimation for dynamical systems whose governing equations are approximated through Koopman operator liftings. While Koopman-based predictors have demonstrated broad approximation…

This paper provides a new observer design methodology for invariant systems whose state evolves on a Lie group with outputs in a collection of related homogeneous spaces and where the measurement of system input is corrupted by an unknown…

We show how the symmetry of attractors of equivariant dynamical systems can be observed by equivariant projections of the phase space. Equivariant projections have long been used, but they can give misleading results if used improperly and…

Stochastic filters for on-line state estimation are a core technology for autonomous systems. The performance of such filters is one of the key limiting factors to a system's capability. Both asymptotic behavior (e.g.,~for regular…

This paper proposes a linear input-output observer design methodology for a population of systems in which each observer uses knowledge of the linear time-invariant dynamics of the particular device. Observers are typically composed of a…

In this article, we consider the implications of unobservable subspaces in the construction of a Kalman filter. In particular, we consider dynamical systems which are invariant with respect to a group action, and which are therefore…

Counter-adversarial system design problems have lately motivated the development of inverse Bayesian filters. For example, inverse Kalman filter (I-KF) has been recently formulated to estimate the adversary's Kalman-filter-tracked estimates…

Providing a metric of uncertainty alongside a state estimate is often crucial when tracking a dynamical system. Classic state estimators, such as the Kalman filter (KF), provide a time-dependent uncertainty measure from knowledge of the…

Visual Inertial Odometry (VIO) is of great interest due the ubiquity of devices equipped with both a monocular camera and Inertial Measurement Unit (IMU). Methods based on the extended Kalman Filter remain popular in VIO due to their low…