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In this work we propose an approximate Minimum Mean-Square Error (MMSE) filter for linear dynamic systems with Gaussian Mixture noise. The proposed estimator tracks each component of the Gaussian Mixture (GM) posterior with an individual…
Using state-space representation, mobile object positioning problems can be described as dynamic systems, with the state representing the unknown location and the observations being the information gathered from the location sensors. For…
We propose a new recursive estimator for linear dynamical systems under Gaussian process noise and non-Gaussian measurement noise. Specifically, we develop an approximate maximum a posteriori (MAP) estimator using dynamic programming and…
Recursive estimation of nonlinear dynamical systems is an important problem that arises in several engineering applications. Consistent and accurate propagation of uncertainties is important to ensuring good estimation performance. It is…
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…
Multi-robot systems must have the ability to accurately estimate relative states between robots in order to perform collaborative tasks, possibly with no external aiding. Three-dimensional relative pose estimation using range measurements…
State estimation in non-linear models is performed by tracking the posterior distribution recursively. A plethora of algorithms have been proposed for this task. Among them, the Gaussian particle filter uses a weighted set of particles to…
Gaussian mixture filters for nonlinear systems usually rely on severe approximations when calculating mixtures in the prediction and filtering step. Thus, offline approximations of noise densities by Gaussian mixture densities to reduce the…
State-space models (SSMs) are a broad class of probabilistic models for dynamical systems with many applications in engineering and science. Bayesian filtering is analytically tractable only in the linear-Gaussian setting, where the Kalman…
In this paper is proposed a novel incremental iterative Gauss-Newton-Markov-Kalman filter method for state estimation of dynamic models given noisy measurements. The mathematical formulation of the proposed filter is based on the…
Estimation of a dynamical system's latent state subject to sensor noise and model inaccuracies remains a critical yet difficult problem in robotics. While Kalman filters provide the optimal solution in the least squared sense for linear and…
This paper develops a new filtering approach for state estimation in polynomial systems corrupted by arbitrary noise, which commonly arise in robotics. We first consider a batch setup where we perform state estimation using all data…
The Kalman filter is extensively used for state estimation for linear systems under Gaussian noise. When non-Gaussian L\'evy noise is present, the conventional Kalman filter may fail to be effective due to the fact that the non-Gaussian…
Particle flow Gaussian particle flow (PFGPF) uses an invertible particle flow to generate a proposal density. It approximates the predictive and posterior distributions as Gaussian densities. In this paper, we use bank of PFGPF filters to…
This paper is the second of a two-part series that discusses the implementation issues and test results of a robust Unscented Kalman Filter (UKF) for power system dynamic state estimation with non-Gaussian synchrophasor measurement noise.…
The factor graph approach to discrete-time linear Gaussian state space models is well developed. The paper extends this approach to continuous-time linear systems/filters that are driven by white Gaussian noise. By Gaussian message passing,…
This work addresses the problem of state estimation in multivariable dynamic systems with quantized outputs, a common scenario in applications involving low-resolution sensors or communication constraints. A novel method is proposed to…
The matched filter (MF) is widely used to detect signals hidden within the noise. If the noise is Gaussian, its performances are well-known and describable in an elegant analytical form. The treatment of non-Gaussian noises is often…
Simultaneous Input and State Estimation (SISE) enables the reconstruction of unknown inputs and internal states in dynamical systems, with applications in fault detection, robotics, and control. While various methods exist for linear…
A novel Gaussian mixture model (GMM) aided sparse Bayesian learning (SBL) framework is proposed for channel state information (CSI) estimation in orthogonal time-frequency space (OTFS) modulated systems. The key attribute of the proposed…