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This paper proposes a novel geometric nonlinear filter for attitude and bias estimation on the Special Orthogonal Group $SO(3)$ using matrix measurements. The structure of the proposed filter is similar to that of the continuous-time…
We investigate dynamics of Gaussian states of continuous variable systems under Gaussianity preserving channels. We introduce a hierarchy of such evolutions encompassing Markovian, weakly and strongly non-Markovian processes, and provide…
We study a novel optical setup which is able to select a specific Fock component from a generic input state. The device allows to synthesize number states and superpositions of few number states, and to measure the photon distribution and…
Characterization and quantification of non-Markovian dynamics in open quantum systems are topical issues in the rapidly developing field of quantum computation and quantum communication. A standard approach based on the notion of…
For a fixed average energy, the simultaneous estimation of multiple phases can provide a better total precision than estimating them individually. We show this for a multimode interferometer with a phase in each mode, using Gaussian inputs…
Quantum state smoothing is a technique for assigning a valid quantum state to a partially observed dynamical system, using measurement records both prior and posterior to an estimation time. We show that the technique is greatly simplified…
Many systems arising in biological applications are subject to periodic forcing. In these systems the forcing parameter is not only time-varying but also known to have a periodic structure. We present an approach to estimating periodic,…
The paper proposes a new recursive filter for non-linear systems that inherently computes a valid bound on the mean square estimation error. The proposed filter, bound based extended Kalman, (BEKF) is in the form of an extended Kalman…
We introduce a family of criteria to detect quantum non-Gaussian states of a harmonic oscillator, that is, quantum states that can not be expressed as a convex mixture of Gaussian states. In particular we prove that, for convex mixtures of…
In a partially observed quantum or classical system the information that we cannot access results in our description of the system becoming mixed even if we have perfect initial knowledge. That is, if the system is quantum the conditional…
Satellite dynamics and tracking remain important challenges in the context of space exploration and communication systems. Accurate state estimation is essential to maintain reliable orbital motion and system performance. This paper…
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…
This study explores a detailed examination of various classes of single- and two-mode Gaussian states as key elements for an estimation process, specifically targeting the evaluation of an unknown squeezing parameter encoded in one mode. To…
We introduce a novel measure to quantify the non-Gaussian character of a quantum state: the quantum relative entropy between the state under examination and a reference Gaussian state. We analyze in details the properties of our measure and…
Filtering is crucial in engineering fields, providing vital state estimation for control systems. However, the nonlinear nature of complex systems and the presence of non-Gaussian noises pose significant challenges to the performance of…
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…
A Conventional centralized state estimators exhibit limited robustness in large-scale grids and face practical deployment hurdles. To overcome these challenges, this paper proposes a decentralized maximum generalized Student's t-kernel…
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…
We present a probabilistic framework for both (i) determining the initial settings of kernel adaptive filters (KAFs) and (ii) constructing fully-adaptive KAFs whereby in addition to weights and dictionaries, kernel parameters are learnt…
This paper investigates an approximation scheme of the optimal nonlinear Bayesian filter based on the Gaussian mixture representation of the state probability distribution function. The resulting filter is similar to the particle filter,…