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The Kalman(-Bucy) filter is the natural choice for the state reconstruction of disturbed, linear dynamical systems based on flawed and incomplete measurements. Taking a deterministic viewpoint this work investigates possible extensions of…
In recent years, several ensemble-based filtering methods have been proposed and studied. The main challenge in such procedures is the updating of a prior ensemble to a posterior ensemble at every step of the filtering recursions. In the…
We investigate a remote estimation problem in which a transmitter observes a Markov source and chooses the power level to transmit it over a time-varying packet-drop channel. The channel is modeled as a channel with Markovian state where…
Nanomechanical resonant sensors are used in mass spectrometry via detection of resonance frequency jumps. There is a fundamental trade-off between detection speed and accuracy. Temporal and size resolution are limited by the resonator…
This paper concerns numerical assessment of Monte Carlo error in particle filters. We show that by keeping track of certain key features of the genealogical structure arising from resampling operations, it is possible to estimate variances…
While the design of optimal peak-to-peak controllers/observers for linear systems is known to be a difficult problem, this problem becomes interestingly much easier in the context of interval observers because of the positive nature of the…
We consider a robust filtering problem where the robust filter is designed according to the least favorable model belonging to a ball about the nominal model. In this approach, the ball radius specifies the modeling error tolerance and the…
The Ensemble Kalman Filter method can be used as an iterative particle numerical scheme for state dynamics estimation and control--to--observable identification problems. In applications it may be required to enforce the solution to satisfy…
This paper studies the distributed state estimation problem for a class of discrete time-varying systems over sensor networks. Firstly, it is shown that a networked Kalman filter with optimal gain parameter is actually a centralized filter,…
Long Short-Term Memory networks trained with gradient descent and back-propagation have received great success in various applications. However, point estimation of the weights of the networks is prone to over-fitting problems and lacks…
This work extends a previous study that introduced an algorithm for state estimation on manifolds within the framework of the Kalman filter. Its objective is to address the limitations of the earlier approach. The reversible Kalman filter…
The Kalman filter is an established tool for the analysis of dynamic systems with normally distributed noise, and it has been successfully applied in numerous application areas. It provides sequentially calculated estimates of the system…
We calculate the error threshold for the linear optics quantum computing proposal by Knill, Laflamme and Milburn [Nature 409, pp. 46--52 (2001)] under an error model where photon detectors have efficiency <100% but all other components --…
The Boolean Kalman Filter and associated Boolean Dynamical System Theory have been proposed to study the spread of infection on computer networks. Such models feature a network where attacks propagate through, an intrusion detection system…
Inertial measurement units are widely used in different fields to estimate the attitude. Many algorithms have been proposed to improve estimation performance. However, most of them still suffer from 1) inaccurate initial estimation, 2)…
In this paper, we consider the peak-covariance stability of Kalman filtering subject to packet losses. The length of consecutive packet losses is governed by a time-homogeneous finite-state Markov chain. We establish a sufficient condition…
In this paper, we present an optimal filter for linear time-varying continuous-time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum-variance sense. We first show that the unknown inputs…
Data assimilation provides algorithms for widespread applications in various fields. It is of practical use to deal with a large amount of information in the complex system that is hard to estimate. Weather forecasting is one of the…
Data assimilation combines dynamical models with observations to improve state estimates. Ensemble filters sequentially assimilate observations by updating a set of samples over time, alternating between a forecast and an analysis step.…
Optimal state estimation for linear discrete-time systems is considered. Motivated by the literature on differential privacy, the measurements are assumed to be corrupted by Laplace noise. The optimal least mean square error estimate of the…