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The Kalman filter (KF) is one of the most widely used tools for data assimilation and sequential estimation. In this work, we show that the state estimates from the KF in a standard linear dynamical system setting are equivalent to those…
We present recent results on the existence of a continuous time limit for Ensemble Kalman Filter algorithms. In the setting of continuous signal and observation processes, we apply the original Ensemble Kalman Filter algorithm proposed by…
The classical state-space approach to optimal estimation of stochastic processes is efficient when the driving noises are generated by martingales. In particular, the weight function of the optimal linear filter, which solves a complicated…
The exponential stability and the concentration properties of a class of extended Kalman-Bucy filters are analyzed. New estimation concentration inequalities around partially observed signals are derived in terms of the stability properties…
Contemporary data assimilation often involves millions of prediction variables. The classical Kalman filter is no longer computationally feasible in such a high dimensional context. This problem can often be resolved by exploiting the…
We consider the problem of reconstructing time sequences of spatially sparse signals (with unknown and time-varying sparsity patterns) from a limited number of linear "incoherent" measurements, in real-time. The signals are sparse in some…
This report derives a generalized, converted measurement Kalman filter for the class of filtering problems with a linear state equation and nonlinear measurement equation, for which a bijective mapping exists between the state and…
Many robotic sensor estimation problems can characterized in terms of nonlinear measurement systems. These systems are contaminated with noise and may be underdetermined from a single observation. In order to get reliable estimation…
The unscented Kalman filter is an algorithm capable of handling nonlinear scenarios. Uncertainty in process noise covariance may decrease the filter estimation performance or even lead to its divergence. Therefore, it is important to adjust…
This paper studies the distributed state estimation in sensor network, where $m$ sensors are deployed to infer the $n$-dimensional state of a linear time-invariant (LTI) Gaussian system. By a lossless decomposition of optimal steady-state…
In this paper, we propose a robust Kalman filtering framework for systems with probabilistic uncertainty in system parameters. We consider two cases, namely discrete time systems, and continuous time systems with discrete measurements. The…
The possible methodologies to handle the uncertain parameter are reviewed. The core idea of the desensitized Kalman filter is introduced. A new cost function consisting of a posterior covariance trace and trace of a weighted norm of the…
Here we revisit the classic problem of linear quadratic estimation, i.e. estimating the trajectory of a linear dynamical system from noisy measurements. The celebrated Kalman filter gives an optimal estimator when the measurement noise is…
The Kalman Filter (KF) parameters are traditionally determined by noise estimation, since under the KF assumptions, the state prediction errors are minimized when the parameters correspond to the noise covariance. However, noise estimation…
This paper is concerned with the linear/nonlinear Kalman-like filtering problem under binary sensors. Since innovation represents new information in the sensor measurement and serves to correct the prediction for the Kalman-like filter…
Fueled by applications in sensor networks, these years have witnessed a surge of interest in distributed estimation and filtering. A new approach is hereby proposed for the Distributed Kalman Filter (DKF) by integrating a local covariance…
Stabilization, disturbance rejection, and control of optical beams and optical spots are ubiquitous problems that are crucial for the development of optical systems for ground and space telescopes, free-space optical communication…
The estimation of spatiotemporal data from limited sensor measurements is a required task across many scientific disciplines. The sensor selection problem, which aims to optimize the placement of sensors, leverages innovations in greedy…
A recently developed data-driven Kalman filter requires offline measurement of the process disturbance; a requirement that is often unmet for many practical applications. We propose a solution that parametrizes the Kalman filter exclusively…
This paper proposes a novel convex optimization framework for designing robust Kalman filters that guarantee a user-specified steady-state error while maximizing process and sensor noise. The proposed framework simultaneously determines the…