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Deep learning has the potential to dramatically impact navigation and tracking state estimation problems critical to autonomous vehicles and robotics. Measurement uncertainties in state estimation systems based on Kalman and other Bayes…
The Kalman filter is a fundamental tool for state estimation in dynamical systems. While originally developed for linear Gaussian settings, it has been extended to nonlinear problems through approaches such as the extended and unscented…
The Global Navigation Satellite System (GNSS) provides critical positioning information globally, but its accuracy in dense urban environments is often compromised by multipath and non-line-of-sight errors. Road network data can be used to…
A recursive state estimation procedure is derived for a linear time varying system with both parametric uncertainties and stochastic measurement droppings. This estimator has a similar form as that of the Kalman filter with intermittent…
We consider a robust state space filtering problem in the case that the transition probability density is unknown and possibly degenerate. The resulting robust filter has a Kalman-like structure and solves a minimax game: the nature selects…
In this paper, we introduce a tensor neural network based machine learning method for solving the elliptic partial differential equations with random coefficients in a bounded physical domain. With the help of tensor product structure, we…
In [1], Sinopoli et al. analyze the problem of optimal estimation for linear Gaussian systems where packets containing observations are dropped according to an i.i.d. Bernoulli process, modeling a memoryless erasure channel. In this case…
Gaussian processes offer a flexible kernel method for regression. While Gaussian processes have many useful theoretical properties and have proven practically useful, they suffer from poor scaling in the number of observations. In…
This paper introduces two new algorithms to accurately estimate the process noise covariance of a discrete-time Kalman filter online for robust orbit determination in the presence of dynamics model uncertainties. Common orbit determination…
Filtering is concerned with online estimation of the state of a dynamical system from partial and noisy observations. In applications where the state of the system is high dimensional, ensemble Kalman filters are often the method of choice.…
The Kalman filter and Rauch-Tung-Striebel (RTS) smoother are optimal for state estimation in linear dynamic systems. With nonlinear systems, the challenge consists in how to propagate uncertainty through the state transitions and output…
Directional estimation is a common problem in many tracking applications. Traditional filters such as the Kalman filter perform poorly because they fail to take the periodic nature of the problem into account. We present a recursive filter…
The Derivative-free nonlinear Kalman Filter is proposed for state estimation and fault diagnosis in distributed parameter systems and particularly in dynamical systems described by partial differential equations of the nonlinear wave type.…
Kalman filtering can provide an optimal estimation of the system state from noisy observation data. This algorithm's performance depends on the accuracy of system modeling and noise statistical characteristics, which are usually challenging…
This work presents a distributionally robust Kalman filter to address uncertainties in noise covariance matrices and predicted covariance estimates. We adopt a distributionally robust formulation using bicausal optimal transport to…
Semiparametric forecasting and filtering are introduced as a method of addressing model errors arising from unresolved physical phenomena. While traditional parametric models are able to learn high-dimensional systems from small data sets,…
The Kalman filter is an algorithm for the estimation of hidden variables in dynamical systems under linear Gauss-Markov assumptions with widespread applications across different fields. Recently, its Bayesian interpretation has received a…
Motivated by the need for accurate frequency information, a novel algorithm for estimating the fundamental frequency and its rate of change in three-phase power systems is developed. This is achieved through two stages of Kalman filtering.…
In this paper, a quantum algorithm based on gaussian process regression model is proposed. The proposed quantum algorithm consists of three sub-algorithms. One is the first quantum subalgorithm to efficiently generate mean predictor. The…
Real-time nonlinear Bayesian filtering algorithms are overwhelmed by data volume, velocity and increasing complexity of computational models. In this paper, we propose a novel ensemble based nonlinear Bayesian filtering approach which only…