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Duality of control and estimation allows mapping recent advances in data-guided control to the estimation setup. This paper formalizes and utilizes such a mapping to consider learning the optimal (steady-state) Kalman gain when process and measurement noise statistics are unknown. Specifically, building on the duality between synthesizing optimal control and estimation gains, the filter design problem is formalized as direct policy learning. In this direction, the duality is used to extend existing theoretical guarantees of direct policy updates for Linear Quadratic Regulator (LQR) to establish global convergence of the Gradient Descent (GD) algorithm for the estimation problem–while addressing subtle differences between the two synthesis problems. Subsequently, a Stochastic Gradient Descent (SGD) approach is adopted to learn the optimal Kalman gain without the knowledge of noise covariances. The results are illustrated via several numerical examples.
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Optimization based data enrichment using stochastic dynamical system models
We develop a general framework for state estimation in systems modeled with noise-polluted continuous time dynamics and discrete time noisy measurements. Our approach is based on maximum likelihood estimation and employs the calculus of variations to derive optimality conditions for continuous time functions. We make no prior assumptions on the form of the mapping from measurements to state-estimate or on the distributions of the noise terms, making the framework more general than Kalman filtering/smoothing where this mapping is assumed to be linear and the noises Gaussian. The optimal solution that arises is interpreted as a continuous time spline, the structure and temporal dependency of which is determined by the system dynamics and the distributions of the process and measurement noise. Similar to Kalman smoothing, the optimal spline yields increased data accuracy at instants when measurements are taken, in addition to providing continuous time estimates outside the measurement instances. We demonstrate the utility and generality of our approach via illustrative examples that render both linear and nonlinear data filters depending on the particular system. Application of the proposed approach to a Monte Carlo simulation exhibits significant performance improvement in comparison to a common existing method.
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- Award ID(s):
- 1750531
- PAR ID:
- 10568963
- Editor(s):
- Zhang, Qichun
- Publisher / Repository:
- PLOS
- Date Published:
- Journal Name:
- PLOS ONE
- Volume:
- 19
- Issue:
- 9
- ISSN:
- 1932-6203
- Page Range / eLocation ID:
- e0310504
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1371/journal.pone.0310504
