TY - GEN
T1 - Kalman Filtering for Discrete-Time Linear Systems with Infinite-Dimensional Observations
AU - Varley, Maxwell M.
AU - Molloy, Timothy L.
AU - Nair, Girish N.
N1 - Publisher Copyright:
© 2022 American Automatic Control Council.
PY - 2022
Y1 - 2022
N2 - Estimating the finite-dimensional state of dynamic systems using modern sensors such as cameras, lidar, and radar involves processing increasingly high-dimensional observations. In this paper, we exploit concepts from the theory of infinite-dimensional systems to examine state estimation in the continuum limit of infinite-dimensional observations. Specifically, we investigate state estimation in discrete-time linear systems with finite-dimensional states and infinite-dimensional observations corrupted by additive noise. In contrast to previous derivations of the Kalman filter for infinite-dimensional observations, we are able to derive an explicit solution for the optimal Kalman gain by modeling the infinite-dimensional observation noise as a stationary Gaussian Process. We demonstrate the utility of our Kalman filter in a simulation of a linearized system derived from the pinhole camera model.
AB - Estimating the finite-dimensional state of dynamic systems using modern sensors such as cameras, lidar, and radar involves processing increasingly high-dimensional observations. In this paper, we exploit concepts from the theory of infinite-dimensional systems to examine state estimation in the continuum limit of infinite-dimensional observations. Specifically, we investigate state estimation in discrete-time linear systems with finite-dimensional states and infinite-dimensional observations corrupted by additive noise. In contrast to previous derivations of the Kalman filter for infinite-dimensional observations, we are able to derive an explicit solution for the optimal Kalman gain by modeling the infinite-dimensional observation noise as a stationary Gaussian Process. We demonstrate the utility of our Kalman filter in a simulation of a linearized system derived from the pinhole camera model.
UR - http://www.scopus.com/inward/record.url?scp=85138496856&partnerID=8YFLogxK
U2 - 10.23919/ACC53348.2022.9867642
DO - 10.23919/ACC53348.2022.9867642
M3 - Conference contribution
AN - SCOPUS:85138496856
T3 - Proceedings of the American Control Conference
SP - 296
EP - 303
BT - 2022 American Control Conference, ACC 2022
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2022 American Control Conference, ACC 2022
Y2 - 8 June 2022 through 10 June 2022
ER -