TY - GEN

T1 - Kalman filtering with partial observation losses

AU - Liu, Xiangheng

AU - Goldsmith, Andrea

PY - 2004

Y1 - 2004

N2 - We study the Kalman filtering problem when part or all of the observation measurements are lost in a random fashion. We formulate the Kalman filtering problem with partial observation losses and derive the Kalman filter updates with partial observation measurements. We show that with these partial measurements the Kalman filter and its error covariance matrix iteration become stochastic, since they now depend on the random packet arrivals of the sensor measurements, which can be lost or delayed when transmitted over a communication network. The communication network needs to provide a sufficient throughput for each of the sensor measurements in order to guarantee the stability of the Kalman filter, where the throughput captures the rate of the sensor measurements correctly received. We investigate the statistical convergence properties of the error covariance matrix iteration as a function of the throughput of the sensor measurements. A throughput region that guarantees the convergence of the error covariance matrix is found by solving a feasibility problem of a linear matrix inequality. We also find an unstable throughput region such that the state estimation error of the Kalman filter is unbounded. The expected error covariance matrix is bounded both from above and from below. The results are illustrated with some simple numerical examples.

AB - We study the Kalman filtering problem when part or all of the observation measurements are lost in a random fashion. We formulate the Kalman filtering problem with partial observation losses and derive the Kalman filter updates with partial observation measurements. We show that with these partial measurements the Kalman filter and its error covariance matrix iteration become stochastic, since they now depend on the random packet arrivals of the sensor measurements, which can be lost or delayed when transmitted over a communication network. The communication network needs to provide a sufficient throughput for each of the sensor measurements in order to guarantee the stability of the Kalman filter, where the throughput captures the rate of the sensor measurements correctly received. We investigate the statistical convergence properties of the error covariance matrix iteration as a function of the throughput of the sensor measurements. A throughput region that guarantees the convergence of the error covariance matrix is found by solving a feasibility problem of a linear matrix inequality. We also find an unstable throughput region such that the state estimation error of the Kalman filter is unbounded. The expected error covariance matrix is bounded both from above and from below. The results are illustrated with some simple numerical examples.

UR - http://www.scopus.com/inward/record.url?scp=14244257885&partnerID=8YFLogxK

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U2 - 10.1109/CDC.2004.1429408

DO - 10.1109/CDC.2004.1429408

M3 - Conference contribution

AN - SCOPUS:14244257885

SN - 0780386825

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 4180

EP - 4186

BT - 2004 43rd IEEE Conference on Decision and Control (CDC)

T2 - 2004 43rd IEEE Conference on Decision and Control (CDC)

Y2 - 14 December 2004 through 17 December 2004

ER -