Kalman filtering with partial observation losses

Xiangheng Liu, Andrea Goldsmith

Research output: Chapter in Book/Report/Conference proceedingConference contribution

300 Scopus citations


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.

Original languageEnglish (US)
Title of host publication2004 43rd IEEE Conference on Decision and Control (CDC)
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages7
ISBN (Print)0780386825
StatePublished - 2004
Externally publishedYes
Event2004 43rd IEEE Conference on Decision and Control (CDC) - Nassau, Bahamas
Duration: Dec 14 2004Dec 17 2004

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370


Other2004 43rd IEEE Conference on Decision and Control (CDC)

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization


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