Tracking and Control of Gauss-Markov Processes over Packet-Drop Channels with Acknowledgments

Anatoly Khina*, Victoria Kostina, Ashish Khisti, Babak Hassibi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


We consider the problem of tracking the state of Gauss-Markov processes over rate-limited erasure-prone links. We concentrate first on the scenario in which several independent processes are seen by a single observer. The observer maps the processes into finite-rate packets that are sent over the erasure-prone links to a state estimator, and are acknowledged upon packet arrivals. The aim of the state estimator is to track the processes with zero delay and with minimum mean square error (MMSE). We show that, in the limit of many processes, greedy quantization with respect to the squared error distortion is optimal. That is, there is no tension between optimizing the MMSE of the process in the current time instant and that of future times. For the case of packet erasures with delayed acknowledgments, we connect the problem to that of compression with side information that is known at the observer and may be known at the state estimator-where the most recent packets serve as side information that may have been erased, and demonstrate that the loss due to a delay by one time unit is rather small. For the scenario where only one process is tracked by the observer-state estimator system, we further show that variable-length coding techniques are within a small gap of the many-process outer bound. We demonstrate the usefulness of the proposed approach for the simple setting of discrete-time scalar linear quadratic Gaussian control with a limited data-rate feedback that is susceptible to packet erasures.

Original languageEnglish
Article number8395023
Pages (from-to)549-560
Number of pages12
JournalIEEE Transactions on Control of Network Systems
Issue number2
StatePublished - Jun 2019


FundersFunder number
Qualcomm, Inc.
National Science FoundationCCF-1751356, CCF-1566567
Jet Propulsion Laboratory
Horizon 2020 Framework Programme
H2020 Marie Skłodowska-Curie Actions708932
Canada Research ChairsCCF-1018927, CCF-1409204, CNS-0932428, CCF-1423663
King Abdullah University of Science and Technology


    • Networked control systems
    • packet loss
    • sequential coding of correlated sources
    • source coding with side information
    • state estimation
    • successive refinement


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