Remote estimation subject to packet loss and quantization noise

Abstract

In this paper we consider the problem of designing coding and decoding schemes to estimate the state of a scalar stable stochastic linear system in the presence of a wireless communication channel between the sensor and the estimator. In particular, we consider a communication channel which is prone to packet loss and includes quantization noise due to its limited capacity. We study two scenarios: the first with channel feedback and the second with no channel feedback. More specifically, in the first scenario the transmitter is aware of the quantization noise and the packet loss history of the channel, while in the second scenario the transmitter is aware of the quantization noise only. We show that in the first scenario, the optimal strategy among all possible linear encoders corresponds to the transmission of the Kalman filter innovation similarly to the differential pulse-code modulation (DPCM). In the second scenario, we show that there is a critical packet loss probability above which it is better to transmit the state rather than the innovation. We also propose a heuristic strategy based on the transmission of a convex combination of the state and the Kalman filter innovation which is shown to provide a performance close to the one obtained with channel feedback.

Remote Estimation With Noisy Measurements Subject to Packet Loss and Quantization Noise

“…In this case, the system description presented in (34) reduces to a second-order system (since in this case x tx t|t = x t ). The corresponding descriptions for all the relevant parameters can be found in [19], or also by substituting σ 2 v = 0, p tx ∞ = 0 in the appropriate equations. With a slight abuse of notation, we use the same notations for this special case to maintain readability.…”

“…For these three strategies we compute their performance and observe that in the low packet loss regime it is better to use strategies that are similar to the IF, while for high packet loss regime it better to use strategies that are similar to the SF. Some preliminary results, which considered the simplified scenario with no measurement noise, can be found in [19].…”

LQG cheap control over SNR-limited lossy channels with delay

“…A subsequent step has been made to include multiple channel limitations into the model, such as packet loss and quantization [28], [15], which however results in complex optimization problems; in the context of filtering over rate limited lossy channels, the work [9] studies possible tradeoffs when no information on the packet loss sequence is available to the source coder. Recent extensions concern the study of transient performance under feedback constraints, see e.g.…”

An Optimal Transmission Strategy for Kalman Filtering Over Packet Dropping Links With Imperfect Acknowledgements

“…In particular, the problem of minimum data rates for achieving bounded average state estimation error in linear systems over lossy channels is studied in [16], [17] (see also [18]), while the problem of state control around a target state trajectory in the case of both signal quantization and packet drops is investigated in [19], [20]. The work in [21] concentrates on designing coding and decoding schemes to remotely estimate the state of a scalar stable stochastic linear system over a communication channel subject to both quantization noise and packet loss.…”

“…Similar to [21], the current paper is concerned with remote state estimation subject to both quantization noise and packet drops. However, rather than considering fixed coding and decoding schemes, we are interested in choosing optimal transmission policies at the smart sensor that decides between sending the sensor's local state estimates or its local innovations.…”