Optimal Estimation with Limited Measurements and Noisy Communication

This paper considers a sequential estimation and sensor scheduling problem with one sensor and one estimator. The sensor makes sequential observations about the state of an underlying memoryless stochastic process, and makes a decision as to whether or not to send this measurement to the estimator. The sensor and the estimator have the common objective of minimizing expected distortion in the estimation of the state of the process, over a finite time horizon, with the constraint that the sensor can transmit its observation only a limited number of times. As opposed to the prior work where communication between the sensor and the estimator was assumed to be perfect (noiseless), in this work an additive noise channel with fixed power constraint is considered; hence, the sensor has to encode its message before transmission. For some specific source and channel noise densities, we obtain the optimal encoding and estimation policies in conjunction with the optimal transmission schedule. The impact of the presence of a noisy channel is analyzed numerically based on dynamic programming. This analysis yields some rather surprising results such as a phase-transition phenomenon in the number of used transmission opportunities, which was not encountered in the noiseless communication setting.Comment: X. Gao, E. Akyol, and T. Basar. Optimal estimation with limited measurements and noisy communication. In 54th IEEE Conference on Decision and Control (CDC15), 2015, to appea

Event-Triggered Estimation of Linear Systems: An Iterative Algorithm and Optimality Properties

This report investigates the optimal design of event-triggered estimation for first-order linear stochastic systems. The problem is posed as a two-player team problem with a partially nested information pattern. The two players are given by an estimator and an event-trigger. The event-trigger has full state information and decides, whether the estimator shall obtain the current state information by transmitting it through a resource constrained channel. The objective is to find an optimal trade-off between the mean squared estimation error and the expected transmission rate. The proposed iterative algorithm alternates between optimizing one player while fixing the other player. It is shown that the solution of the algorithm converges to a linear predictor and a symmetric threshold policy, if the densities of the initial state and the noise variables are even and radially decreasing functions. The effectiveness of the approach is illustrated on a numerical example. In case of a multimodal distribution of the noise variables a significant performance improvement can be achieved compared to a separate design that assumes a linear prediction and a symmetric threshold policy