Optimal Scheduling of Multiple Sensors Over Lossy and Bandwidth Limited Channels

Abstract

This work considers the sensor scheduling for multiple dynamic processes. We consider n linear dynamic processes. The state of each process is measured by a sensor, which transmits its local state estimate over one wireless channel to a remote estimator with certain communication costs. At each time step, only a portion of the sensors are allowed to transmit data to the remote estimator and the packet might be lost due to unreliability of the wireless channels. Our goal is to find a scheduling policy which coordinates the sensors in a centralized manner to minimize the total expected estimation error of the remote estimator and the communication costs. We formulate the problem as a Markov decision process. We develop an algorithm to check whether there exists a deterministic stationary optimal policy. We show the optimality of monotone policies, which saves the computational effort of finding an optimal policy and facilitates practical implementation. Nevertheless, obtaining an exact optimal policy still suffers from curse of dimensionality when the number of processes is large. We further provide an index-based heuristic to avoid brute force computation. We derive analytic expressions of the indices and show that this heuristic is asymptotically optimal. Numerical examples are presented to illustrate the theoretical results.Index Terms-Kalman filtering; Sensor scheduling; lossy network; monotone policy; Markov decision process; index policy I. INTRODUCTIONThe development of device, sensing and communication technologies enables wide range of applications of wireless sensor networks. After the pioneering work on event-based sensor data scheduling proposed in [1], a variety of studies has been done to balance the estimation performance and the communication overhead in [2]- [4].A large number of works on sensor scheduling focused on remote estimation of a linear time-invariant (LTI) dynamic process. There are also some other works addressing static processes and nonlinear models. However, the static models [5], [6] are special cases of LTI systems and nonlinear models either involve approximation of a linear system [7], [8] or the solution method requires numerically solving a partially observable Markov decision process, which is computationally inefficient [9]-[11]. A few works [12], [13] considered control

Sensor Scheduling Design for Complex Networks under a Distributed State Estimation Framework

“…Remark 3 Compared to the strategy of transmitting raw measurements, the strategy of performing distributed estimation in advance by smart sensors and then transmitting state estimates to nodes is more preferable, since the loss of transmitted measurements in the former strategy will have an unerasable effect on the estimation performance at future steps while the loss of transmitted state estimates in the latter strategy will not be so, as soon as the future state estimate is received. Actually, the latter strategy has been widely adopted in existing works on sensor scheduling for a single system or multiple independent systems [7,23,28]. Here, this idea is extended to complex networks.…”

“…Remark 4 Compared to relevant problems investigated in [7,28], Problem 1 possesses two key coupled features simultaneously. First, the performance index P k,i depends heavily on the scheduling indices of neighbors at the previous step, i.e., P k−1,j , j ∈ N i .…”

“…Remark 6 Compared to the sufficient condition based on a recursive algorithm in [28], the condition in Assumption 1 is easier to satisfy. In particular, when N = M and no coupling exists in the system dynamics, this condition collapses to (1 − λ)ρ 2 (A) < 1, which is a sufficient and necessary condition for independent processes in [28].…”

“…Later, using a Markov decision process (MDP) approach, the result was extended to cases with multiple independent processes in [7,20]. Recently, to make the MDP technique more computationally efficient, Whittle index-based techniques were applied in [25,28]. Besides the MDP methods, a prioritizing scheduler based on the concept of Value of Information was designed in [18].…”

Optimizing Age Penalty in Time-Varying Networks with Markovian and Error-Prone Channel State

“…Proof sketch: The complete proof is provided in Appendix B and Appendix C , which is similar to Theorem 2 in [ 23 ]. Despite the complex proof, the intuition is simple.…”