Joint estimation and scheduling for sensor networks is considered in a system formed by two sensors, a scheduler and a remote estimator. Each sensor observes a Gaussian source, which may be correlated. The scheduler observes the output of both sensors and chooses which of the two is revealed to the remote estimator. The goal is to jointly design scheduling and estimation policies that minimize a mean-squared estimation error criterion. The person-by-person optimality of a policy pair called "max-scheduling/mean-estimation" is established, where the measurement with the largest absolute value is revealed to the estimator, which uses a corresponding conditional mean operator. This result is obtained for independent sources, and in the case of correlated sources and symmetric variances. We also consider the joint design of scheduling and linear estimation policies for two correlated Gaussian sources with an arbitrary correlation structure. In this case, the optimization problem can be cast a difference-of-convex program, and locally optimal solutions can be efficiently found using a simple numerical procedure.
Joint optimization of scheduling and estimation policies is considered for a system with two sensors and two noncollocated estimators. Each sensor produces an independent and identically distributed sequence of random variables, and each estimator forms estimates of the corresponding sequence with respect to the mean-squared error sense.The data generated by the sensors is transmitted to the corresponding estimators, over a bandwidth constrained wireless network that can support a single packet per time slot. The access to the limited communication resources is determined by a scheduler who decides which sensor measurement to transmit based on both observations. The scheduler has an energy-harvesting battery of limited capacity, which couples the decision-making problem in time.Despite the overall lack of convexity of the team decision problem, it is shown that this system admits a globally optimal scheduling and estimation strategies under the assumption that the distributions of the random variables at the sensors are symmetric and unimodal. Additionally, the optimal scheduling policy has a structure characterized by a threshold function that depends on the time index and energy level. A recursive algorithm for threshold computation is provided.
I. INTRODUCTIONReliable real-time wireless networking is an important requirement of modern cyber-physical and networked control systems [1], [2]. Due to their large scale, these systems are typically formed by multiple physically distributed subsystems, that communicate over a wireless network of limited capacity. One way to model this communication constraint is to assume that, at any time instant, only one packet can be reliably transmitted over the network to its destination. This constraint forces the system designer to use strategies that allocate the shared communication resources among multiple transmitting nodes. In addition to degrading the performance of the overall system, the fact that the communication among the different agents in cyber-physical systems is imperfect often leads to teamdecision problems with nonclassical information structures. Such problems are usually non-convex, and are, in general, difficult to solve.We consider a sequential remote estimation problem over a finite time horizon with non-collocated sensors and estimators. The system is comprised of multiple sensors, each of which has a stochastic process associated with M. M. Vasconcelos, M. Gagrani, A. Nayyar and U. Mitra are with the Ming Hsieh
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