Observation-driven scheduling for remote estimation of two Gaussian sources
This work provides theoretical guarantees and practical algorithms for sensor scheduling in remote estimation, addressing a fundamental problem in networked control systems.
The paper studies joint scheduling and estimation for two Gaussian sources, showing that a 'max-scheduling/mean-estimation' policy is person-by-person optimal for independent sources and symmetric correlated sources. For arbitrary correlations, the problem is formulated as a difference-of-convex program, enabling efficient local optimization.
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.