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The existence of redundant sensors in sensor networks is a common occurrence,yet their true significance remains elusive. This paper comprehensivelyinvestigates the effects and optimal design of redundant sensors in sensornetworks that use Kalman filtering to estimate the state of a random process.The paper presents two main results: a theoretical analysis of the effects ofredundant sensors and an engineering-oriented optimal design of redundantsensors. In the theoretical analysis, the paper leverages Riccati equations andSymplectic matrix theory to unveil the explicit role of redundant sensors incooperative state estimation. The results unequivocally demonstrate that theaddition of redundant sensors enhances the estimation performance of the sensornetwork, aligning with the principle of ``more is better". Moreover, the paperestablishes a precise sufficient and necessary condition to assess whether theinclusion of redundant sensors improves the estimation performance for allstate elements simultaneously. Moving towards engineering-oriented designoptimization, the paper proposes a novel algorithm to tackle the optimal designproblem of redundant sensors. By employing linear matrix inequalities anditerative semi-definite programming techniques, the algorithm effectivelyhandles the nonlinear constraints inherent in the optimization problem.Importantly, the convergence of the proposed algorithm is guaranteed. Numericalsimulations are provided to demonstrate and validate the results.

On the Effects and Optimal Design of Redundant Sensors in Sensor Networks