  The existence of redundant sensors in collaborative state estimation is a
common occurrence, yet their true significance remains elusive. This paper
comprehensively investigates the effects and optimal design of redundant
sensors in sensor networks that use Kalman filtering to estimate the state of a
random process collaboratively. The paper presents two main results: a
theoretical analysis of the effects of redundant sensors and an
engineering-oriented optimal design of redundant sensors. In the theoretical
analysis, the paper leverages Riccati equations and Symplectic matrix theory to
unveil the explicit role of redundant sensors in cooperative state estimation.
The results unequivocally demonstrate that the addition of redundant sensors
enhances the estimation performance of the sensor network, aligning with the
principle of ``more is better". Moreover, the paper establishes a precise
sufficient and necessary condition to assess whether the inclusion of redundant
sensors improves the overall estimation performance. Moving towards
engineering-oriented design optimization, the paper proposes a novel algorithm
to tackle the optimal design problem of redundant sensors, and the convergence
of the proposed algorithm is guaranteed. Numerical simulations are provided to
demonstrate the results.
