Distributed Estimation Recovery Under Sensor Failure

Single-time-scale distributed estimation of dynamic systems via a network of sensors/estimators is addressed in this letter. In single-time-scale distributed estimation, the two fusion steps, consensus and measurement exchange, are implemented only once, in contrast to, e.g., a large number of consensus iterations at every step of the system dynamics. We particularly discuss the problem of failure in the sensor/estimator network and how to recover for distributed estimation by adding new sensor measurements from equivalent states. We separately discuss the recovery for two types of sensors, namely <inline-formula><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$\beta$</tex-math></inline-formula> sensors. We propose polynomial-order algorithms to find equivalent state nodes in graph representation of the system to recover for distributed observability. The polynomial-order solution is particularly significant for large-scale systems.

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