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 α and β 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.