Robust Dynamic Multinode Parameter Calibration in Open-Loop Airborne Coherent Distributed Arrays

An open-loop coherent distributed array (CDA) enables beam steering to arbitrary angles without feedback, provided that stringent electrical state alignment among distributed nodes can be achieved using perfect knowledge of range, range rate, and direction cosine relative to each node toward any assumed destination. When nodes are mounted on aircraft, the state-relying systematic parameters, including positions, velocities, and affiliated aircraft attitudes of node swarms, drift unpredictably over time, inducing dynamic registration errors in node ranges, range rates, and direction cosines, and further failure of coherent beam steering. To address this in practical air-launched vehicle applications with outliers, we develop a set of outlier-resistant extended Kalman filters (OREKFs) for calibration of multinode systematic parameters, which vary in terms of covariances of reweighted predictive state and observation noise based on various robust kernel functions. To circumvent parameter unidentifiability arising from array translation and rotation and pursue a higher level of calibration accuracy than nodes obtain independently, the measurements from internode paths and ground auxiliary transmitter (GAT)-node paths are combined along with shared information from the global positioning system (GPS). Recognizing that artificial bias may exist in reported GAT positions, one merges GAT position bias and measurement noise as equivalent observation noise, which allows filtering gain to account for the inaccuracy of GAT positions. Space-time registration of mobile nodes is thus done based on online estimates of multinode parameters for coherence maintenance. Simulations confirm well with the theoretical developments.