Array Algorithms for H and H Estimation

Currently the preferred method for implementing H esti mation algorithms is what is called the array form and includes two main families square root array algorithms which are typically more stable than conventional ones and fast array algorithms which when the system is time invariant typically o er an order of magnitude reduction in the com putational e ort Using our recent observation that H ltering coincides with Kalman ltering in Krein space in this paper we develop array algo rithms for H ltering These can be regarded as natural generalizations of their H counterparts and involve propagating the inde nite square roots of the quantities of interest The H square root and fast array algorithms both have the interesting feature that one does not need to explicitly check for the positivity conditions required for the existence of H lters These conditions are built into the algorithms themselves so that an H esti mator of the desired level exists if and only if the algorithms can be executed However since H square root algorithms predominantly use J unitary transformations rather than the unitary transformations required in the H case further investigation is needed to determine the numerical behaviour of such algorithms This work was supported in part by DARPA through the Department of Air Force under contract F P and by the Joint Service Electronics Program at Stanford under contract DAAH G P i