Array Algorithms for H 2 and H ∞ Estimation
Babak Hassibi, T. Kailath, Ali H. Sayed · Birkhäuser Boston eBooks · 1999
Currently, the preferred method for implementing H 2 estimation algorithms is what is called the array form, and includes two main families: square-root array algorithms, that are typically more stable than conventional ones, and fast array algorithms, which, when the system is time-invariant, typically offer an order of magnitude reduction in the computational effort. Using our recent observation that H ∞ filtering coincides with Kalman filtering in Krein space, in this chapter we develop array algorithms for H ∞ filtering. These can be regarded as natural generalizations of their H 2 counterparts, and involve propagating the indefinite 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 ∞ filters. These conditions are built into the algorithms themselves so that an H ∞ estimator 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 2 case, further investigation is needed to determine the numerical behavior of such algorithms. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.