Numerically stable fast convergence least-squares algorithms for multichannel active sound cancellation systems and sound deconvolution systems

In recent years,rec,yAT# least-squares (RLS) algorithms and fast-transversal-#lters (FTF) algorithms have beenintroducy for multicyLDDD actic sound cndyAxx:AyL (ASC) systems andmulticHyLDD sounddecyDxHTzyLD (MSD) systems. It was reported that these algorithmscl greatlyimprove thecyCH#HCyLD speed of the ASC=MSD systems using adaptive FIR #lters. However,numericA instabilityof the algorithms is an issue that needs to be resolved. In this paper, extensions of numericyLDAAQAyc realisations of RLS algorithmssuc as the inverse QR-RLS, the QRdecz#DyLDTTQ least-squares-lattic (QRD-LSL) and the symmetry preserving RLS algorithms are introducL for thespecDH problem ofmulticyLCz# ASC=MSD. Multic#HAyL versions of some of these algorithms have previouslybeen published for predicQyL oridenti#cC:z: systems, but not forcryzxA systems. The cey of underdetermined ASC=MSD systems (i.e. systems with moreaceyHCHC than error sensors) is also cyATCHCyLC to show that in these cese it maybe required to usecyDH#DQyLC algorithms in order to have numeric# stability. Constrained algorithms formultic#yLCH ASC=MSD systems are thereforeintroducD for two types of cyH##HTyLCH minimisation of theacyAx#C signals power and minimization of the adaptive filters squarecareyHACDD Simulation results are shown to verifythe numerical stability of the algorithms introducs in the paper