Continuous-time recursive least-squares algorithms

Two continuous-time recursive least-squares (RLS) algorithms are derived in this work in a unified approach, one for the Gramm-Schmidt orthogonalization (GSO) of multiple signals and the other for the lattice filter with time-shifted data. The GSO algorithm is derived in the continuous-time domain directly in the sense of the exact minimization of integral-squared-error. Then, the lattice algorithm can be obtained by applying the developed GSO to the updates of the forward and backward predictions of time-shifted data. The two algorithms are highly modular and use the same kind of module. Unlike the discrete-time RLS algorithms, no extra parameters are required to link the modules, and each module performs independently a standard order-one continuous-time RLS weight update using its present local information of the inputs and the feedback of the output