Recursive least squares filter

About: Recursive least squares filter is a research topic. Over the lifetime, 8907 publications have been published within this topic receiving 191933 citations.

Recursive least squares ladder forms for fast parameter tracking

Abstract: A discussion of some of the most interesting recent developments in the area of real time (or "on-line") algorithm for estimation and parameter tracking using ladder canonical forms for AR and ARMA modeling is presented. Besides their interesting connections to stability and scattering theory, partial correlations and matrix square-roots, they also seem to have well behaved numerical properties. Ladder forms seem to be a "natural" form for Wiener (or whitening) filters due to the fact that the optimal whitening filter is time-varying (even for stationary processes), except for ladder form coefficients, which are constants "switched on" at the appropriate time. This leads to the fact that this parametrization is very well suited for tracking rapidly varying sources. Compared to gradient type techniques, our exact least-squares ladder recursions have only a slightly increased number of operations. This increase is due to the recursively computed likelihood variables which act as optimal gains on the data, enabling the ladder filter to lock rapidly on to a transient. Several ladder form applications will be briefly discussed, such as speech modeling, "zero startup" equalisers, and "noise cancelling and inversion". Computer simulations will be presented at the conference

Adaptive Frequency-Domain Equalization in Mode-Division Multiplexing Systems

Abstract: Long-haul mode-division multiplexing (MDM) employs adaptive multi-input multi-output (MIMO) equalization to compensate for modal crosstalk and modal dispersion. MDM systems must typically use MIMO frequency-domain equalization (FDE) to minimize computational complexity, in contrast to polarization-division-multiplexed systems in single-mode fiber, where time-domain equalization (TDE) has low complexity and is often employed to compensate for polarization effects. We study two adaptive algorithms for MIMO FDE: least mean squares (LMS) and recursive least squares (RLS). We analyze tradeoffs between computational complexity, cyclic prefix efficiency, adaptation time and output symbol-error ratio (SER), and the impact of channel group delay spread and fast Fourier transform (FFT) block length on these. Using FDE, computational complexity increases sublinearly with the number of modes, in contrast to TDE. Adaptation to an initially unknown fiber can be achieved in ~3-5 μs using RLS or ~15-25 μs using LMS in fibers supporting 6-30 modes. As compared to LMS, RLS achieves faster adaptation, higher cyclic prefix efficiency, lower SER, and greater tolerance to mode-dependent loss, but at the cost of higher complexity per FFT block. To ensure low computational complexity and fast adaptation in an MDM system, a low overall group delay spread is required. This is achieved here by a family of graded-index graded depressed-cladding fibers in which the uncoupled group delay spread decreases with an increasing number of modes, in concert with strong mode coupling.

Fast, rank adaptive subspace tracking and applications

Abstract: High computational complexity and inadequate parallelism have deterred the use of subspace-based algorithms in real-time systems. We proposed a new class of fast subspace tracking (FST) algorithms that overcome these problems by exploiting the matrix structure inherent in multisensor processing. These algorithms simultaneously track an orthonormal basis for the signal subspace and preserve signal eigenstructure information while requiring only O(Nr) operations per update (where N is the number of channels, and r is the effective rank). Because of their low computational complexity, these algorithms have applications in both recursive and block data processing. Because they preserve the signal eigenstructure as well as compute an orthonormal basis for the signal subspace, these algorithms may be used in a wide range of sensor array applications including bearing estimation, beamforming, and recursive least squares. We present a detailed description of the FST algorithm and its rank adaptive variation (RA-FST) as well as a number of enhancements. We also demonstrate the FST's rapid convergence properties in a number of application scenarios.

The recursive least squares identification algorithm for a class of Wiener nonlinear systems

Abstract: Many physical systems can be modeled by a Wiener nonlinear model, which consists of a linear dynamic system followed by a nonlinear static function. This work is concerned with the identification of Wiener systems whose output nonlinear function is assumed to be continuous and invertible. A recursive least squares algorithm is presented based on the auxiliary model identification idea. To solve the difficulty of the information vector including the unmeasurable variables, the unknown terms in the information vector are replaced with their estimates, which are computed through the preceding parameter estimates. Finally, an example is given to support the proposed method.