Fast square-root RLS adaptive filtering algorithms

We present a new, doubly fast algorithm for recursive least-squares (RLS) adaptive filtering that uses displacement structure and subsampled-updating. The fast subsampled-updating stabilized fast transversal filter (FSU SFTF) algorithm is mathematically equivalent to the classical fast transversal filter (FTF) algorithm. The FTF algorithm exploits the shift invariance that is present in the RLS adaptation of an FIR filter. The FTF algorithm is in essence the application of a rotation matrix to a set of filters and in that respect resembles the Levinson (1947) algorithm. In the subsampled-updating approach, we accumulate the rotation matrices over some time interval before applying them to the filters. It turns out that the successive rotation matrices themselves can be obtained from a Schur-type algorithm that, once properly initialized, does not require inner products. The various convolutions that appear In the algorithm are done using the fast Fourier transform (FFT). The resulting algorithm is doubly fast since it exploits FTF and FFTs. The roundoff error propagation in the FSU SFTF algorithm is identical to that in the SFTF algorithm: a numerically stabilized version of the classical FTF algorithm. The roundoff error generation, on the other hand, seems somewhat smaller. For relatively long filters, the computational complexity of the new algorithm is smaller than that of the well-known LMS algorithm, rendering it especially suitable for applications such as acoustic echo cancellation.

The existing derivations of fast RLS adaptive filters are dependent on the shift structure in the input regression vectors. This structure arises when a tapped-delay line (FIR) filter is used as a modeling filter. We show, unlike what original derivations may suggest, that fast fixed-order RLS adaptive algorithms are not limited to FIR filter structures. We show that fast recursions in both explicit and array forms exist for more general data structures, such as orthonormally-based models. One of the benefits of working with an orthonormal basis is that fewer parameters can be used to model long impulse responses.

A generalized least squares fast transversal filter algorithm for the decision feedback equalization of dispersive channels

The speech enhancement is one of the effective techniques to solve speech degraded by noise. In this paper a fast speech enhancement method for noisy speech signals is presented, which is based on improved Kalman filtering. The conventional Kalman filter algorithm for speech enhancement needs to calculate the parameters of AR (auto-regressive) model, and perform a lot of matrix operations, which usually is non-adaptive. The speech enhancement algorithm proposed in this paper eliminates the matrix operations and reduces the calculating time by only constantly updating the first value of state vector X(n). We design a coefficient factor for adaptive filtering, to automatically amend the estimation of environmental noise by the observation data. Simulation results show that the fast adaptive algorithm using Kalman filtering is effective for speech enhancement.

The use of UD factorization in adaptive RLS algorithms is interesting for its numeric robustness and because no square-root operations at all are involved. We describe a square root free fast RLS algorithm based on the UD factorization of the autocorrelation matrix. Numerous finite precision simulations tend to indicate that this algorithm is numerically stable. The algorithm requires /spl Oscr/(/spl Nscr/) operations, where /spl Nscr/ is the linear filter order.

The backward predictor based least squares (BPLS) algorithm, which is derived from the fast recursive least squares (FRLS) algorithms, demonstrates a very stable and robust numerical performance compared with the RLS and FRLS algorithms. However, the computational load of the BPLS algorithms is O(N/sup 2/). This makes it difficult to be implemented in real time applications even using today's DSP technology. In order to overcome this difficulty, a method for reducing the computational complexity of the BPLS algorithms is proposed. The result (we call it the fast BPLS algorithm) is consistent with the fast Newton transversal filters (FNTF) algorithms, but the derivation is much simpler to understand. The most important characteristic of the fast BPLS algorithm is its good numerical property. Theoretical analysis and computer simulations show that the fast BPLS algorithm provides a much improved numerical performance compared with the FNTF algorithms under a finite-precision implementation.

In this paper, a novel combined leakage CMA and direct decision (DD) adaptive algorithm using automatic iteration step adaptive blind equalizer is presented. In contrast to known CMA algorithm, the novel algorithm can approach the performance of mean-square error and fast convergent rate. For adaption of filters, efficient automatic iteration step and DD algorithm is present. The novel algorithm is lower computational complexity withO(N) and N is the filter order. Furthermore, the relation of novel algorithm to CMA algorithm is investigated. Finally, it is shown that proposed combined LCMA-DD algorithm is robust against amplitude and phase offset with fast convergence and mean-square error.

A fast complex-valued adaptive filtering algorithm based on the Euclidean direction set (EDS) method is presented in this paper. A mathematical analysis of the complex-valued EDS (CEDS) algorithm is also performed in this paper. It is shown that the CEDS algorithm has a computational complexity of O ( N ) for each system update, and that the CEDS converges to the true solution. Computer simulations illustrate that this complex algorithm is very efficient in complex adaptive FIR and IIR filtering.

A new solution to the numerical instability of fast recursive least squares adaptive filter algorithms is presented. Using interval arithmetic, an error analysis is effectively performed in parallel with the computations of the algorithm. If necessary the algorithm will be rescued, preventing divergence. This is shown in software simulations and in a hardware implementation of an adaptive equaliser.

The generalized fast transversal filter (FTF) algorithm is the computationally most efficient algorithm for a general multichannel adaptive filtering problem with an unequal number of stages in different filters, such as decision feedback equalization of dispersion channels. The normalized generalized FTF algorithm is presented, with special emphasis on initialization aspects, which, if not addressed, may result in divergence of the algorithm. It is shown that the soft constrained initialization with a judicious choice of mu stabilizes the solution. The mean square error convergence characteristics for decision feedback equalization of quadrature phase shift keying (QPSK) data transmitted over a dispersive channel are obtained by computer simulation. >

We present a fast adaptive PARAFAC decomposition algorithm with low computational complexity. The proposed algorithm generalizes the Orthonormal Projection Approximation Subspace Tracking (OPAST) approach for tracking a class of third-order tensors which have one dimension growing with time. It has linear complexity, good convergence rate and good estimation accuracy. To deal with large-scale problems, a parallel implementation can be applied to reduce both computational complexity and storage. We illustrate the effectiveness of our algorithm in comparison with the state-of-the-art algorithms through simulation experiments.

SummaryWith the hot issues such as smart city and ecological city put forward, the development of intelligence and informatization of urban space has been established, especially the Internet of Things. With the wide application of location‐based social networks, users can share their location of interest in location. By analyzing users' historical geographic information, location service recommendation can recommend geographic locations to users to help users obtain better access experience. Combined with genetic algorithm (GA) algorithm, a recommendation algorithm based on geographic location service optimization is proposed, which can better recommend to users. Aiming at the problem of slow convergence speed of GA, a fast adaptive genetic algorithm (FAGA) method is proposed to optimize location services. In the experimental part, comparing several functions, FAGA's test effect and convergence are ideal. By comparing FAGA‐least squares support vector machine (LSSVM) algorithm with other methods in location service recommendation, FAGA‐LSSVM method has more advantages.

Fast adaptive phase unwrapping algorithm based on improved bucket sorting

In this paper, a two-dimensional (2-D) fast adaptive filtering algorithm based on the exponentially weighted least squares errors is developed for the non linear canonical piecewise quadratic (CPWQ) model. This algorithm take advantages of the non linear CPWQ modeling and the fast convergence of the exponentially weighted least squares adaptive algorithm. The simulation results show that the proposed method gives good results in image restoration. Experimental comparison with the canonical piecewise linear (CPWL) model shows the superiority of the non linear filter in term of image enhancement.

Underwater acoustic communication channels vary from stationary with sparse arrivals to rapidly varying and fully reverberant. A receiver structure capable of operating over this wide range of characteristics has evolved and consists of a fractionally-spaced multi-channel combiner, a sparse DFE, and an embedded PLL. At the computational heart of this receiver is an adaptation algorithm, used to update the various equalizer parameters, The adaptation algorithm may use one of the standard strategies such as adaptive step-size LMS, RLS, adaptive memory RLS, or a hybrid of these. The choice of algorithm involves trade-offs between training time, tracking-rate, operating SNR, and computational requirements of the receiver. To maximize the receiver throughput, we wish to select the least computational algorithm for which the error-rate is still acceptable and, given the volatility of the underwater channel, this choice should be made for each received packet, In this paper, we compare the performance of several LMS and RLS adaptation algorithms over a range of real acoustic data. We show that the computationally-efficient adaptive step-size LMS performs well for many channel classes, but that the faster tracking of RLS is essential for some complex non-stationary channels. The results provide a first step towards the automatic selection of adaptation algorithm, as would be required in a fully autonomous receiver.