Reza Arablouei

Distributed Least Mean-Square Estimation With Partial Diffusion

Distributed estimation of a common unknown parameter vector can be realized efficiently and robustly over an adaptive network employing diffusion strategies. In the adapt-then-combine implementation of these strategies, each node combines the intermediate estimates of the nodes within its closed neighborhood. This requires the nodes to transmit their intermediate estimates to all their neighbors after each update. In this paper, we consider transmitting a subset of the entries of the intermediate estimate vectors and examine two different schemes for selecting the transmitted entries at each iteration. Accordingly, we propose a partial-diffusion least mean-square (PDLMS) algorithm that reduces the internode communications while retaining the benefits of cooperation and provides a convenient trade-off between communication cost and estimation performance. Through analysis, we show that the PDLMS algorithm is asymptotically unbiased and converges in the mean-square sense. We also calculate its theoretical transient and steady-state mean-square deviation. Our numerical studies corroborate the effectiveness of the PDLMS algorithm and show a good agreement between analytical performance predictions and experimental observations.

Adaptive Distributed Estimation Based on Recursive Least-Squares and Partial Diffusion

Using the diffusion strategies, an unknown parameter vector can be estimated over an adaptive network by combining the intermediate estimates of neighboring nodes at each node. We propose an extension to the diffusion recursive least-squares algorithm by allowing partial sharing of the entries of the intermediate estimate vectors among the neighbors. Accordingly, the proposed algorithm, termed partial-diffusion recursive least-squares (PDRLS), enables a trade-off between estimation performance and communication cost. We analyze the performance of the PDRLS algorithm and prove its convergence in both mean and mean-square senses. We also derive a theoretical expression for its steady-state mean-square deviation. Simulation results substantiate the efficacy of the PDRLS algorithm and demonstrate a good match between theory and experiment.

Analysis of the Gradient-Descent Total Least-Squares Adaptive Filtering Algorithm

The gradient-descent total least-squares (GD-TLS) algorithm is a stochastic-gradient adaptive filtering algorithm that compensates for error in both input and output data. We study the local convergence of the GD-TLS algoritlun and find bounds for its step-size that ensure its stability. We also analyze the steady-state performance of the GD-TLS algorithm and calculate its steady-state mean-square deviation. Our steady-state analysis is inspired by the energy-conservation-based approach to the performance analysis of adaptive filters. The results predicted by the analysis show good agreement with the simulation experiments.

Analysis of a reduced-communication diffusion LMS algorithm

In diffusion-based algorithms for adaptive distributed estimation, each node of an adaptive network estimates a target parameter vector by creating an intermediate estimate and then combining the intermediate estimates available within its closed neighborhood. We analyze the performance of a reduced-communication diffusion least mean-square (RC-DLMS) algorithm, which allows each node to receive the intermediate estimates of only a subset of its neighbors at each iteration. This algorithm eases the usage of network communication resources and delivers a trade-off between estimation performance and communication cost. We show analytically that the RC-DLMS algorithm is stable and convergent in both mean and mean-square senses. We also calculate its theoretical steady-state mean-square deviation. Simulation results demonstrate a good match between theory and experiment.

Affine projection algorithm with selective projections

In the affine projection adaptive filtering algorithm, convergence is sped up by increasing the projection order but with an unwelcome consequence of increased steady-state misalignment. To address this unfavorable compromise, we propose a new affine projection algorithm with selective projections. This algorithm adaptively changes the projection order according to the estimated variance of the filter output error. The error variance is estimated using exponential window averaging with a variable forgetting factor and a simple moving averaging technique. The input regressors are selected according to two different criteria to update the filter coefficients at each iteration. Simulations, carried out for different adaptive filtering applications, demonstrate that the new algorithm provides fast initial convergence and low steady-state misalignment without necessarily trading off one for the other in addition to a significant reduction in average computational complexity.

Reduced-Complexity Constrained Recursive Least-Squares Adaptive Filtering Algorithm

A linearly-constrained recursive least-squares adaptive filtering algorithm based on the method of weighting and the dichotomous coordinate descent (DCD) iterations is proposed. The method of weighting is employed to incorporate the linear constraints into the least-squares problem. The normal equations of the resultant unconstrained least-squares problem are then solved using the DCD iterations. The proposed algorithm has a significantly smaller computational complexity than the previously proposed constrained recursive least square (CRLS) algorithm while delivering convergence performance on par with CRLS. The effectiveness of the proposed algorithm is demonstrated by simulation examples.

Linearly-Constrained Recursive Total Least-Squares Algorithm

We develop a new linearly-constrained recursive total least squares adaptive filtering algorithm by incorporating the linear constraints into the underlying total least squares problem using an approach similar to the method of weighting and searching for the solution (filter weights) along the input vector. The proposed algorithm outperforms the previously proposed constrained recursive least square (CRLS) algorithm when both input and output data are observed with noise. It also has a significantly smaller computational complexity than CRLS. Simulations demonstrate the efficacy of the proposed algorithm.

Unbiased Recursive Least-Squares Estimation Utilizing Dichotomous Coordinate-Descent Iterations

We propose an unbiased recursive least-squares algorithm for errors-in-variables system identification. The proposed algorithm, called URLS, removes the noise-induced bias when both input and output are contaminated with noise and the input noise is colored and correlated with the output noise. To develop the algorithm, we define an exponentially-weighted least-squares optimization problem that yields an unbiased estimate. Then, we solve the system of linear equations of the associated normal equations utilizing the dichotomous coordinate-descent iterations. The URLS algorithm features significantly reduced computational complexity as well as improved numerical stability compared with a previously proposed bias-compensated recursive least-squares algorithm while having similar estimation performance. We show that the URLS algorithm is asymptotically unbiased and convergent in the mean-square sense. We also calculate its steady-state mean-square deviation. Simulation results corroborate the efficacy of the URLS algorithm and the accuracy of the theoretical findings.

Adaptive frequency estimation of three-phase power systems

The frequency of a three-phase power system can be estimated by identifying the parameter of a second-order autoregressive (AR2) linear predictive model for the complex-valued αβ signal of the system. Since, in practice, both input and output of the AR2 model are observed with noise, the recursive least-squares (RLS) estimate of the system frequency using this model is biased. We show that the estimation bias can be evaluated and subtracted from the RLS estimate to yield a bias-compensated RLS (BCRLS) estimate if the variance of the noise is known a priori. Moreover, in order to simultaneously compensate for the noise on both input and output of the AR2 model, we utilize the concept of total least-square (TLS) estimation and calculate a recursive TLS (RTLS) estimate of the system frequency by employing the inverse power method. Unlike the BCRLS algorithm, the RTLS algorithm does not require the prior knowledge of the noise variance. We prove mean convergence and asymptotic unbiasedness of the BCRLS and RTLS algorithms. Simulation results show that the RTLS algorithm outperforms the RLS and BCRLS algorithms as well as a recently-proposed widely-linear TLS-based algorithm in estimating the frequency of both balanced and unbalanced three-phase power systems. We show that the recursive least-squares (RLS) estimate of the frequency of a three-phase power system using the second-order autoregressive (AR2) linear predictive model for the complex-valued αβ signal is biased when the voltage readings are noisy.We show that the frequency estimation bias can be evaluated and subtracted from the RLS estimate to yield a bias-compensated RLS (BCRLS) estimate if the noise variance is known a priori.We also utilize the concept of total least-square (TLS) estimation and calculate a recursive TLS (RTLS) estimate of the system frequency by employing the inverse power method with no need for the prior knowledge of the noise variance.We prove mean convergence and asymptotic unbiasedness of the BCRLS and RTLS algorithms.Simulation results show that the RTLS algorithm outperforms the RLS and BCRLS algorithms as well as a recently-proposed widely-linear TLS-based algorithm in estimating the frequency of both balanced and unbalanced three-phase power systems.

Recursive Total Least-Squares Algorithm Based on Inverse Power Method and Dichotomous Coordinate-Descent Iterations

We develop a recursive total least-squares (RTLS) algorithm for errors-in-variables system identification utilizing the inverse power method and the dichotomous coordinate-descent (DCD) iterations. The proposed algorithm, called DCD-RTLS, outperforms the previously proposed RTLS algorithms, which are based on the line-search method, with reduced computational complexity. We perform a comprehensive analysis of the DCD-RTLS algorithm and show that it is asymptotically unbiased as well as being stable in the mean. We also find a lower bound for the forgetting factor that ensures mean-square stability of the algorithm and calculate the theoretical steady-state mean-square deviation (MSD). We verify the effectiveness of the proposed algorithm and the accuracy of the predicted steady-state MSD via simulations.