Neural Network Based Recursive Least Square Technique for Indoor Wireless Positioning

<p> Fast emerging wireless indoor positioning enables many location based services. However, fluctuation receive signal strength due to multipath propagation is a major challenge. Different Machine Learning (ML) approaches are attempted to improve the accuracy in indoor positioning. In this paper, a hybrid technique combining Recursive Least Square (RLS) with Artificial Neural Network (ANN) has been presented to solve a multilateration problem with different sets of anchor nodes. Instead of using directly measured distances, estimated distances using ANN are used in RLS implementation. Results from the hybrid RLS-ANN are compared with pure RLS, pure least square (LS) and LS-ANN approaches. Hybrid RLS-ANN provides the least Root Mean Square Error (RMSE) among all the techniques and improves the accuracy up to 80% compared to the pure LS multilateration technique. Complexity of the proposed technique is relatively low with good accuracy </p>

Envelope tracking has many important applications in electrical distribution systems for either flicker meters or flicker compensators. This paper presents a novel control technique for flicker mitigation. This technique is based on the instantaneous tracking of the measured voltage envelope. The ADAptive LINEar neuron (ADALINE) algorithm, and the Recursive Least Square (RLS) algorithm are introduced for the flicker envelope tracking. The ADALINE algorithm is characterized by a light computational demand, unlike that of existing techniques; the RLS algorithm outperforms the ADALINE algorithm by its fast convergence and robust tracking performance. Both the ADALINE and the RLS algorithms give accurate results even under rapid dynamic changes. The paper investigates the effects of different parameters on the performance of the ADALINE algorithm and that of the RLS algorithm. Extensive simulations of the proposed flicker tracking algorithms are conducted to evaluate their performance for the tracking and mitigation of voltage flicker. The ADALINE and the RLS algorithms are examined by tracking and mitigating the flicker produced by a resistance welder and an arc furnace in a simple distribution system simulated in the PSCAD/EMTDC package.

Vanadium redox flow battery (VRB) energy storage system has been widely utilized in renewable energy applications such as wind power integration and green buildings. An online electrical model of VRB is needed to monitor and estimate battery states by using real time data since the internal parameters of battery are varying during operation. In this paper, an improved second-order Thevenin model is proposed to describe the operating characteristics of VRB. To overcome the drawback of recursive least squares (RLS) algorithm in tracking parameter identification, this paper proposes a method based on time-varying forgetting factor recursive least Squares (TFF-RLS) algorithm to identify model parameters. According to the data collected by the pulse charging experiment, the RLS algorithm and the TFF-RLS algorithm are used to identify the model parameters. Experiments are carried out on a 5kWh/3kWh VRB experimental platform in Wuhan University of Technology. Two online identification methods are compared. The results show that the TFF-RLS method demonstrates a better performance on tracking the variation of parameters dynamically, and improving estimation accuracy compared with the RLS method.

In this paper, a method of updating filter coefficients is proposed in which the RLS (Recursive Least Squares) algorithm is applied to a noise canceler with a filter for crosstalk removal. The RLS algorithm has an advantage over the Least Mean Square algorithm by virtue of better convergence. When the filter coefficients are updated including the filter for crosstalk removal, the error signal becomes nonlinear in terms of filter coefficients. Hence, a nonlinear RLS algorithm is derived in which such nonlinearity is taken into account. It is shown that the convergence is further improved in comparison with the conventional RLS algorithm. Finally, a method is proposed to reduce the noise contained in the transmitted voice signals of telephone by means of the present noise canceler and its effectiveness is evaluated. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(5): 36–44, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10039

The Cerebellar Model Articulation Controller (CMAC) neural network is an associative memory that is biologically inspired by the cerebellum, which is found in the brains of animals. The standard CMAC uses the least mean squares algorithm to train the weights. Recently, the recursive least squares (RLS) algorithm was proposed as a superior algorithm for training the CMAC online as it can converge in just one epoch, and does not require tuning of a learning rate. However, the RLS algorithm was found to be very computationally demanding as its computational complexity is dependent on the square of the number of weights required which can be huge for the CMAC. Here, we show a more efficient RLS algorithm that uses inverse QR decomposition and additionally provides a regularized solution, improving generalization. However, while the inverse QR decomposition based RLS algorithm reduces computation time significantly; it is still not fast enough for use in CMACs greater than two dimensions. To further improve efficiency we show that by using kernel methods the CMAC computational complexity can be transformed to become dependent on the number of unique training data. Additionally, it is shown how modeling error can be improved through use of higher order basis functions.

A new recursive least square (RLS) algorithm based on nonlinear principal component analysis (NPCA) is proposed to address the blind source separation (BSS) problem in non-stationary environment. Forgetting factor is introduced to improve the tracking ability in non-stationary environment. The Kalman filter is used to solve the NPCA problem since its outstanding tracking performance in non-stationary environments. Simulations using the real speech source signals are used to illustrate the performance of the new RLS algorithm in static and non-stationary environments. Results show that the new RLS algorithm has faster convergence rate and better tracking capacity compared with the stochastic gradient algorithm, and previous RLS algorithm.

The recursive least square (RLS) algorithm is insensitive to the dispersions of the correlation matrix. Consequently, the usage of the RLS algorithm to update the adaptive recursive filter coefficients are attractive for the system modeling and identification fields. In this paper, an error function RLS (EFRLS) algorithm is derived for the adaptive recursive filter. Furthermore, a scaled version of the EFRLS algorithm is proposed where the computation complexity is significantly reduced. The scaled EFRLS algorithm can be realized in real time using the available digital signal processors. The convergence to the optimal solution of both the EFRLS algorithm and its scaled version is ensured while the general RLS algorithm fails to converge to the optimal solution for the multimodal performance criterion.

The state of charge (SOC) and state of health (SOH) of lithium-ion batteries (LIB) are two major indices of the battery management system (BMS) for system monitoring, health prognosis, and optimal usage. This paper presents a new SOC and SOH estimation method based on two recursive least squares (RLS) algorithms. First, a second-order equivalent circuit model is used to describe battery dynamics. Second, an open-circuit-voltage (OCV) and internal resistance estimation method is proposed based on the RLS algorithm. Instead of using SOC as a state in a state space model, the OCV is estimated from a linear regression directly. The battery total capacity is then estimated by a combination of the estimated OCV and another RLS algorithm. The accurate battery SOC and SOH can be obtained without a priori knowledge of battery parameters. Simulation results highlight the accuracy and robustness of the proposed method.

In this paper, we proposed a recurrent kernel recursive least square (RLS) algorithm for online learning. In classical kernel methods, the kernel function number grows as the number of training sample increases, which makes the computational cost of the algorithm very high and only applicable for offline learning. In order to make the kernel methods suitable for online learning where the system is updated when a new training sample is obtained, a compact dictionary (support vectors set) should be chosen to represent the whole training data, which in turn reduces the number of kernel functions. For this purpose, a sparsification method based on the Hessian matrix of the loss function is applied to continuously examine the importance of the new training sample and determine the update of the dictionary according to the importance measure. We show that the Hessian matrix is equivalent to the correlation matrix of the training samples in the RLS algorithm. This makes the sparsification method able to be easily incorporated into the RLS algorithm and reduce the computational cost futher. Simulation results show that our algorithm is an effective learning method for online chaotic signal prediction and nonlinear system identification.

Recursive least squares (RLS)-based algorithms are a class of fast online training algorithms for feedforward multilayered neural networks (FMNNs). Though the standard RLS algorithm has an implicit weight decay term in its energy function, the weight decay effect decreases linearly as the number of learning epochs increases, thus rendering a diminishing weight decay effect as training progresses. In this paper, we derive two modified RLS algorithms to tackle this problem. In the first algorithm, namely, the true weight decay RLS (TWDRLS) algorithm, we consider a modified energy function whereby the weight decay effect remains constant, irrespective of the number of learning epochs. The second version, the input perturbation RLS (IPRLS) algorithm, is derived by requiring robustness in its prediction performance to input perturbations. Simulation results show that both algorithms improve the generalization capability of the trained network.

In this thesis, four methods specifically designed for sparse systems estimation are originally developed and presented, which were called here: Relaxations method, Successive Expansions method, l 1 -norm Minimization method and Automatic Adjustment of the Regularization Factor method. The four proposed methods are based on the Least Squares (LS) Estimation method and incorporate techniques related to convex optimization and to the theory of compressive sensing. The simulation results show that the proposed methods herein present superior performance than the ordinary LS estimation method and the Recursive Least Squares (RLS) with convex regularization method (l 1 -RLS), in many cases achieving the same optimal performance presented by the LS Oracle method. Furthermore, the proposed methods demand lower computational cost than the l 1 -RLS method.

Sparse adaptive filtering algorithms are utilized to exploit potential sparse structure information as well as to mitigate noises in many unknown sparse systems. Sparse recursive least square (RLS) algorithms have been attracted intensely attentions due to their low-complexity and easy- implementation. Basically, these algorithms are constructed by standard RLS algorithm and sparse penalty functions (e.g., l_1-norm). However, existing sparse RLS algorithms do not exploit the sparsity efficiently. In this paper, an improved adaptive filtering algorithm is proposed by incorporating a novel correntropy induced metric (CIM) constraint into RLS, which is termed as RLS- CIM algorithm. Specifically, we adopt a well-known Gaussian kernel in CIM and further devise a novel variable kernel width to control the sparse penalty in different transient-error scenarios. Numerical simulation results are given to corroborate the proposed algorithm via mean square deviation (MSD).

Digital‐domain self‐interference cancellation (SIC) technology effectively mitigates self‐interference by reconstructing the SI signal. Due to the high computational complexity of the traditional recursive least squares (RLS) algorithm in SIC, its real‐time engineering application capability is limited. To overcome this limitation, this paper proposes the application of the DCD‐RLS algorithm to SIC. The proposed method transforms the standard normal equations of the RLS algorithm into auxiliary normal equations and incorporates a bisection search strategy, thereby significantly reducing the computational complexity while maintaining optimal convergence performance. Simulation results demonstrate that the proposed algorithm not only achieves a significant reduction in computational complexity but also retains SIC performance, thus enhancing the implementation value of in‐band full‐duplex (IBFD) communication systems.We propose an RLS‐SIC algorithm based on dichotomous coordinate descent (DCD), that converts the RLS normal equations into auxiliary equations and uses a bisection search to greatly reduce computational complexity while preserving optimal convergence. Simulations show, the method maintains self‐interference cancellation performance with much lower complexity, improving the real‐time feasibility of in‐band full‐duplex communication systems.

Recursive least squares (RLS) is widely used in identification and estimation. An unfortunate weakness of RLS is the divergence of its covariance matrix in cases where the data are not sufficiently persistent. To solve this problem, [1] introduced the exponential forgetting and resetting algorithm (EFRA), whose covariance update equation is modified so that the covariance matrix remains bounded. Unfortunately, EFRA does not include RLS as a special or limiting case, and cannot easily approximate RLS estimates. In this paper, we derive a modified RLS variant of EFRA that includes RLS without forgetting as a limiting case, and that can closely approximate RLS with forgetting. An additional advantage of MRLS relative to EFRA is greater ease in choosing parameters to set the covariance bounds.

This chapter presents recursive least-squares (RLS) algorithms, which are based on numerically robust Householder transformations. Section 7.1 introduces the conventional orthogonal Householder transform and provides its geometrical interpretation. The hyperbolic Householder and the row (orthogonal and hyperbolic) Householder transforms are also briefly described. In Section 7.2, the Householder RLS (HRLS) algorithm is presented, its relation with the other known square-root RLS algorithms is discussed, and two applications, where the HRLS algorithm has been successfully applied, are presented. By considering a block-by-block update approach to the RLS problem, the block exact Householder QRD-RLS algorithm is developed in Section 7.3, which constitutes a generalization of the conventional QRD-RLS algorithm. Section 7.4 presents an inverse QRD-RLS algorithm, which employs block updating via the application of appropriate row orthogonal Householder transformations. Finally, a sliding window block RLS algorithm, which comprises a pair of row Householder transforms, is introduced in Section 7.5.