The single-hidden-layer feedforward neural networks (SLFNs) are frequently used in machine learning due to their ability which can form boundaries with arbitrary shapes if the activation function of hidden units is chosen properly. Most learning algorithms for the neural networks based on gradient descent are still slow because of the many learning steps. Recently, a learning algorithm called extreme learning machine (ELM) has been proposed for training SLFNs to overcome this problem. It randomly chooses the input weights and hidden-layer biases, and analytically determines the output weights by the matrix inverse operation. This algorithm can achieve good generalization performance with high learning speed in many applications. However, this algorithm often requires a large number of hidden units and takes long time for classification of new observations. In this paper, a new approach for training SLFNs called least-squares extreme learning machine (LS-ELM) is proposed. Unlike the gradient descent-based algorithms and the ELM, our approach analytically determines the input weights, hidden-layer biases and output weights based on linear models. For training with a large number of input patterns, an online training scheme with sub-blocks of the training set is also introduced. Experimental results for real applications show that our proposed algorithm offers high classification accuracy with a smaller number of hidden units and extremely high speed in both learning and testing.

This paper proposes a channel estimation technique which uses a postfixed pseudo-noise (PN) sequence combined with zero padding to accurately estimate the channel impulse response for mobile orthogonal frequency division multiplexing (OFDM) communications. The major advantage of the proposed techniques is the periodical insertion of PN sequences after each OFDM symbol within the original guard interval in conventional zero-padded OFDM or within the original cyclic prefix (CP) in conventional CP-OFDM. In addition, the proposed technique takes advantage of null samples padded after the PN sequences for reducing inter-symbol interference occurring with the information detection in conventional pseudo-random-postfix OFDM. The proposed technique successfully applies either (1) least-squares algorithm with decision-directed data-assistance, (2) approximate least-squares estimation, or (3) maximum-likelihood scheme with various observation windows for the purpose of improving channel estimation performance. Some comparative simulations are given to illustrate the excellent performance of the proposed channel estimation techniques in mobile environments.

Localization of mobile terminals has received considerable attention in wireless communications. In this letter, we present a covariance shaping least squares (CSLS) estimator using time-of-arrival measurements of the signal from the mobile station received at three or more base stations. It is shown that the CSLS estimator yields better performance than the other LS estimators at low signal-to-noise ratio conditions.

In this letter, we suggest a noise estimation method which can be applied for speech enhancement in various noise environments. The proposed method consists of the following two main processes to analyze and estimate efficiently the noise from the noisy speech. First, a least-squares line is used, which is obtained by applying coefficient magnitudes in node with a uniform wavelet packet transform to a least squares method. Next, a differential forgetting factor and a correlation coefficient per subband are applied, where each subband consists of several nodes with the uniform wavelet packet transform. In particular, this approach has the ability to update noise estimation by using the estimated noise at the previous frame only instead of employing the statistical information of long past frames and explicit nonspeech frames detection consisted of noise signals. In objective assessments, we observed that the performance of the proposed method was better than that of the compared methods. Furthermore, our method showed a reliable result even at low SNR.

In this paper, we treat a design problem for IIR digital filters described by rational transfer function in discrete space. First, we form the filter design problem using the modified least-squares (MLS) criterion and express it as the quadratic form with respect to the numerator and denominator coefficients. Next, we show the relaxation method using the Lagrange multiplier method in order to search for the good solution efficiently. Additionally we can check the filter stability when designing the denominator coefficients. Finally, we show the effectiveness of the proposed method using a numerical example.

This paper discusses the least-squares linear filtering and smoothing (fixed-point and fixed-interval) problems of discrete-time signals from observations, perturbed by additive white noise, which can be randomly delayed by one sampling time. It is assumed that the Bernoulli random variables characterizing delay measurements are correlated in consecutive time instants. The marginal distribution of each of these variables, specified by the probability of a delay in the measurement, as well as their correlation function, are known. Using an innovation approach, the filtering, fixed-point and fixed-interval smoothing recursive algorithms are obtained without requiring the state-space model generating the signal; they use only the covariance functions of the signal and the noise, the delay probabilities and the correlation function of the Bernoulli variables. The algorithms are applied to a particular transmission model with stand-by sensors for the immediate replacement of a failed unit.

This paper presents the selective orthogonal matrix least-squares (SOM-LS) method for representing a multiport network characterized by sampled data with the rational matrix, improving the previous works, and providing new criteria. Recently, it is needed in a circuit design to evaluate physical effects of interconnects and package, and the evaluation is done by numerical electromagnetic analysis or measurement by network analyzer. Here, the SOM-LS method with the criteria will play an important role for generating the macromodels of interconnects and package in circuit simulation level. The accuracy of the macromodels is predictable and controllable, that is, the SOM-LS method fits the rational matrix to the sampled data, selecting the dominant poles of the rational matrix. In examples, simple PCB models are analyzed, where the rational matrices are described by Verilog-A, and some simulations are carried out on a commercial circuit simulator.

This paper presents a new fast and robust circle extraction method that is capable of extracting circles from images with complicated backgrounds. It is not based on the Hough transform (HT) that requires a time-consuming voting process. The proposed method uses a least-squares circle fitting algorithm for extracting circles. The arcs are fitted by extended digital lines that are extracted by a fast line extraction method. The proposed method calculates accurate circle parameters using the fitted arcs instead of evidence histograms in the parameter space. Tests performed on various real-world images show that the proposed method quickly and accurately extracts circles from complicated and heavily corrupted images.

In a high-rate indoor wireless personal communication system, the delay spread due to multi-path propagation results in intersymbol interference which can significantly increase the transmission bit error rate (BER). The technique most commonly used for combating the intersymbol interference and frequency-selective fading found in communications channels is the adaptive equalization. In this paper, we propose a novel neural detector based on self-organizing map (SOM) to improve the system performance of the receiver. In the proposed scheme, the SOM is used as an adaptive detector of equalizer, which updates the decision levels to follow the received faded signal. To adapt the proposed scheme to the time-varying channel, we use the Euclidean distance, which will be updated automatically according to the received faded signal, as an adaptive radius to define the neighborhood of the winning neuron of the SOM algorithm. Simulations on a 16 QAM system show that the receiver using the proposed neural detector has a significantly better BER performance than the traditional receiver.

In this paper, we proposed a novel two-stage channel estimation (2S-CE) method. In contrast to conventional channel estimation methods, this method makes the maximum use of the information contributed by the known data in every transmission burst. In the first stage, the least-squares (LS) algorithm was used to estimate the channel impulse response (CIR) based on the normal training sequence. Then the maximum channel memory was estimated and used to locate the uncorrupted data in the guard interval. In the second stage, the uncorrupted data together with the normal training sequence were sent to the LS algorithm again to obtain the fine-tuned CIR. To verify the efficiency of the proposed 2S-CE method, both a theoretical analysis and computer simulations have been done. Computer simulation results confirm the analysis results and demonstrate that the proposed 2S-CE method outperforms a conventional single-stage channel estimation method.

This paper considers the least-squares linear estimation problem of signals from randomly delayed observations when the additive white noise is correlated with the signal. The delay values are treated as unknown variables, modelled by a binary white noise with values zero or one; these values indicate that the measurements arrive in time or they are delayed by one sampling time. A recursive one-stage prediction and filtering algorithm is obtained by an innovation approach and do not use the state-space model of the signal. It is assumed that both, the autocovariance functions of the signal and the crosscovariance function between the signal and the observation noise are expressed in a semi-degenerate kernel form; using this information and the delay probabilities, the estimators are recursively obtained.

This paper proposes a new correction technique for a linear amplification with nonlinear components (LINC) transmitter. The technique, which is based on the minimum mean squared error (MMSE) criterion, estimates the gain and phase imbalance between the two amplifier branches. With information on the estimation, the imbalance is offset by controlling the amplitude and phase of the input signal that is fed into one of the two amplifiers. Computer simulations with a DS-CDMA system demonstrate that this method can compensate for the imbalance and sufficiently suppress the out-of-band distortion spectrum.

In this paper, we propose a simple method to find the optimal rational function, with a fixed denominator, which minimizes an integral of polynomially weighted squared error to given analytic function. Firstly, we present a generalization of the Walsh's theorem. By using the knowledge on the zeros of the fixed denominator, this theorem characterizes the optimal rational function with a system of linear equations on the coefficients of its numerator polynomial. Moreover when the analytic function is specially given as a polynomial, we show that the optimal numerator can be derived without using any numerical integration or any root finding technique. Numerical examples demonstrate the practical applicability of the proposed method.

The jaw movements can be measured by estimating the position and orientation of two small permanent magnets attached on the upper and lower jaws. It is a difficult problem to estimate the positions and orientations of the magnets from magnetic field because it is a typical inverse problem. The back propagation neural networks (BPNN) are applicable to solve this problem in short processing time. But its precision is not enough to apply to practical measurement. In the other hand, precise estimation is possible by using the nonlinear least-square (NLS) method. However, it takes long processing time for iterative calculation, and the solutions may be trapped in the local minima. In this paper, we propose a precise and fast measurement system which makes use of the estimation algorithm combining BPNN with NLS method. In this method, the BPNN performs an approximate estimation of magnet parameters in short processing time, and its result is used as the initial value of iterative calculation of NLS method. The cost function is solved by Gauss-Newton iteration algorithm. Precision, processing time and noise immunity were examined by computer simulations. These results shows the proposed system has satisfactory ability to be applied to practical measurement.

The interconnect analysis of on- and off-chips is very important in the design of high-speed signal processing, digital communication, and microwave electronic systems. When the interconnects are characterized by sampled data via electromagnetic analysis, the circuit-level simulation of the network requires rational approximation of the sampled data. Since the frequency band of the sampled data is more than 10 GHz, the rational function must fit into it at many frequency points. The rational function is approximated using the orthogonal least-squares method. With an increase in the number of the fitting data, the least-squares method suffers from a singularity problem. To avoid this, the sampled data are hierarchically approximated in this paper. Moreover, to reduce the computational cost of the circuit-level simulation, the parameter matrix of the interconnects is approximated by a rational matrix with one common denominator polynomial, and the selective orthogonalization procedure is presented.

This paper presents an approach to the blind identification of multichannel communication systems by using partial knowledge of the channel. The received signal is first processed by a filter constructed by the known component of the channel and then a blind identification algorithm based on the second-order statistics is applied to the filtered signal. It is shown that, if the unknown component satisfies the identifiability condition, the channel can be identified even though the channel does not satisfy the identifiability condition. Simulation results are presented to show the performance of the proposed approach. A comparison to the existing approaches is also presented.

This paper proposes adaptive line enhancers with new coefficient update algorithms on the basis of least-square-error criteria. Adaptive algorithms by least-squares are known to converge faster than stochastic-gradient ones. However they have high computational complexity due to matrix inversion. To avoid matrix inversion the proposed algorithms adapt only one coefficient to detect one sinusoid. Both FIR and IIR types of adaptive algorithm are presented, and the techniques to reduce the influence of additive noise is described in this paper. The proposed adaptive line enhancers have simple structures and show excellent convergence characteristics. While the convergence of gradient-based algorithms largely depend on their stepsize parameters, the proposed ones are free from them.

In this paper, a clustering-based method is proposed for automatically constructing a multi-input Takagi-Sugeno (TS) fuzzy model where only the input-output data of the identified system are available. The TS fuzzy model is automatically generated by the process of structure identification and parameter identification. In the structure identification step, a clustering method is proposed to provide a systematic procedure to partition the input space so that the number of fuzzy rules and the shapes of fuzzy sets in the premise part are determined from the given input-output data. In the parameter identification step, the recursive least-squares algorithm is applied to choose the parameter values in the consequent part from the given input-output data. Finally, two examples are used to illustrate the effectiveness of the proposed method.

A new structure for adaptive AR spectral estimation based on multi-band decomposition of the linear prediction error is introduced and the mathematical background for the soulution of the related adaptive filtering problem is derived. The presented structure gives rise to AR spectral estimates that represent the true underlying spectrum with better fidelity than conventional LS methods by allowing an arbitrary trade-off between variance of spectral estimates and tracking ability of the estimator along the frequency spectrum. The linear prediction error is decomposed through a filter bank and components of each band are analyzed by different window lengths, allowing long windows to track slowly varying signals and short windows to observe fastly varying components. The correlation matrix of the input signal is shown to satisfy both time-update and order-update properties for rectangular windowing functions, and an RLS algorithm based on each property is presented. Adaptive forward and backward relations are used to derive a mathematical framework that serves as a basis for the design of fast RLS alogorithms. Also, computer experiments comparing the performance of conventional and the proposed multi-band methods are depicted and discussed.

This paper is devoted to a new design method for infinite impulse response approximate inverse system of a nonminimum phase system. The design is carried out such that the convolution of the nonminimum phase polynomial and its approximate inverse system can be represented by an approximately linear phase all-pass filter. A method for estimating the time delay and order of an approximate inverse system is also presented. Using infinite impulse response approximate inverse systems better accuracy is achieved with reduced computational complexity. Numerical examples are included to show the effectiveness of the proposed method.