It is well known that KT method proposed by R. Kumaresan and D. W. Tufts is used as a popular parameter estimation method of exponentially damped signal. It is based on linear backward-prediction method and singular value decomposition (SVD). However, it is difficult to estimate parameters correctly by KT method in the case when high noise exists in the signal. In this paper, we propose a parameter (frequency components and damping factors) estimation method to improve the performance of KT method under high noise. In our proposed method, we find the signal zero groups by calculating zeros with different data record lengths according to the combination of forward-prediction and backward-prediction, the mean value of the zeros in the signal zero groups are calculated to estimate the parameters of the signal. The proposed method can estimate parameters correctly and accurately even when high noise exists in the signal. Simulation results are shown to confirm the effectiveness of the proposed method.

Implementation of Multi-Input Multi-Output (MIMO) channel sounder is considered, taking hardware cost and realtime measurement into account. A remarkable difference between MIMO and conventional Single-Input Multi-Output (SIMO) channel sounding is that the MIMO sounder needs some kind of multiplexing to distinguish transmitting antennas. We compared three types of multiplexing TDM, FDM, and CDM for the sounding purpose, then we chose FDM based technique to achieve cost effectiveness and realtime measurement. In the framework of FDM, we have proposed an algorithm to estimate MIMO channel parameters. Furthermore the proposed algorithm was implemented into the hardware, and the validity of the proposed algorithm was evaluated through measurements in an anechoic chamber.

We present a new family of algorithms that solve the bias problem in the equation-error based adaptive infinite impulse response (IIR) filtering. A novel constraint, called the constant-norm constraint, unifies the quadratic constraint and the monic one. By imposing the monic constraint on the mean square error (MSE) optimization, the merits of both constraints are inherited and the shortcomings are overcome. A new cost function based on the constant-norm constraint and Lagrange multiplier is defined. Minimizing the cost function gives birth to a new family of bias-free adaptive IIR filtering algorithms. For example, two efficient algorithms belonging to the family are proposed. The analysis of the stationary points is presented to show that the proposed methods can indeed produce bias-free parameter estimates in the presence of white noise. The simulation results demonstrate that the proposed methods indeed produce unbiased parameter estimation, while being simple both in computation and implementation.

A modified version of the SAGE algorithm is presented for joint delay-azimuth-attenuation parameters' estimation in a multiuser DS-CDMA system. The introduced modification consists of using different time interval lengths when calculating the time correlations for optimizing the different channel parameters. This modification was proposed for the purpose of a further reduction in the algorithm's computational weight in case of receiving sufficiently resolvable waves. Specifically, we found that short interval windows are sufficient for estimating delays and azimuth angles, which is quite effective in reducing the computational burden in their optimization processes. As for the estimation of the attenuation parameters, a longer time window, equal to the preamble length, is considered for more accurate estimation. Also two other estimators are proposed. The first one combining the modified SAGE with a sequential estimation of the attenuation parameters, suitable for slowly varying channels. Another one, similar to the first, and primarily designed to alleviate the influence of present strong interferers. Through a numerical example, the performances of the three presented estimation schemes, in terms of their near-far resistance, are compared. And it is shown that the proposed second combined estimator outperforms the modified SAGE in environments with high MAI levels.

This paper deals with a method of estimating the parameters and the order of a linear system using differential digital filters and the resultant. From the observed signals of the input and output of an objective system, we extract the differential signals from the zero order to an appropriate high order with the same phase characteristics, using several digital filters. On the assumption that the system order is known, we estimate the parameters of the transfer function and evaluate the estimation error bounds. We propose a criterion function generated by the product of the highest order coefficients and the resultant of the numerator and denominator of the estimated transfer function. Applying this criterion function, we can estimate the order of the objective system. The threshold corresponding to this criterion function is evaluated from the deviation in the frequency characteristics of the used differential filters and the error bound of the estimated parameters. In order to demonstrate the propriety of the proposed method, some numerical simulations are presented.

Effects of the model order estimation error in the TLS-ESPRIT algorithm were investigated. It was found that if the model order is overestimated true signal parameters are preserved even though spurious signals of which power values are negligibly small appear, whereas if the model order is underestimated some signals degenerate to each others, resulting in the erroneous estimates.

An unbiased estimation method for symmetric noncausal ARMA model parameters is presented. The proposed algorithm works in two steps: first, a spectrally equivalent causal system is identified by lattice whitening filter and then the equivalent noncausal system is reconstructed. For AR system with noise or ARMA system without noise, the proposed method does not need any iteration method nor any optimization procedure. An estimation method of noise variance when the observation is made in noisy situation is discussed. The potential capabilities of the algorithm are demonstrated by using some numerical examples.

Image restoration using estimated parameters of image model and noise statistics is presented. The image is modeled as the output of a 2-D noncausal autoregressive (NCAR) model. The parameter estimation process is done by using the autocorrelation function and a biased term to a conventional least-squares (LS) method for the noncausal modeling. It is shown that the proposed method gives better results than the other parameter estimation methods which ignore the presence of the noise in the observation data. An appropriate image model selection process is also presented. A genetic algorithm (GA) for solving a multiobjective function with single constraint is discussed.

From an information geometric viewpoint, we investigate a characteristic of the submanifold of a mixture or exponential family in the manifold of finite discrete distributions. Using the characteristic, we derive a direct calculation method for an em-geodesic in the submanifold. In this method, the value of the primal parameter on the geodesic can be obtained without iterations for a gradient system which represents the geodesic. We also derive the similar algorithms for both problems of parameter estimation and functional extension of the submanifold for a data in the ambient manifold. These theoretical approaches from geometric analysis will contribute to the development of an efficient algorithm in computational complexity.

This paper describes a new high resolution algorithm for the two-dimensional (2-D) frequency estimation problem, which, in particular, is noise insensitive in view of the fact that in many practical applications the contaminated noise may not be white noise. For this purpose, the approach is set in the context of higher-order statistics (HOS), which has demonstrated to be an effective approach under a colored noise environment. The algorithm begins with the consideration of the fourth-order moments of the available 2-D data. Two auxiliary matrices, constituted by a novel stacking of the diagonal slice of the computed fourth-order moments, are then introduced and through which the two frequency components can be precisely determined, respectively, via matrix factorizations along with the subspace rotational invariance (SRI) technique. Simulation results are also provided to verify the proposed algorithm.

In this work, a new algorithm for tracking the directions-of-arrival (DOA's) of moving targets by introducing a linear approximation is proposed. The targets are assumed to move with constant angular velocities within a short time and emitting continuously narrow-band signals that impinge on an array of sensors. Therefore the trajectories of targets can be approximated by linear functions of time, which consist of the DOA's and the angular velocities, within the short time. In the condition that the number of targets is known and the outputs vector of the sensors including the additive white complex Gaussian noises is observed continuously, a cost function which consists of the squared residual error vectors is defined. The estimation of the DOA's and the angular velocities of targets is performed by minimizing this cost function. By estimating both the DOA's and the angular velocities at the same time, the proposed algorithm is able to improve the tracking performance for rapidly moving targets. In computer simulations, the performance of the proposed algorithm is compared with the ESPRIT method, which is one of the typical subspace methods with super resolution.

The parameter estimation problem of point spread function is one of the most challenging and important task for image restoration. A new method for the parameter estimation in the case of motion blur is presented here. It is based on the principle that the power spectrum of the motion blurred image contains periodical minima relevant directly to the motion derection and length. Though the principle is very simple and effective in certain cases, the direct use of it may lead to poor performance an the signal-to-noise ratio (SNR) gets lower. To improve the estimation accuracy, by analyzing image noise effect on the detection of the minima, we propose a method to greatly reduce spectral noise, and give the lowest allowed SNR at which the minima may still be identified reliably. We also estimate the power spectrum of the original image, which is a must for the Wiener restoration filter, from the noisy blurred image based on a noncasual autoregressive model. Once above parameters are decided, the Wiener filter is used to restore the noisy blurred image. Our method is very practical; no parameter needs to be known a priori, or to be adjusted manually to fit into various application problems. The proposed method is finally applied to systhesized and real motion blurred images to demonstrate its effectiveness.

The estimation of model parameter is essentially important for an MRF image model to work well. Because the maximum likelihood estimate (MLE), which is statistically optimal, is too difficult to implement, the conventional estimates such as the maximum pseudo-likelihood estimate (MPLE), the coding method estimate (CME), and the least-squares estimate (LSE) are all based on the (conditional) pixel probabilities for simplicity. However, the conventional pixel-based estimators are not very satisfactorily accurate, especially when the interactions of pixels are strong. We therefore propose two window-based estimators to improve the estimation accuracy: the adjoining-conditional-window (ACW) scheme and the separated-conditional-window (SCW) scheme. The replacement of the pixel probabilities by the joint probabilities of window pixels was inspired by the fact that the pixels in an image present information in a joint way and hence the more pixels we deal with the joint probabilities of, the more accurate the estimate should be. The window-based estimators include the pixel-based ones as special cases. We present respectively the relationship between the MLE and each of the two window-based estimates. Through the relationships we provide a unified view that the conventional pixel-based estimates and our window-based estimates all approximate the MLE. The accuracy of all the estimates can be described by two types of superiority: the cross-scheme superiority that an ACW estimate is more accurate than the SCW estimate with the same window size, and the in-scheme superiority that an ACW (or SCW) estimate more accurate than another ACW (or SCW) estimate which uses smaller window size. The experimental results showed the two types of superiority and particularly the significant improvement in estimation accuracy due to using window probabilities instead of pixel probabilities.

We present a new method for the identification of time-invariant multichannel autoregressive (AR) processes corrupted by additive white observation noise. The method is based on the Yule-Walker equations and identifies the autoregressive parameters from a finite set of measured data. The input signals to the underlying process are assumed to be unknown. An inverse filtering technique is used to estimate the AR parameters and the observation noise variance, simultaneously. The procedure is iterative. Computer simulation results that demonstrate the performance of the identification method are presented.

This letter presents new estimation algorithm of ARMAX systems which do not always satisfy the strictly positive real (SPR) condition. We show how estimated parameters can converge to their true values based on the overparameterized system. Finally, the results of computer simulation are presented to illustrate the effectiveness of the proposed method.

This paper presents a modified disparity measurement to recover the depth and a robust method to estimate motion parameters. First, this paper considers phase correspondence for the computation of disparity. It has less computation for disparity than previous methods that use the disparity from correspondence and from correlation. This modified disparity measurement uses the Gabor filter to analyze the local phase property and the exponential filter to analyze the global phase property. These two phases are added to make quasi-linear phases of the stereo image channels which are used for the stereo disparity finding and the structure recovery of scene. Then, we use feature-based correspondence to find the corresponding feature points in temporal image pair. Finally, we combine the depth map and use disparity motion stereo to estimate 3-D motion parameters.

This paper introduces some modelling methods of time-varying stochastic process and its linear/nonlinear adaptive identification. Time-varying models are often identified by using a least square criterion. However the criterion should assume a time invariant stochastic model and infinite observed data. In order to adjust these serious different assumptions, some windowing techniques are introduced. Although the windows are usually applied to a batch processing of parameter estimates, all adaptive methods should also consider them at difference point of view. In this paper, two typical windowing techniques are explained into adaptive processing. In addition to the use of windows, time-varying stochastic ARMA models are built with these criterions and windows. By using these criterions and models, this paper explains nonlinear parameter estimation and the property of estimation convergence. On these discussions, some approaches are introduced, i.e., sophisticated stochastic modelling and multi-rate processing.

In many applications involving the processing of noisy signals, it is desired to know the noise variance. This paper proposes a new method for estimating the noise variance from the signals of autoregressive (AR) and autoregressive moving-average (ARMA) systems corrupted by additive white noise. The method proposed here uses the low-order Yule-Walker (LOYW) equations and the lattice filter (LF) algorithm for the estimation of noise variance from the noisy output measurements of AR and ARMA systems, respectively. Two techniques are proposed here: iterative technique and recursive one. The accuracy of the methods depends on SNR levels, more specifically on the inherent accuracy of the Yule-Walker and lattice filter methods for signal plus noise system. The estimated noise variance is used for the blind indentification of AR and ARMA systems. Finally, to demonstrate the effectiveness of the method proposed here many numerical results are presented.

This paper addresses the problem of estimating the parameters of multivariate ARMA processes by using higher-order statistics called cumulants. The main objective in this paper is to extend the idea of the q-slice algorithm in univariate ARMA processes to multivariate ARMA processes. It is shown for a multivariate ARMA process that the MA coefficient matrices can be estimated up to postmultiplication of a permutation matrix by using the third-order cumulants and of an extended permutation matrix by using the fourth-order cumulants. Simulation examples are included to demonstrate the effectiveness of the proposed method.

This letter extends the Yule-Walker method to the estimation of ARMA parameters from output measurements corrupted by noise. In the proposed method it is assumed that the noise variance and the input are unknown. An algorithm for the estimation of noise variance is, therefore, given. The use of the variance estimation method proposed here together with the Yule-Walker equations allow the estimation of the parameters of a minimum phase ARMA model based only on noisy measurements of its output. Moreover, using this method it is not necessary to slove a set of nonlinear equations for MA parameter estimation as required in the conventional correlation based methods.