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Abstract - SSAP13 |
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SSAP13.1 |
On Adaptive Local Polynomial Approximation with Varying Bandwidth V. Katkovnik (University of South Africa, South Africa) The local polynomial approximation (LPA) of noisy data is considered with the new adaptive procedure for varying bandwidth selection. The algorithm is simple to implement and nearly optimal within ln N factor in the point-wise risk for estimating the function and its derivatives. The adaptive varying bandwidth enables the algorithm to be spatial adaptive over a wide range of the classes of functions in the sense that its quality is close to that which one could achieve if smoothness of the estimated function was known in advance. It is shown that the cross-validation adjustment of the threshold parameter of the algorithm significantly improves its accuracy. In particular, simulation demonstrates that the adaptive algorithm with the adjusted threshold parameter performs better than the wavelet estimators. |
| SSAP13.2 |
Computationally Efficient Maximum-Likelihood Estimation of Structured Covariance Matrices H. Li (University of Florida, USA); P. Stoica (Uppsala University, Sweden); J. Li (University of Florida, USA) A computationally efficient method for structured covariance matrix estimation is presented. The proposed method provides an Asymptotic (for large samples) Maximum Likelihood estimate of a structured covariance matrix and is referred to as AML. A closed-form formula for estimating Hermitian Toeplitz covariance matrices is derived which makes AML computationally much simpler than most existing Hermitian Toeplitz matrix estimation algorithms. The AML covariance matrix estimator can be used in a variety of applications. We focus on array processing herein and show that AML enhances the performance of angle estimation algorithms, such as MUSIC, by making them attain the corresponding Cramer-Rao bound (CRB) for uncorrelated signals. |
| SSAP13.3 |
Unbiased Identification of Autoregressive Signals Observed in Colored Noise W. Zheng (Unversity of Western Sydney, Australia) Autoregressive (AR) modeling has played an important role in many signal processing applications. This paper is concerned with identification of AR model parameters using observations corrupted with colored noise. A novel formulation of an auxiliary least-squares estimator is introduced so that the autocovariance functions of the colored observation noise can be estimated in a straightforward manner. With this, the colored-noise-induced estimation bias can be removed to yield the unbiased estimate of the AR parameters. The performance of the proposed unbiased estimation algorithm is illustrated by simulation results. The presented work greatly extends the author's previous method that was developed for identification of AR signals observed in white noise. |
| SSAP13.4 |
Continuous-Time AR Process Parameter Estimation from Discrete-Time Data H. Fan (University of Cincinnati, USA); T. Soderstrom, M. Mossberg, B. Carlsson (Uppsala University, Sweden); Y. Zou (University of Cincinnati, USA) The problem of estimating continuous-time autoregressive process parameters from discrete-time data is considered. The basic approach used here is based on replacing the derivatives in the model by discrete-time differences, forming a linear regression and using the least squares method. It is known, however, that all standard approximations of the highest order derivative give a biased least squares estimate even as the sampling interval tends to zero. Some of our previous approaches to overcome this problem are briefly reviewed. Then two new methods are presented. One of them, termed bias compensation, can be easily implemented efficiently in an order recursive manner. Comparative simulation results are also presented. |
| SSAP13.5 |
Blind Frequency Offset and Delay Estimation of Linearly Modulated Signals Using Second Order Cyclic Statistics V. Manimohan, W. Fitzgerald (University of Cambridge, UK) A blind (non-data aided), open-loop, joint frequency offset-delay estimation algorithm for a linearly modulated signal in additive stationary noise is developed by exploiting the cyclostationarity of the signal. By considering the sample cyclic autocorrelation function of the received signal and the probability distribution of the estimation error, a general linear model representation of the problem is obtained, from which the parameters are estimated using a Bayesian approach. The algorithm is then extended to a multiple signals of interest scenario. The algorithm is simulated for both single and multiple BPSK signals. |
| SSAP13.6 |
Parameter Estimation Using Volterra Series M. Hsieh, P. Rayner (University of Cambridge, England, UK) A polynomial approximation to the likelihood function allows for marginalised estimates of model parameters to be obtained in the form of a Volterra series. The series can be applied directly to the observed data vector in an iterative fashion, to converge upon a set of parameter MAP estimates with low computational cost. A sample application towards OCR is used as an illustration. |
| SSAP13.7 |
Wavelet-Domain Modeling and Estimation of Poisson Processes K. Timmermann, R. Nowak (Michigan State University, USA) This paper develops a new wavelet-domain Bayesian framework for modeling and estimating the intensity of a Poisson process directly from count observations. A new multiscale, multiplicative innovations model is developed as a prior for the underlying intensity function. The new prior model leads to a simple and efficient close-form estimator that requires order N computations, where N is the dimension of the intensity function. We compare the new method with previously proposed wavelet-based approach to this problem. |
| SSAP13.8 |
Toeplitz and Hankel Matrix Approximation Using Structured Approach A. Shaw, S. Pokala (Wright State University, USA); R. Kumaresan (University of Rhode Island, USA) Algorithms are presented for least-squares approximation of Toeplitz and Hankel matrices from noise corrupted of ill-composed matrices, which may not have correct structural or rank properties. Utilizing Caratheodery's Theorem on complex number representation to model the Toeplitz and Hankel matrices, it is shown that these matrices possess specific row and column structures. The inherent structures of the matrices are exploited to develop a computational algorithm for estimation of the matrices that are closest, in the Frobenius norm sense, to the given noisy or rank-excessive matrices. Simulation studies bear out the effectiveness of the proposed algorithms providing significantly better results than the state-space methods. |
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