Estimation of Autoregressive Parameters from Noisy Observations Using Iterated Covariance Updates

Estimating the parameters of the autoregressive (AR) random process is a problem that has been well-studied. In many applications, only noisy measurements of AR process are available. The effect of the additive noise is that the system can be modeled as an AR model with colored noise, even when the measurement noise is white, where the correlation matrix depends on the AR parameters. Because of the correlation, it is expedient to compute using multiple stacked observations. Performing a weighted least-squares estimation of the AR parameters using an inverse covariance weighting can provide significantly better parameter estimates, with improvement increasing with the stack depth. The estimation algorithm is essentially a vector RLS adaptive filter, with time-varying covariance matrix. Different ways of estimating the unknown covariance are presented, as well as a method to estimate the variances of the AR and observation noise. The notation is extended to vector autoregressive (VAR) processes. Simulation results demonstrate performance improvements in coefficient error and in spectrum estimation

Frequency estimation : Survey of parametric methods

This paper is a survey of parametric modeling applied to frequency estimation of sinusoidal signals corrupted by an additive noise . A summary of major estimation methods using second or higher order statistics is presented . Discussed techniques include classica l AR modeling (based on Yule-Walker equations) and "High Resolution" methods (Truncated SVD, Root-MUSIC and ESPRIT) . Th e maximum likelihood estimator and Bayesian methods are also under interest . But the selection of the model order in these method s is often a critical one . Thus major model order estimation methods are reviewed . Finally, the efficiency of each method is examined through a simulation example .Le but de cet article est de dresser un panorama des méthodes paramétriques appliquées à l'estimation de fréquences de signaux sinusoïdaux bruités (bruit additif). Nous rappelons les principales méthodes d'estimation basées sur les moments du signal : méthodes classiques déduites des équations de Yule-Walker et méthodes « Haute Résolution » (SVD tronquée, Root-MUSIC et ESPRIT). Nous présentons aussi l'estimateur du maximum de vraisemblance et l'estimation Bayésienne. L'efficacité de ces méthodes étant souvent liée au choix de l'ordre du modèle, nous rappelons les principaux estimateurs de l'ordre. Enfin, une comparaison des méthodes met en évidence les performances de chacune

Oversampled A/D Conversion and Error-Rate Dependence of Non-Bandlimited Signals with Finite Rate of Innovation

We study the problem of A/D conversion and error-rate dependence of a class of non-bandlimited signals which have a finite rate of innovation, particularly, a continuous periodic stream of Diracs, characterized by a finite set of time positions and weights. Previous research has only considered sampling of this type of signals, ignoring the presence of quantization, which is necessary for any practical application. We first define the concept of consistent reconstruction for these signals and introduce the operations of both: a) oversampling in frequency, determined by the bandwidth of the low pass filtering used in the signal acquisition, and b) oversampling in time, determined by the number of samples in time taken from the filtered signal. Accuracy in a consistent reconstruction is achieved by enforcing the reconstructed signal to satisfy three sets of constrains, defined by: the low-pass filtering operation, the quantization operation itself and the signal space of continuous periodic streams of Diracs. We provide two schemes to reconstruct the signal. For the first one, we prove that the mean squared error (MSE) of the time positions is of the order of O(1/R_t^2R_f^3), where R_t and R_f are the oversampling ratios in time and in frequency, respectively. For the second scheme, which has a higher complexity, it is experimentally observed that the MSE of the time positions is of the order of O(1/R_t^2R_f^5). Our experimental results show a clear advantage of consistent reconstruction over non-consistent reconstruction. Regarding the rate, we consider a threshold crossing based scheme where, as opposed to previous research, both oversampling in time and also in frequency influence the coding rate. We compare the error-rate dependence behavior that is obtained from both increasing the oversampling in time and in frequency, on the one hand, and on the other hand, from decreasing the quantization stepsize

Ship target recognition

Includes bibliographical references.In this report the classification of ship targets using a low resolution radar system is investigated. The thesis can be divided into two major parts. The first part summarizes research into the applications of neural networks to the low resolution non-cooperative ship target recognition problem. Three very different neural architectures are investigated and compared, namely; the Feedforward Network with Back-propagation, Kohonen's Supervised Learning Vector Quantization Network, and Simpson's Fuzzy Min-Max neural network. In all cases, pre-processing in the form of the Fourier-Modified Discrete Mellin Transform is used as a means of extracting feature vectors which are insensitive to the aspect angle of the radar. Classification tests are based on both simulated and real data. Classification accuracies of up to 93 are reported. The second part is of a purely investigative nature, and summarizes a body of research aimed at exploring new ground. The crux of this work is centered on the proposal to use synthetic range profiling in order to achieve a much higher range resolution (and hence better classification accuracies). Included in this work is a comprehensive investigation into the use of super-resolution and noise reducing eigendecomposition techniques. Algorithms investigated include the Principal Eigenvector Method, the Total Least Squares Method, and the MUSIC method. A final proposal for future research and development concerns the use of time domain averaging to improve the classification performance of the radar system. The use of an iterative correlation algorithm is investigated

Exact and approximate Strang-Fix conditions to reconstruct signals with finite rate of innovation from samples taken with arbitrary kernels

In the last few years, several new methods have been developed for the sampling and exact reconstruction of specific classes of non-bandlimited signals known as signals with finite rate of innovation (FRI). This is achieved by using adequate sampling kernels and reconstruction schemes. An example of valid kernels, which we use throughout the thesis, is given by the family of exponential reproducing functions. These satisfy the generalised Strang-Fix conditions, which ensure that proper linear combinations of the kernel with its shifted versions reproduce polynomials or exponentials exactly. The first contribution of the thesis is to analyse the behaviour of these kernels in the case of noisy measurements in order to provide clear guidelines on how to choose the exponential reproducing kernel that leads to the most stable reconstruction when estimating FRI signals from noisy samples. We then depart from the situation in which we can choose the sampling kernel and develop a new strategy that is universal in that it works with any kernel. We do so by noting that meeting the exact exponential reproduction condition is too stringent a constraint. We thus allow for a controlled error in the reproduction formula in order to use the exponential reproduction idea with arbitrary kernels and develop a universal reconstruction method which is stable and robust to noise. Numerical results validate the various contributions of the thesis and in particular show that the approximate exponential reproduction strategy leads to more stable and accurate reconstruction results than those obtained when using the exact recovery methods.Open Acces

Exploiting the spatio-temporal channel properties of multiple antenna systems

The spatio-temporal channel properties of multiple antenna systems are exploited to obtain new approaches to localization and channel prediction. It is shown that a mobile station can be localized in multipath environments under the explicit consideration of scatterers. Thus, unlike conventional localization systems, the scatterers are used as an aid in localization. Moreover, it is shown that channel prediction in multiple antenna systems can be performed using linear prediction filters. This result is used to propose optimal and computationally inexpensive suboptimal channel predictors

Separation of multiple time delays using new spectral estimation schemes

Includes bibliographical references.The problem of estimating multiple time delays in presence of colored noise is considered in this paper. This problem is first converted to a high-resolution frequency estimation problem. Then, the sample lagged covariance matrices of the resulting signal are computed and studied in terms of their eigenstructure. These matrices are shown to be as effective in extracting bases for the signal and noise subspaces as the standard autocorrelation matrix, which is normally used in MUSIC and the pencil-based methods. Frequency estimators are then derived using these subspaces. The effectiveness of the method is demonstrated on two examples: a standard frequency estimation problem in presence of colored noise and a real-world problem that involves separation of multiple specular components from the acoustic backscattered from an underwater target.This work was supported by the Office of Naval Research (ONR 321TS). The Technical Agent was Coastal Systems Station, Panama City, FL

System Identification Based on Errors-In-Variables System Models

We study the identification problem for errors-in-variables (EIV) systems. Such an EIV model assumes that the measurement data at both input and output of the system involve corrupting noises. The least square (LS) algorithm has been widely used in this area. However, it results in biased estimates for the EIV-based system identification. In contrast, the total least squares (TLS) algorithm is unbiased, which is now well-known, and has been effective for estimating the system parameters in the EIV system identification. In this dissertation, we first show that the TLS algorithm computes the approximate maximum likelihood estimate (MLE) of the system parameters and that the approximation error converges to zero asymptotically as the number of measurement data approaches infinity. Then we propose a graph subspace approach (GSA) to tackle the same EIV-based system identification problem and derive a new estimation algorithm that is more general than the TLS algorithm. Several numerical examples are worked out to illustrate our proposed estimation algorithm for the EIV-based system identification. We also study the problem of the EIV system identification without assuming equal noise variances at the system input and output. Firstly, we review the Frisch scheme, which is a well-known method for estimating the noise variances. Then we propose a new method which is GSA in combination with the Frisch scheme (GSA-Frisch) algorithm via estimating the ratio of the noise variances and the system parameters iteratively. Finally, a new identification algorithm is proposed to estimate the system parameters based on the subspace interpretation without estimating noise variances or the ratio. This new algorithm is unbiased, and achieves the consistency of the parameter estimates. Moreover, it is low in complexity. The performance of the identification algorithm is examined by several numerical examples, and compared to the N4SID algorithm that has the Matlab codes available in Matlab toolboxes, and also to the GSA-Frisch algorithm

Narrowband Interference Suppression in Spread Spectrum Communication Systems

Of significant interest to the United States military is the ability of an enemy to deny or disrupt the operation of the Global Positioning System. To combat this threat the GPS JPO initiated the Tactical GPS AntiJam Technology project, which yielded a prototype Digital Excision Filter (DEF) to remove narrowband jammers. This research describes the work performed to get the DEF hardware operational and extends the previous research performed in this area. Comdisco\u27s Signal Processing Worksystem was used to examine the effect of the DEF on the probability of bit error. This research uses peak to average correlation value, probability of bit error, and percent jammer power removed to examine the performance of the DEF. Fourteen jamming scenarios are examined using CW, pulsed CW, and broadband noise jammers. The DEF effectively rejected all of the jammers except the broadband noise jammer. In scenarios other than the broadband noise jammer, the DEF removed over 98% of the jammer power. The bit error rate curves show that the DEF significantly enhanced the performance of the system in extreme jamming environments. The results presented in this research show that the DEF is a viable, robust option to remove narrowband interference

Parameter recovery for transient signals

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (p. 115-118).Transient signals naturally arise in numerous disciplines for which the decay rates and amplitudes carry some informational significance. Even when the decay rates are known, solving for the amplitudes results in an ill-conditioned formulation. Transient signals in the presence of noise are further complicated as the signal-to-noise ratio asymptotically decreases in time. In this thesis the Discrete-Time Transient Transform and the Discrete Transient Transform are defined in order to represent a general signal using a linear combination of decaying exponential signals. A common approach to computing a change of basis is to make use of the dual basis. Two algorithms are proposed for generating a dual basis: the first algorithm is specific to a general exponential basis, e.g., real exponential or harmonically related complex exponential bases are special cases of the general exponential basis, while the second algorithm is usable for any general basis. Several properties of a transient domain representation are discussed. Algorithms for computing numerically stable approximate transient spectra are additionally proposed. The inherent infinite bandwidth of a continuous-time transient signal motivates in part the development of a framework for recovering the decay rates and amplitudes of a discrete-time lowpass filtered transient signal. This framework takes advantage of existing parameter modeling, identification, and recovery techniques to determine the decay rates while an alternating projection method utilizing the Discrete Transient Transform determines the amplitudes.by Tarek A. Lahlou.S.M