eLearning

Blind Subspace-Based Signature Estimation in DS-CDMA Systems With Unknown Wide-Sense Stationary Interference

Keyvan Zarifi; Alex B. Gershman IEEE Transactions on Signal Processing, 2007

In this paper, we propose a new blind subspace-based signature waveform estimation technique for direct-sequence code division multiple-access (DS- CDMA) communication systems operating in the presence of unknown wide-sense stationary interference. Unlike the existing algorithms, the proposed technique requires just a single receive antenna and is applicable to the case of arbitrary transmitted symbol constellations. Necessary and sufficient conditions for ...

Receive array pattern modification using covariance matrix augmentation

R. J. Mailloux Proceedings of International Symposium on Phased Array Systems and Technology, 1996

Techniques are presented to produce array pattern troughs in response to discrete sources of interference. The basic technique is adaptive and is implemented by a simple modification of the measured covariance matrix. It can be used to form troughs in both the near and far zones. A related technique is shown to be useful for deterministically producing nulls or troughs ...

Local failure localization in large sensor networks

Romain Couillet; Walid Hachem 2011 Conference Record of the Forty Fifth Asilomar Conference on Signals, Systems and Computers (ASILOMAR), 2011

The joint fluctuations of the extreme eigenvalues and eigenvectors of large sample covariance matrices of the spiked-model type are analyzed. This result is used to develop an original framework for the diagnosis of local failures in sensor networks, corroborated by simulations.

Applications of Optical Signal Processing to Adaptive Antennas

E. C. Malarkey; P. R. Beaudet; J. C. Bradley; J. H. Mims MILCOM 1987 - IEEE Military Communications Conference - Crisis Communications: The Promise and Reality, 1987

A method of factoring within the prime modular subprocessors in an optical processor which employs residue number systems in solution of adaptive antenna problems is described. The resultant system is shown to afford the same degree of computational accuracy at substantial reductions in the numbers of optical components required. Illustrative examples are given for a very small modulus, and the ...

A bilinear extension of subspace identification for systems subject to white inputs

W. Favoreel; B. De Moor; P. Van Overschee Proceedings of the 1997 American Control Conference (Cat. No.97CH36041), 1997

We generalize a class of existing linear subspace identification techniques to subspace identification algorithms for bilinear, discrete time, time invariant systems. A major assumption we make is that the input should be white. It is shown that in that case most of the properties of linear subspace identification theory can be extended to equivalent properties for bilinear systems. The practical ...

More eLearning Resources

IEEE-USA E-Books

• Differential Entropic Clustering of Multivariate Gaussians

  Gaussian data is pervasive and many learning algorithms (e.g., k-means) model their inputs as a single sample drawn from a multivariate Gaussian. However, in many real-life settings, each input object is best described by multiple samples drawn from a multivariate Gaussian. Such data can arise, for example, in a movie review database where each movie is rated by several users, or in time-series domains such as sensor networks. Here, each input can be naturally described by both a mean vector and covariance matrix which parameterize the Gaussian distribution. In this paper, we consider the problem of clustering such input objects, each represented as a multivariate Gaussian. We formulate the problem using an information theoretic approach and draw several interesting theoretical connections to Bregman divergences and also Bregman matrix divergences. We evaluate our method across several domains, including synthetic data, sensor network data, and a statistical debugging application.

• Vector Radiative Transfer

  Chapter 2 introduces the vector radiative transfer (VRT) theory of random media. It provides the scattering, absorption and extinction coefficients and the phase matrix of non-spherical scatterers in natural media. The first-order Mueller matrix solution of VRT for vegetation canopy model is derived. Polarization indexes, eigen-analysis and entropy are presented. Statistics of multi-look SAR images and covariance matrix are also investigated.

• Some Probability and Stochastic Convergence Fundamentals

  This chapter contains sections titled: Notations and Definitions The Covariance Matrix of a Function of a Random Variable Sample Variables Mixing Random Variables Preliminary Example Definitions of Stochastic Limits Interrelations between Stochastic Limits Properties of Stochastic Limits Laws of Large Numbers Central Limit Theorems Properties of Estimators Cramér-Rao Lower Bound How to Prove Asymptotic Properties of Estimators? Pitfalls Preliminary Example - Continued Properties of the Noise after a Discrete Fourier Transform Exercises Appendixes

• A Serial Approach to Handling High-Dimensional Measurements in the Sigma-Point Kalman Filter

  Pose estimation is a critical skill in mobile robotics and is often accomplished using onboard sensors and a Kalman filter estimation technique. For systems to run online, computational efficiency of the filter design is crucial, especially when faced with limited computing resources. In this paper, we present a novel approach to serially process high-dimensional measurements in the Sigma-Point Kalman Filter (SPKF), in order to achieve a low computational cost that is linear is the measurement dimension. Although the concept of serially processing measurements has been around for quite some time in the context of the Extended Kalman Filter (EKF), few have considered this approach with the SPKF. At first glance, it may be tempting to apply the SPKF update step serially. However, we prove that without re-drawing sigma points, this 'naive' approach cannot guarantee the positive-definiteness of the state covariance matrix (not the case for the EKF). We then introduce a novel method for the Sigma-Point Kalman Filter to process high-dimensional, uncorrelated measurements serially that is algebraically equivalent to processing the measurements in parallel, but still achieves a computational cost linear in the measurement dimension.

• Normal Equations

  This chapter contains sections titled: Mean-Square Error Criterion Minimization by Differentiation Minimization by Completion of Squares Minimization of the Error Covariance Matrix Optimal Linear Estimator

• Barankin Bounds on Parameter Estimation

  The Schwarz inequality is used to derive the Barankin lowerbounds on the covariance matrix of unbiased estimates of a vector parameter. The bound is applied to communications and radar problems in which the unknown parameter is embedded in a signal of known form and observed in the presence of additive white Gaussian noise. Within this context it is shown that the Barankin bound reducesto the Cramér-Rao bound when the signal-to-noise ratio (SNR) is large. However, as the SNR is reduced beyond a critical value, the Barankln bound deviates radically from the Cramér-Rao bound, exhibiting the so-called threshold effect. The bounds were applied to the linear FM waveform, and within the resulting class of bounds it waspossible to selectone that led to a closed-form expression for the lower bound on the variance of an unbiased range estimate. This expression clearly demonstrates the threshold behavior one must expect when using a nonlinear modulation system. Tighter bounds were easily obtained, but these had to be evaluated numerically. The sidelobe structure of the linear FM compressed pulse leads to a significant increase in the variance of the estimate. For a practical linear FM pulse of 1-s duration and 40-MHz bandwidth, the radar must operate at an SNR greater than 10 dB if meaningful unbiased range estimates are to be obtained.

• Estimation with Unknown Noise Model - Standard Solutions

  This chapter contains sections titled: Introduction Discussion of the Disturbing Noise Assumptions Properties of the ML Estimator Using a Sample Covariance Matrix Properties of the GTLS Estimator Using a Sample Covariance Matrix Properties of the BTLS Estimator Using a Sample Covariance Matrix Properties of the SUB Estimator Using a Sample Covariance Matrix Identification in the Presence of Nonlinear Distortions Illustration and Overview of the Properties Identification of Parametric Noise Models Identification in Feedback Appendixes

• MeanSquared Error and Threshold SNR Prediction of MaximumLikelihood Signal Parameter Estimation With Estimated Colored Noise Covariances

  An interval error-based method (MIE) of predicting mean squared error (MSE) performance of maximum-likelihood estimators (MLEs) is extended to the case of signal parameter estimation requiring intermediate estimation of an unknown colored noise covariance matrix; an intermediate step central to adaptive array detection and parameter estimation. The successful application of MIE requires good approximations of two quantities: 1) interval error probabilities and 2) asymptotic (SNR local MSE performance of the MLE. Exact general expressions for the pairwise error probabilities that include the effects of signal model mismatch are derived herein, that in conjunction with the Union Bound provide accurate prediction of the required interval error probabilities. The Cramér-Ran Bound (CRB) often provides adequate prediction of the asymptotic local MSE performance of MLE. The signal parameters, however, are decoupled from the colored noise parameters in the Fisher Information Matrix for the deterministic signal model, rendering the CRB incapable of reflecting loss due to colored noise covariance estimation. A new modification of the CRB involving a complex central beta random variable different from, but analogous to the Reed, Mallett, and Brennan beta loss factor provides a working solution to this problem, facilitating MSE prediction well into the threshold region with remarkable accuracy.

• Utilization of Modified Polar Coordinates for BearingsOnly Tracking

  Previous studies have shown that the Cartesian coordinate extended Kalman filter exhibits unstable behavior characteristics when utilized for bearings- only target motion analysis (TMA). In contrast. fonnulating the TMA estimation problem in modified polar (MP) coordinates leads to an extended Kalman filter which is both stable and asymptotically unbiased. Exact state equations for the MP filter are derived without imposing any restrictions on own-ship motion; thus, prediction accuracy inherent in the traditional Cartesian formulation is completely preserved. In addition, these equations reveal that MP coordinates are well-suited for bearings-only TMA because they automatically decouple observable and unobservable components of the estimated state vector.Such decoupling is shown to prevent covariance matrix ill- condttioning, which is the primary cause of filter instability. Further investigation also confirms that the MP state estimates are asymptotically unbiased. Realistic simulation data are presented to support these findings and to compare algorithm performance with respect to the Cramer-Rao lower bound (ideal) as well as the Cartesian and pseudolinear filters.

• Analysis of Contour Motions

  A reliable motion estimation algorithm must function under a wide range of conditions. One regime, which we consider here, is the case of moving objects with contours but no visible texture. Tracking distinctive features such as corners can disambiguate the motion of contours, but spurious features such as T-junctions can be badly misleading. It is difficult to determine the reliability of motion from local measurements, since a full rank covariance matrix can result from both real and spurious features. We propose a novel approach that avoids these points altogether, and derives global motion estimates by utilizing information from three levels of contour analysis: edgelets, boundary fragments and contours. Boundary fragment are chains of orientated edgelets, for which we derive motion estimates from local evidence. The uncertainties of the local estimates are disambiguated after the boundary fragments are properly grouped into contours. The grouping is done by constructing a graphical model and marginalizing it using importance sampling. We propose two equivalent representations in this graphical model, reversible switch variables attached to the ends of fragments and fragment chains, to capture both local and global statistics of boundaries. Our system is successfully applied to both synthetic and real video sequences containing high-contrast boundaries and textureless regions. The system produces good motion estimates along with properly grouped and completed contours.