eLearning

Multi-resolution matching of uncalibrated images utilizing epipolar geometry and its uncertainty

S. Brandt; J. Heikkonen Proceedings 2001 International Conference on Image Processing (Cat. No.01CH37205), 2001

We have developed a simple and efficient wavelet-based technique for matching points in uncalibrated images. The results show that with the proposed method the probability for obtaining a false match practically vanishes when natural images are used. We also show how the uncertainty of the fundamental matrix can be interpreted from image matching viewpoint and explain how the disparity information ...

Land Cover Change Detection Using the Internal Covariance Matrix of the Extended Kalman Filter Over Multiple Spectral Bands

Brian Paxton Salmon; Waldo Kleynhans; Frans van den Bergh; Jan Corne Olivier; Trienko Lups Grobler; Konrad Johan Wessels IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2013

In this paper, the internal operations of an Extended Kalman Filter is investigated to observe if information can be derived to detect land cover change in a MODerate-resolution Imaging Spectroradiometer (MODIS) time series. The concept is based on the internal covariance matrix used by the Extended Kalman Filter, which adjusts the internal state of the filter for any changes occurring ...

On Multi-User Gain in MIMO Systems with Rate Constraints

Peng Wang; Li Ping IEEE GLOBECOM 2007 - IEEE Global Telecommunications Conference, 2007

In this paper, we study the advantages of multi-user concurrent transmission, measured using the multi-user gain (MUG), in multiple-input multiple-output (MIMO) systems with rate constraints. Our focus is on a maximum eigenmode beamforming (MEB) strategy. We derive a closed-form expression for the transmitted sum power required by the MEB strategy and prove that this strategy is asymptotically optimal. The simple ...

Whitening Dual-Polarized Weather Radar Signals With a Hermitian Transformation

Erich Hefner; V. Chandrasekar IEEE Transactions on Geoscience and Remote Sensing, 2008

Oversampling weather radar signals in range and then whitening these signals has been shown to improve the accuracy of spectral moments. For dual-polarized radar, the polarimetric variables depend upon information gleaned from the cross correlation of the different received signals. Theoretical improvements to the polarimetric variables have been provided to date, but experimental evidence of improvements through whitening has been ...

Data driven fault detection with robustness to uncertain parameters identified in closed loop

Jianfei Dong; Michel Verhaegen; Fredrik Gustafsson 49th IEEE Conference on Decision and Control (CDC), 2010

This paper presents a new robustified data-driven fault detection approach, connected to closed-loop subspace identification. Although data-driven detection methods have recently been reported in the literature, attention has not yet been given to a robust solution coping with identification errors. The key idea of this paper is to analytically quantify the effect of the identification errors on the residual generator ...

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• Approaches to High-Dimensional Covariance and Precision Matrix Estimations

  This chapter introduces several recent developments for estimating large covariance and precision matrices without assuming the covariance matrix to be sparse. It explains two methods for covariance estimation: namely covariance estimation via factor analysis, and precision Matrix Estimation and Graphical Models. The low rank plus sparse representation holds on the population covariance matrix. The chapter presents several applications of these methods, including graph estimation for gene expression data, and several financial applications. It then shows how estimating covariance matrices of high- dimensional asset excess returns play a central role in applications of portfolio allocations and in risk management. The chapter explains the factor pricing model, which is one of the most fundamental results in finance. It elucidates estimating risks of large portfolios and large panel test of factor pricing models. The chapter illustrates the recent developments of efficient estimations in panel data models.

• 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.

• A New Approach to Linear Filtering and Prediction Problems

  The clssical filleting and prediclion problem is re-examined using the Bode- Shannon representation of random processes and the ¿stat-tran-sition¿ method of analysis of dynamic systems. New result are: (1) The formulation and Methods of solution of the problm apply, without modification to stationary and nonstationary stalistics end to growing-memory and infinile -memory filters. (2) A nonlinear difference (or differential) equalion is dericed for the covariance matrix of the optimal estimalion error. From the solution of this equation the coefficients of the difference, (or differential) equation of the optimal linear filter are obtained without further caleulations. (3) Tke fillering problem is shoum to be the dual of the nois-free regulator problem. The new method developed here, is applied to do well-known problems, confirming and extending, earlier results. The discussion is largely, self- contatained, and proceeds from first principles; basic concepts of the theory of random processes are reviewed in the Appendix.

• 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.

• 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

• 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.

• Estimation with Unknown Noise Model

  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

• 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

• Covariance, Subspace, and Intrinsic CramrRao Bounds

  Cramï¿¿r-Rao bounds on estimation accuracy are established for estimation problems on arbitrary manifolds in which no set of intrinsic coordinates exists. The frequently encountered examples of estimating either an unknown subspace or a covariance matrix are examined in detail. The set of subspaces, called the Grassmann manifold, and the set of covariance (positive-definite Hermitian) matrices have no fixed coordinate system associated with them and do not possess a vector space structure, both of which are required for deriving classical Cramï¿¿r-Rao bounds. Intrinsic versions of the Cramï¿¿r-Rao bound on manifolds utilizing an arbitrary affine connection with arbitrary geodesics are derived for both biased and unbiased estimators. In the example of covariance matrix estimation, closed-form expressions for both the intrinsic and flat bounds are derived and compared with the root-mean-square error (RMSE) of the sample covariance matrix (SCM) estimator for varying sample support K. The accuracy bound on unbiased covariance matrix estimators is shown to be about (10/log 10)n/K 1/2 dB, where n is the matrix order. Remarkably, it is shown that from an intrinsic perspective, the SCM is a biased and inefficient estimator and that the bias term reveals the dependency of estimation accuracy on sample support observed in theory and practice. The RMSE of the standard method of estimating subspaces using the singular value decomposition (SVD)is compared with the intrinsic subspace Cramï¿¿r-Rao bound derived in closed form by varying both the signal-to-noise ratio (SNR) of the unknown p-dimensional subspace and the sample support. In the simplest case, the Cramï¿¿r-Rao bound on subspace estimation accuracy is shown to be about (p(n - p)1/2 K-1/2SN-1/2 rad for p-dimensional subspaces. It is seen that the SVD-based method yields accuracies very close to the Cramï¿¿r-Rao bound, esta blishing that the principal invariant subspace of a random sample provides an excellent estimator of an unknown subspace. The analysis approach developed is directly applicable to many other estimation problems on manifolds encountered in signal processing and elsewhere, such as estimating rotation matrices in computer vision and estimating subspace basis vectors in blind source separation.