Sensitivity oftls and minimum norm methods ofdoa estimation to errors due to either finite data or sensor gain and phase perturbations

In thedoa (direction of arrival) estimation problem, we encounter either finite data or insufficient knowledge in array characterisation or both. It is therefore important to study how the subspace-based methods perform under these conditions. In this paper, we first consider the finite data case and establish two results: (i) the total least-squares approach to the linear prediction method (which we refer to astls-flp method) is equivalent to the minimum norm (min. norm), method and (ii) thetls-fblp method yields a 3 dB lower mean-square error (mse) in thedoa estimates as compared to thetls-flp method. Next, we consider the asymptotic performance of the min. norm method in the presence of sensor gain and phase perturbations, and derive the expressions for themse in thedoa estimates assuming an uniform linear array. For the special case of a single source, we also obtain a simple and explicit expression for themse which, when compared with the corresponding result for themusic algorithm, shows that the min. norm method is more sensitive than themusic when the number of sensors exceeds 2. Computer simulations are included to support the theoretical predictions. This work is supported in part by the Electronics and Radar Development Establishment, Bangalore.     

Performance ofesprit in the presence of gain and phase mismatches in sensor doublets

esprit, an acronym for Estimation of Signal Parameters via Rotational Invariance Technique, is a novel method for estimating the Directions of Arrival (doa) of plane waves using an arbitrary array of sensor doublets. However,esprit requires an identical pair of sensors in each doublet, that is the gain and phase characteristics of the sensors in a doublet have to be matched, which may be difficult to ensure in practical situations. In this paper, assuming the sources to be uncorrelated, we analyse the performance ofesprit when the gain and phase characteristics of the sensors in a doublet are not identical. It is shown that the angle estimates are unbiased and expressions are derived for the variance in the estimates ofdoa, when gain and phase mismatches exist in doublets. Computer simulation results are also presented to assert the theoretical predictions.     

Overview of quantum error prevention and leakage elimination

Abstract

Quantum error prevention strategies will be required to produce a scalable quantum computing device and are of central importance in this regard. Progress in this area has been quite rapid in the past few years. In order to provide an overview of the achievements in this area, we discuss the three major classes of error prevention strategies, the abilities of these methods and the shortcomings. We then discuss the combinations of these strategies which have recently been proposed in the literature. Finally, we present recent results in reducing errors on encoded subspaces using decoupling controls. We show how to generally remove mixing of an encoded subspace with external states (termed leakage errors) using decoupling controls. Such controls are known as ‘leakage elimination operations’ or ‘LEOs’.     

Combined error correction techniques for quantum computing architectures

Abstract

Proposals for quantum computing devices are many and varied. They each have unique noise processes that make none of them fully reliable at this time. There are several error correction/avoidance techniques which are valuable for reducing or eliminating errors, but not one, alone, will serve as a panacea. One must therefore take advantage of the strength of each of these techniques so that we may extend the coherence times of the quantum systems and create more reliable computing devices. To this end we give a general strategy for using dynamical decoupling operations on encoded subspaces. These encodings may be of any form; of particular importance are decoherence-free subspaces and quantum error correction codes. We then give means for empirically determining an appropriate set of dynamical decoupling operations for a given experiment. Using these techniques, we then propose a comprehensive encoding solution to many of the problems of quantum computing proposals which use exchange-type interactions. This uses a decoherence-free subspace and an efficient set of dynamical decoupling operations. It also addresses the problem of controllability in solid-state quantum dot devices.     

Multivariate calibration of non-replicated measurements for the factored noise model

The accuracy of a multivariate calibration (MVC) model for relating concentrations of multicomponent mixtures to their spectral measurements depends on effective handling of errors in the measured data. For the case when error variances vary along only one mode (either along mixtures or along wavelengths), a method to estimate the error variances simultaneously along with the spectral subspace was developed by Narasimhan and Shah (Control Engineering Practice, 16, (2008), 146–155). This method was exploited by Bhatt et al. (Chemom. Intell. Lab. Syst., 85, (2007), 70–81) to develop an iterative principal component regression (IPCR) MVC model, which was shown to be more accurate than models developed using PCR. In this work, the IPCR method is extended to deal with measurement errors whose variances vary along both modes, by using a factored noise model. As a first step, an iterative procedure is developed to estimate the error variance factors along with the spectral subspace, which is subsequently used in developing the regression model. Using simulated and experimental data, it is shown that the quality of the MVC model developed using the proposed method is better than that obtained using PCR, and is as good as the model obtained using Maximum Likelihood PCR, which requires knowledge of the error variances. For dealing with large data sets, a sub-optimal approach is also proposed for estimating the large number of error variances.     

An efficient block preconditioner for Jacobian‐free global–local multiscale methods

In this paper, we develop a block preconditioner for Jacobian‐free global–local multiscale methods, in which the explicit computation of the Jacobian may be circumvented at the macroscale by using a Newton–Krylov process. Effective preconditioning is necessary for the Krylov subspace iterations (e.g. GMRES) to enhance computational efficiency. This is, however, challenging since no explicit information regarding the Jacobian matrix is available. The block preconditioning technique developed in this paper circumvents this problem by effectively deflating the spectrum of the Jacobian matrix at the current Newton step using information about only the Krylov subspaces corresponding to the Jacobian matrices in the previous Newton steps and their representations on those subspaces. This approach is optimal and results in exponential convergence of the GMRES iterations within each Newton step, thus minimizing expensive microscale computations without requiring explicit Jacobian formation in any step. In terms of both computational cost and storage requirements, the action of a single block of the preconditioner per GMRES step scales linearly as the number of degrees of freedom of the macroscale problem as well as the dimension of the invariant subspace of the preconditioned Jacobian matrix. Copyright © 2011 John Wiley & Sons, Ltd.     

Comparing the states of many quantum systems

Abstract

We investigate how to determine whether the states of a set of quantum systems are identical or not. This paper treats both error-free comparison, and comparison where errors in the result are allowed. Error-free comparison means that we aim to obtain definite answers, which are known to be correct, as often as possible. In general, we will also have to accept inconclusive results, giving no information. To obtain a definite answer that the states of the systems are not identical is always possible, whereas in the situation considered here, a definite answer that they are identical will not be possible. The optimal universal error-free comparison strategy is a projection onto the totally symmetric and the different non-symmetric subspaces, invariant under permutations and unitary transformations. We also show how to construct optimal comparison strategies when allowing for some errors in the result, minimizing either the error probability, or the average cost of making an error. We point out that it is possible to realize universal error-free comparison strategies using only linear elements and particle detectors, albeit with less than ideal efficiency. Also minimum-error and minimum-cost strategies may sometimes be realized in this way. This is of great significance for practical applications of quantum comparison.     

一种用阈值提取子空间的多步匹配场反演方法

在分析已有的匹配场反演方法的基础上,构造了一种用阈值提取子空间的多步匹配场反演方法。它根据一定反演环境下参数的不同敏感性将参数划分为子集（子空间）,并依次在各敏感子空间内反演。反演时用一定的阈值将目标函数优于阈值的参数区域提取出,最后在提取出的已相对缩减的区域和最后一个子空间（通常是不敏感参数子空间）内联合反演全部参数,求得最优值。这样既可减少反演参数空间又能可靠地保证精确度,避免了已有的子空间方法反演结果受非反演参数失配影响的问题。仿真研究结果表明,本算法比已有的两类算法性能上有明显提高。     

Computer-aided reliability analysis of fault-tolerant systems

We present an overview of the major problems inherent in reliability modelling of fault-tolerant systems. The problems faced while modelling such systems include the need to consider a very large state space, non-exponential distributions, error analysis, the need to perform a combined evaluation of performance and reliability, and the need to include the details of fault/error handling behaviour. Some of the proposed solutions are discussed and current tools (harp, save, deep andsharpe) to facilitate evaluation of such systems are described. References are provided to many of the important techniques utilized in reliability, availability, and performance modelling of such systems. This research was supported in part by the Air Force Office of Scientific Research under grant AFOSR-84-0132, by the Army Research Office under contract DAAG29-84-0045 and by the National Aeronautics and Space Administration under grant NAG1-70.