Fixed Covariance Matrix Research Articles

Analysis of continuous-variable quantum teleportation enhanced by measurement-based noiseless quantum amplification.

Continuous-variable quantum teleportation enables deterministic teleportation of quantum states of optical modes. However, the state transfer is imperfect and limited by the amount of squeezing in the shared two-mode entangled state. Recently, it has been proposed and experimentally demonstrated that the performance of continuous-variable teleportation can be conditionally improved using a measurement-based noiseless quantum amplification [J. Zhao et al., Nat. Commun.14, 4745 (2023)10.1038/s41467-023-40438-z]. An inverse Gaussian filter with sufficiently high cut-off is applied to outcomes of the continuous-variable Bell measurement, which can increase the fidelity of state teleportation and the cost of making the protocol probabilistic. Here we provide a detailed theoretical analysis of this protocol and discuss its effects and limitations. We focus on teleportation of classes of Gaussian states with fixed covariance matrix and variable displacement. The measurement-based noiseless amplification conditionally improves the precision of estimation of the coherent displacement of the teleported state from the outcomes of continuous-variable Bell measurement. Therefore, more information about the teleported state is revealed and unity-gain teleportation becomes possible with a lower added thermal noise as compared to deterministic teleportation.

Accuracy improvement of cooperative localization using UAV and UGV

In a simultaneous localization and mapping (SLAM) system, in general, distribution estimation based on a particle filter is used for localization of Unmanned Ground Vehicle (UGV) with a laser rangefinder, and point estimation based on optimization is used for Unmanned Aerial Vehicle (UAV) with a monocular camera. In order for such robots to perform cooperative localization to improve accuracy, it is necessary to convert the localization results of point estimation and distribution estimation into a format that can be introduced to each other. In this paper, we propose an integration method of estimation results for cooperative localization by UAV and UGV. The UAV point estimation result is converted to a normal distribution by giving a fixed covariance matrix in order to introduce it as the observation likelihood of the UGV. On the other hand, the particle pose with maximum weight obtained from the UGV distribution estimation result is added to the current pose constraint in UAV optimization. As a result, this allows stable localization of both by correcting with the estimation result of the other even in an environment where either one is disadvantageous for localization.

Subspace-based distributed target detection in compound-Gaussian clutter

This paper investigates the problem of radar detection of distributed targets embedded in unknown compound-Gaussian clutter. To solve the problem, we first derive two detectors for fixed covariance matrix according to Rao and Wald tests with the use of order statistics theory. Then, the unknown covariance matrix is estimated by the approximate maximum likelihood (AML) estimation. Numerical examples through simulated and real data show that the Wald test-based detector has a higher probability of detection (PD) than existing detectors.

Multivariate Uncertainty in Deep Learning.

Deep learning has the potential to dramatically impact navigation and tracking state estimation problems critical to autonomous vehicles and robotics. Measurement uncertainties in state estimation systems based on Kalman and other Bayes filters are typically assumed to be a fixed covariance matrix. This assumption is risky, particularly for "black box" deep learning models, in which uncertainty can vary dramatically and unexpectedly. Accurate quantification of multivariate uncertainty will allow for the full potential of deep learning to be used more safely and reliably in these applications. We show how to model multivariate uncertainty for regression problems with neural networks, incorporating both aleatoric and epistemic sources of heteroscedastic uncertainty. We train a deep uncertainty covariance matrix model in two ways: directly using a multivariate Gaussian density loss function and indirectly using end-to-end training through a Kalman filter. We experimentally show in a visual tracking problem the large impact that accurate multivariate uncertainty quantification can have on the Kalman filter performance for both in-domain and out-of-domain evaluation data. We additionally show, in a challenging visual odometry problem, how end-to-end filter training can allow uncertainty predictions to compensate for filter weaknesses.

Improved Dynamic Portfolio Selection Model with DCC-GARCH: Evidence from the U.S. Stock Market

As an important financial instrument in real financial market, the selection and management of portfolio has always been a significant and hot issue in the field of economics. This study collects data of stocks daily returns in the real US stock market to test whether DCC-GARCH model can improve the performance of portfolio return compared with the original static model when the assumption of fixed covariance matrix is relaxed. This study also compares the performance of improved portfolio with that of S&P500. The result shows that portfolio returns obtained by the dynamic model outperform the original static portfolio and market performance by a large margin. This shows that, without taking into account transaction costs, an effective way to enhance the traditional mean-variance model is to fit and predict the dynamic covariance using DCC-GARCH model.

The effect on cosmological parameter estimation of a parameter dependent covariance matrix

Cosmological large-scale structure analyses based on two-point correlation functions often assume a Gaussian likelihood function with a fixed covariance matrix. We study the impact on cosmological parameter estimation of ignoring the parameter dependence of this covariance matrix, focusing on the particular case of joint weak-lensing and galaxy clustering analyses. Using a Fisher matrix formalism (calibrated against exact likelihood evaluation in particular simple cases), we quantify the effect of using a parameter dependent covariance matrix on both the bias and variance of the parameters. We confirm that the approximation of a parameter-independent covariance matrix is exceptionally good in all realistic scenarios. The information content in the covariance matrix (in comparison with the two point functions themselves) does not change with the fractional sky coverage. Therefore the increase in information due to the parameter dependent covariance matrix becomes negligible as the number of modes increases. Even for surveys covering less than 1% of the sky, this effect only causes a bias of up to of order 10% of the statistical uncertainties, with a misestimation of the parameter uncertainties at the same level or lower. The effect will only be smaller with future large-area surveys. Thus for most analyses the effect of a parameter-dependent covariance matrix can be ignored both in terms of the accuracy and precision of the recovered cosmological constraints.

Multiple Access Channels With Full-Duplex Amplify-and-Forward Transmitter Cooperations

In this paper, a full-duplex (FD) transmitter cooperative scheme is proposed to improve the achievable rate for multiple access channels (MACs). In the proposed scheme, by leveraging the FD amplify-and-forward (AF) protocol, two FD transmitters send their own signals and forward the received signals from their counterparts to the receiver, which adopts both the forward and backward decoding schemes to decode the source messages. First, the analyses of the equivalent channel model and the statistics of the accumulated additive white Gaussian noise and residual self-interference (ANRI) caused by imperfect self-interference cancellation are performed. Then, the achievable rate regions are obtained by utilizing both the forward and backward decoding schemes, and a two-stage iterative algorithm is proposed to characterize these regions: in each iteration, the covariance matrix of the ANRI is first updated; then, for the fixed covariance matrix of the ANRI, the transmission parameters of the two transmitters are calculated by a two-step iterative algorithm based on the parametric Dinkelbach algorithm, sequential convex programming (SCP), and semidefinite relaxation (SDR). The numerical results show that the proposed scheme outperforms the half-duplex cooperative scheme and conventional MAC scheme without cooperations when the channels between the two transmitters are in good condition.

Cosmological parameter inference from galaxy clustering: the effect of the posterior distribution of the power spectrum

We consider the shape of the posterior distribution to be used when fitting cosmological models to power spectra measured from galaxy surveys. At very large scales, Gaussian posterior distributions in the power do not approximate the posterior distribution $\mathcal{P}_R$ we expect for a Gaussian density field $\delta_k$, even if we vary the covariance matrix according to the model to be tested. We compare alternative posterior distributions with $\mathcal{P}_R$, both mode-by-mode and in terms of expected measurements of primordial non-Gaussianity parameterised by $f_\mathrm{NL}$. Marginalising over a Gaussian posterior distribution $\mathcal{P}_f$ with fixed covariance matrix yields a posterior mean value of $f_\mathrm{NL}$ which, for a data set with the characteristics of Euclid, will be underestimated by $\triangle f_\mathrm{NL}=0.4$, while for the data release 9 (DR9) of the Sloan Digital Sky Survey (SDSS)-III Baryon Oscillation Spectroscopic Survey (BOSS) it will be underestimated by $\triangle f_\mathrm{NL}=19.1$. Adopting a different form of the posterior function means that we do not necessarily require a different covariance matrix for each model to be tested: this dependence is absorbed into the functional form of the posterior. Thus, the computational burden of analysis is significantly reduced.

Empirical stationary correlations for semi-supervised learning on graphs

In semi-supervised learning on graphs, response variables observed at one node are used to estimate missing values at other nodes. The methods exploit correlations between nearby nodes in the graph. In this paper we prove that many such proposals are equivalent to kriging predictors based on a fixed covariance matrix driven by the link structure of the graph. We then propose a data-driven estimator of the correlation structure that exploits patterns among the observed response values. By incorporating even a small fraction of observed covariation into the predictions, we are able to obtain much improved prediction on two graph data sets.

Optimizing multiple-input single-output (miso) communication systems with general gaussian channels: nontrivial covariance and nonzero mean

We consider a narrow-band point-to-point communication system with many (input) transmitters and a single (output) receiver (i.e., a multiple-input single output (MISO) system). We assume the receiver has perfect knowledge of the channel but the transmitter only knows the channel distribution. We focus on two canonical classes of Gaussian channel models: (a) the channel has zero mean with a fixed covariance matrix and (b) the channel has nonzero mean with covariance matrix proportional to the identity. In both cases, we are able to derive simple analytic expressions for the ergodic average and the cumulative distribution function (c.d.f.) of the mutual information for arbitrary input (transmission) signal covariance. With minimal numerical effort, we then determine the ergodic and outage capacities and the corresponding capacity-achieving input signal covariances. Interestingly, we find that the optimal signal covariances for the ergodic and outage cases have very different behavior. In particular, under certain conditions, the outage capacity optimal covariance is a discontinuous function of the parameters describing the channel (such as strength of the correlations or the nonzero mean of the channel).

Generation of poisson and gamma random vectors with given marginals and covariance matrix

In simulation studies we usually require the use sampling techniques involving the generation of random vectors from a multivariate population with given marginal distributions and specified correlation structure.This paper proposes two procedures for generating multivariate Poisson and Gamma random vectors having given non—identical marginal distrbutions and fixed covariance matrix with general positive entires.The generating procedures are based on a multivariate transformation method analogous to that used in the simulation of normal random vector.Properties and generating algorithms of the proposed procedures are given..

TRANSFORMATIONS, GENERATION AND MEASUREMENT OF PHOTONIC STATES THAT POSSESS A GAUSSIAN DENSITY MATRIX

In this paper, we consider issues of importance in dealing with 1-mode and 2-mode photonic states that possess a Gaussian density matrix. By a Gaussian density matrix or a Gaussian “rho”, we mean an exponential of a quadratic polynomial of the creation and annihilation operators of the modes. Gaussian-rho states, which include the socalled squeezed states of light, are uniquely specified by the covariance matrix of their modes (provided we assume zero mean fields). We discuss the set of all possible linear transformations of N modes into an equal number of modes. This set is shown to be a group that is isomorphic to one of the symplectic groups. We propose a device, which we call a covmuter, that can perform any linear transformation in this group. Given a fixed covariance matrix Vo of a Gaussian-rho state, we find all covariance matrices V for which there exists a multi-mode linear transformation that takes Vo to V. We study the conservation laws obeyed by such transformations. Finally, we show that a covmuter can be used both to generate and to measure 1-mode and 2-mode Gaussian-rho states.

A priori fixed covariance matrices of disturbance estimators

This article is a sequel to articles by Abrahamse and Koerts [1] and Abrahamse and Louter [2]. An a priori fixed covariance matrix of the disturbance estimator in the linear model is established on empirical data from the field of economic time series analysis. The empirical results agree with theoretical results of spectral analysis. In practice this appears to be too great a burden for a single fixed covariance matrix to satisfy in all test cases. Selection of a matrix from a given set of fixed covariance matrices according to a device generally gives very good results.

New Estimators of Disturbances in Regression Analysis

Abstract In this article, an alternative v for the vector u of least-squares residuals in the linear model is derived. It is best in the class of all linear unbiased estimators' of u having a certain fixed covariance matrix chosen a priori. Under the normality assumption, the distribution of the Von Neumann Ratio based on v is independent of the regression vectors, so that v is particularly useful for testing on serial correlation of the disturbances. It is pointed out that the existing tests for serial correlation in economic time-series models might be improved by using v based on an appropriate covariance matrix; the Durbin-Watson upper-bound tables can be used for this purpose.

New Estimators of Disturbances in Regression Analysis

Abstract In this article, an alternative v for the vector û of least-squares residuals in the linear model is derived. It is best in the class of all linear unbiased estimators' of u having a certain fixed covariance matrix chosen a priori. Under the normality assumption, the distribution of the Von Neumann Ratio based on v is independent of the regression vectors, so that v is particularly useful for testing on serial correlation of the disturbances. It is pointed out that the existing tests for serial correlation in economic time-series models might be improved by using v based on an appropriate covariance matrix; the Durbin-Watson upper-bound tables can be used for this purpose.