总体或样本的协方差(矩阵)和相关系数(矩阵)的系统定义

文章按照统一的思路系统地定义了总体或样本的协方差(矩阵)和相关系数(矩阵)。同时也给出了这些概念的一些性质。

Robust range-parameterized cubature Kalman filter for bearings-only tracking

In order to improve tracking accuracy when initial estimate is inaccurate or outliers exist,a bearings-only tracking approach called the robust range-parameterized cubature Kalman filter(RRPCKF)was proposed.Firstly,the robust extremal rule based on the pollution distribution was introduced to the cubature Kalman filter(CKF)framework.The improved Turkey weight function was subsequently constructed to identify the outliers whose weights were reduced by establishing equivalent innovation covariance matrix in the CKF.Furthermore,the improved range-parameterize(RP)strategy which divides the filter into some weighted robust CKFs each with a different initial estimate was utilized to solve the fuzzy initial estimation problem efficiently.Simulations show that the result of the RRPCKF is more accurate and more robust whether outliers exist or not,whereas that of the conventional algorithms becomes distorted seriously when outliers appear.

An Ocean Reanalysis System for the Joining Area of Asia and Indian-Pacific Ocean

An ocean reanalysis system for the joining area of Asia and Indian-Pacific Ocean (AIPO) has been developed and is currently delivering reanalysis data sets for study on the air-sea interaction over AIPO and its climate variation over China in the inter-annual time scale.This system consists of a nested ocean model forced by atmospheric reanalysis,an ensemble-based multivariate ocean data assimilation system and various ocean observations.The following report describes the main components of the data assimilation system in detail.The system adopts an ensemble optimal interpolation scheme that uses a seasonal update from a free running model to estimate the background error covariance matrix.In view of the systematic biases in some observation systems,some treatments were performed on the observations before the assimilation.A coarse resolution reanalysis dataset from the system is preliminarily evaluated to demonstrate the performance of the system for the period 1992 to 2006 by comparing this dataset with other observations or reanalysis data.

Geomagnetic jerk extraction based on the covariance matrix

We normalize data from 43 Chinese observatories and select data from ten Chinese observatories with most continuous records to assess the secular variations(SVs)and geomagnetic jerks by calculating the deviations between annual observed and CHAOS-6 model monthly means.The variations in the north,east,and vertical eigendirections are studied by using the covariance matrix of the residuals,and we find that the vertical direction is strongly affected by magnetospheric ring currents.To obtain noise-free data,we rely on the covariance matrix of the residuals to remove the noise contributions from the largest eigenvalue or vectors owing to ring currents.Finally,we compare the data from the ten Chinese observatories to seven European observatories.Clearly,the covariance matrix method can simulate the SVs of Dst,the jerk of the northward component in 2014 and that of the eastward component in 2003.5 in China are highly agree with that of Vertically downward component in Europe,compare to CHAOS-6,covariance matrix method can show more details of SVs.

Interference Alignment Based on Subspace Tracking in MIMO Cognitive Networks with Multiple Primary Users

The interference alignment （IA） algorithm based on FDPM subspace tracking （FDPM-ST IA） is proposed for MIMO cognitive network （CRN） with multiple primary users in this paper. The feasibility conditions of FDPM-ST IA is also got. Futherly, IA scheme of secondary network and IA scheme of primary network are given respectively without assuming a priori knowledge of interference covariance matrices. Moreover, the paper analyses the computational complexity of FDPM-ST IA. Simulation results and theoretical calculations show that the proposed algorithm can achieve higher sum rate with lower computational complexity.

The REMO Ocean Data Assimilation System into HYCOM(RODAS_H):General Description and Preliminary Results

The first version of the Brazilian Oceano- graphic Modeling and Observation Network （REMO） ocean data assimilation system into the Hybrid Coordi- nate Ocean Model （HYCOM） （RODAS H） has recently been constructed for research and operational purposes. The system is based on a multivariate Ensemble Optimal Interpolation （EnOI） scheme and considers the high fre- quency variability of the model error co-variance matrix. The EnOl can assimilate sea surface temperature （SST）, satellite along-track and gridded sea level anomalies （SLA）, and vertical profiles of temperature （T） and salinity （S） from Argo. The first observing system experiment was carried out over the Atlantic Ocean （78°S-50°N, 100°W-20°E） with HYCOM forced with atmospheric reanalysis from 1 January to 30 June 2010. Five integra- tions were performed, including the control run without assimilation. In the other four, different observations were assimilated： SST only （A SST）; Argo T-S profiles only （AArgo）; along-track SLA only （A_SLA）; and all data employed in the previous runs （A_All）. The A_SST, A_Argo, and A_SLA runs were very effective in improv- ing the representation of the assimilated variables, but they had relatively little impact on the variables that were not assimilated. In particular, only the assimilation of S was able to reduce the deviation of S with respect to ob- servations. Overall, the A_All run produced a good analy- sis by reducing the deviation of SST, T, and S with respect to the control run by 39%, 18%, and 30%, respectively, and by increasing the correlation of SLA by 81%.

Two-Hop Gaussian Relay Channel with Linear Relaying： Achievable Rate and Optimization Design

The relay node with linear relaying transmits the linear combination of its past received signals.The optimization of two-hop relay channel with linear relaying is discussed in this paper.The capacity for the two-hop Gaussian relay channel with linear relaying is derived,which can be formulated as an optimization problem over the relaying matrix and the covariance matrix of the signals transmitted at the source.It is proved that the solution to this optimization problem is equivalent to a "single-letter" optimization problem.We also show that the solution to this "single-letter" optimization problem has the same form as the expression of the rate achieved by Time-Sharing Amplify and Forward(TSAF).In order to solve this equivalent problem,we proposed an iterative algorithm.Simulation results show that if channel gain of one hop is relatively smaller,the achievable rate with TSAF is closer to the max-flow min-cut capacity bound,but at a lower complexity.

Study on Complete Analysis of LRE Test Samples Based on PCA

Incomplete data samples have a serious impact on the effectiveness of data mining.Aiming at the LRE historical test samples,based on correlation analysis of condition parameter,this paper introduced principle component analysis(PCA)and proposed a complete analysis method based on PCA for incomplete samples.At first,the covariance matrix of complete data set was calculated;Then,according to corresponding eigenvalues which were in descending,a principle matrix composed of eigen-vectors of covariance matrix was made;Finally,the vacant data was estimated based on the principle matrix and the known data.Compared with traditional method validated the method proposed in this paper has a better effect on complete test samples.An application example shows that the method suggested in this paper can update the value in use of historical test data.

Multi-sensor federated unscented Kalman filtering algorithm in intermittent observations

Aiming at the adverse effect caused by limited detecting probability of sensors on filtering preci- sion of a nonlinear system state, a novel muhi-sensor federated unscented Kalman filtering algorithm is proposed. Firstly, combined with the residual detection strategy, effective observations are cor- rectly identified. Secondly, according to the missing characteristic of observations and the structural feature of unscented Kalman filter, the iterative process of the single-sensor unscented Kalman filter in intermittent observations is given. The key idea is that the state estimation and its error covariance matrix are replaced by the state one-step prediction and its error covariance matrix, when the phe- nomenon of observations missing occurs. Finally, based on the realization mechanism of federated filter, a new fusion framework of state estimation from each local node is designed. And the filtering precision of system state is improved further by the effective management of observations missing and the rational utilization of redundancy and complementary information among multi-sensor observa- tions. The theory analysis and simulation results show the feasibility and effectiveness of the pro- posed algorithm.

Measurement of Incompatible Probability in Information Retrieval:A Case Study with User Clicks

The incompatible probability represents an important non-classical phenomenon, and it describes conflicting observed marginal probabilities, which cannot be satisfied with a joint probability. First, the incompatibility of random variables was defined and discussed via the non-positive semi-definiteness of their covariance matrixes. Then, a method was proposed to verify the existence of incompatible probability for variables. A hypothesis testing was also applied to reexamine the likelihood of the observed marginal probabilities being integrated into a joint probability space, thus showing the statistical significance of incompatible probability cases. A case study with user click-through data provided the initial evidence of the incompatible probability in information retrieval (IR), particularly in user interaction. The experiments indicate that both incompatible and compatible cases can be found in IR data, and informational queries are more likely to be compatible than navigational queries. The results inspire new theoretical perspectives of modeling the complex interactions and phenomena in IR.

Principal Component Analysis （PCA） on Multivariate Data of Lard Analysis in Cooking Oil

Discrimination of fatty acids （FAs） of lard in used cooking oil is important in halal determination. The aim of this study was to find the information related to the changes FAs of lard when frying in cooking oil. Quantitative analysis of FAs composition extracted from a series of experiments which involving frying cooking oil spiked with lard at three different parameters; concentration of spiked lard, heating temperatures and period of frying. The samples were analyzed using Gas Chromatography （GC） and Principal Components Analysis （PCA） technique. Multivariate data from chromatograms of FAs were standardized and computed using Unscrambler X10 into covariance matrix and eigenvectors correspond to Principal Components （PCs）. Results have shown that the first and second PCs contribute to the FAs mapping which can be visualized by scores and loading plots to discriminate FAs of lard in used cooking oil

Two Stage Estimation and Its Covariance Matrix in Multivariate Seemingly Unrelated Regression System

Multivariate seemingly unrelated regression system is raised first and the two stage estimation and its covariance matrix are given. The results of the literatures[1-5] are extended in this paper.

Strong Convergence of Empirical Distribution for a Class of Random Matrices

Let {vij}, i, j = 1, 2, …, be i.i.d, random variables with Ev11 = 0, Ev11^2 = 1 and a1 = （ai1,…, aiM） be random vectors with {aij} being i.i.d, random variables. Define XN =（x1,…, xk） and SN =XNXN^T,where xi=ai×si and si=1/√N（v1i,…, vN,i）^T. The spectral distribution of SN is proven to converge, with probability one, to a nonrandom distribution function under mild conditions.

Maximum Likelihood Blind Separation of Convolutively Mixed Discrete Sources

In this paper,a Maximum Likelihood(ML) approach,implemented by Expectation-Maximization(EM) algorithm,is proposed to blind separation of convolutively mixed discrete sources.In order to carry out the expectation procedure of the EM algorithm with a less computational load,the algorithm named Iterative Maximum Likelihood algorithm(IML) is proposed to calculate the likelihood and recover the source signals.An important feature of the ML approach is that it has robust performance in noise environments by treating the covariance matrix of the additive Gaussian noise as a parameter.Another striking feature of the ML approach is that it is possible to separate more sources than sensors by exploiting the finite alphabet property of the sources.Simulation results show that the proposed ML approach works well either in determined mixtures or underdetermined mixtures.Furthermore,the performance of the proposed ML algorithm is close to the performance with perfect knowledge of the channel filters.

An infrared human face recognition method based on 2DPCA

Aimed at the problems of infrared image recognition under varying illumination,face disguise,etc.,we bring out an infrared human face recognition algorithm based on 2DPCA.The proposed algorithm can work out the covariance matrix of the training sample easily and directly;at the same time,it costs less time to work out the eigenvector.Relevant experiments are carried out,and the result indicates that compared with the traditional recognition algorithm,the proposed recognition method is swift and has a good adaptability to the changes of human face posture.

Effect of Heteroscedastic Variance Covariance Matrices on Two Groups Linear Classification Techniques

The authors investigate the comparative classification performance of the two groups linear classification techniques. They compared the Fisher linear classification analysis, its robust version based on the minimum covariance determinant with the Filter linear classification rule and the linear combination linear classification technique. These procedures are investigated using laboratory reared aedes albopictus mosquito data set and simulated data set generated based on heteroscedastic covariance matrices with various proportion of contamination. The evaluation procedure is based on the effect of contamination on the mean probabilities of correct classification obtain for each technique. The comparative analysis revealed that the robust Fisher linear classification rule and the linear combination linear classification rule are robust and comparable than the other procedures.

Theoretical research on reservoir closed-loop production management

Closed-loop production management combines the process of history matching and production optimization together to peri-odically updates the reservoir model and determine the optimal control strategy for production development to realize the goal of decreasing the knowledge of model uncertainty as well as maximize the economic benefits for the expected reservoir life. The adjoint-gradient-based methods seem to be the most efficient algorithms for closed-loop management. Due to complicated calculation and limited availability of adjoint-gradient in commercial reservoir simulators, the application of this method is still prohibited for real fields. In this paper, a simultaneous perturbation stochastic approximation (SPSA) algorithm is proposed for reservoir closed-loop production management with the combination of a parameterization way for history matching and a co-variance matrix to smooth well controls for production optimization. By using a set of unconditional realizations, the proposed parameterization method can transform the minimization of the objective function in history matching from a higher dimension to a lower dimension, which is quite useful for large scale history matching problem. Then the SPSA algorithm minimizes the objective function iteratively to get an optimal estimate reservoir model. Based on a prior covariance matrix for production op-timization, the SPSA algorithm generates a smooth stochastic search direction which is always uphill and has a certain time correlation for well controls. The example application shows that the SPSA algorithm for closed-loop production management can decrease the geological uncertainty and provide a reasonable estimate reservoir model without the calculation of the ad-joint-gradient. Meanwhile, the well controls optimized by the alternative SPSA algorithm are fairly smooth and significantly improve the effect of waterflooding with a higher NPV and a better sweep efficiency than the reactive control strategy.

Horizontal crustal movement in China fitted by adaptive collocation with embedded Euler vector

The crustal movements of the Chinese mainland include an average regional movement trend of the mainland and complex local deformations. Thus, both trends in the crustal movement of the mainland and local distortions should be simultaneously taken into consideration in crustal movement estimations. A combined collocation model based on Euler vector (taken as trend parameters) and local distortions (taken as signals) is proposed in this paper. We assume that prior covariance matrices between signals and observations should be consistent with their uncertainties. Otherwise, the station movement estimates provided by the collocation will be distorted. Thus, an adaptive collocation estimator based on simplified Helmert variance components is applied. This means that the contributions of signals and observations to estimates of crustal movements are balanced and reasonable, and consistent covariance matrices of the signals and observations are achieved through the adjustment of the adaptive factor. The calculation of actual horizontal movements of the Chinese crust shows that the estimates of horizontal crustal movement velocities are made more accurate by the adaptive collocation model.

Robust high-resolution beam-forming based on high order cross sensor processing method

In order to obtain the robust high-resolution beamforming, a high order cross sensor processing(CSP) approach is developed. According to the relation ship between the target bearing and the phase difference of each element receiving signal, this method exploits the property that the same diagonal of covariance matrix with the same phase difference and obtains(2M-1)(N-1)virtual elements(N is the original array number) by executing M order CSP. The extended virtual elements can effectively increase the physical aperture of linear array, reduce the main lobe width of beam-forming, and improve the bearing resolution. The CSP method accumulates the data on the same sub-diagonal of the covariance matrix, which can decrease the impact of background noise on beam-forming. The theoretical analysis and experimental results both show that this method has high resolution in bearing estimation, compared with the MUSIC method, which has better robustness under the lower signal-to-noise ratio(SNR).

Berry-Esseen bounds and Cramér type large deviations for eigenvalues of random matrices.

We establish Berry-Esseen bounds and Cramér type large deviations for the eigenvalues of Wigner Hermitian matrices in the bulk and at the edge cases. Similar results are also obtained for covariance matrices.