Hypothesis testing analysis and unknown parameter estimation of GPS signal detection

Hypothesis testing analysis and unknown parameter estimation of both the intermediate frequency(IF) and baseband GPS signal detection are given by using the generalized likelihood ratio test(GLRT) approach,applying the model of GPS signal in white Gaussian noise,It is proved that the test statistic follows central or noncentral F distribution,It is also pointed out that the test statistic is nearly identical to central or noncentral chi-squared distribution because the processing samples are large enough to be considered as infinite in GPS acquisition problem.It is also proved that the probability of false alarm,the probability of detection and the threshold are affected largely when the hypothesis testing refers to the full pseudorandom noise(PRN) code phase and Doppler frequency search space cells instead of each individual cell.The performance of the test statistic is also given with combining the noncoherent integration.

The Latest Progress in Varying-coefficient Models

Varying-coefficient models are a useful extension of classical linear model. They are widely applied to economics, biomedicine, epidemiology, and so on. There are extensive studies on them in the latest three decade years. In this paper, many of models related to varying-coefficient models are gathered up. All kinds of the estimation procedures and theory of hypothesis test on the varying-coefficients model are summarized. Prom my opinion, some aspects waiting to study are proposed.

Constraining the Generalized and Superfluid Chaplygin Gas Models with the Sandage-Loeb Test

The Sandage Loeb （SL） test is a direct measurement of the cosmic expansion by probing the redshift drifts of quasi-stellar objects in the ＇redshift desert＇ of 2 〈 z 〈 5. In this work, we investigate its constraints on the unified dark energy and dark matter models including the generalized Chaplygin gas and the superfluid Chaplygin gas. In addition, type Ia supernovae （SNIa） data and the distance ratios derived from the cosmic microwave background radiation and baryon acoustic oscillation observations （CMB/BAO） are also used. We find that the mock SL data gives the tightest constraints on the model parameters and it can help to reduce the parameter regions allowed by the present SNIa＋CMB/BAO by about 75% when all datasets considered are combined. Thus the SL test is a worthy and long awaited measurement to probe effectively the cosmic expanding history and the properties of dark energy.

Efficient Centralized Cooperative Spectrum Sensing Techniques for Cognitive Networks

Wireless Communication is a system for communicating information from one point to other,without utilizing any connections like wire,cable,or other physical medium.Cognitive Radio(CR)based systems and networks are a revolutionary new perception in wireless communications.Spectrum sensing is a vital task of CR to avert destructive intrusion with licensed primary or main users and discover the accessible spectrum for the efficient utilization of the spectrum.Centralized Cooperative Spectrum Sensing(CSS)is a kind of spectrum sensing.Most of the test metrics designed till now for sensing the spectrum is produced by using the Sample Covariance Matrix(SCM)of the received signal.Some of the methods that use the SCM for the process of detection are Pietra-Ricci Index Detector(PRIDe),Hadamard Ratio(HR)detector,Gini Index Detector(GID),etc.This paper presents the simulation and comparative perfor-mance analysis of PRIDe with various other detectors like GID,HR,Arithmetic to Geometric Mean(AGM),Volume-based Detector number 1(VD1),Maximum-to-Minimum Eigenvalue Detection(MMED),and Generalized Likelihood Ratio Test(GLRT)using the MATLAB software.The PRIDe provides better performance in the presence of variations in the power of the signal and the noise power with less computational complexity.

Distribution-based CFAR detectors in SAR images

As traditional two-parameter constant false alarm rate （CFAR） target detec-tion algorithms in SAR images ignore target distribution, their performances are not the best or near best. As the resolution of SAR images increases, small targets present more pixels in SAR images. So the target distribution is of much significance. Distribution-based CFAR detection algorithm is presented. We unite the pixels around the test cell, and estimate the distribution of test cell by them. Generalized Likelihood Ratio Test （GLRT） is used to deduce the detectors. The performance of the distribution-based CFAR （DBCFAR） detectors is analyzed theoretically. False alarms of DBCFAR detection are fewer than those of CFAR at the same detection rate. Finally experiments are done and the results show the performance of DBCFAR is out of conventional CFAR. False alarms of DBCFAR detection are concentrated while those of CFAR detection are dispersive.

Adaptive detector design of MIMO radar with unknown covariance matrix

The problem of detecting signal with multiple input mul-tiple output （MIMO） radar in correlated Gaussian clutter dominated scenario with unknown covariance matrix is dealt with. The gen-eral MIMO model, with widely separated sub-arrays and co-located antennas at each sub-array, is adopted. Firstly, the generalized likelihood ratio test （GLRT） with known covariance matrix is ob-tained, and then the Rao and Wald detectors are devised, which have proved that the Rao and Wald test coincide with GLRT detec-tor. To make the detectors fully adaptive, the secondary data with signal-free will be collected to estimate the covariance. The per-formance of the proposed detector is analyzed, however, it is just ancillary. A thorough performance assessment by several numer-ical examples is also given, which has considered the sense with co-located antennas configure of transmitters and receivers array. The results show that the performance the proposed adaptive de-tector is better than LJ-GLRT, and the loss can be acceptable in comparison to their non-adaptive counterparts.

Improved AR-Based GLRT Detector for Range-Spread Targets in Compound-Gaussian Clutter without Secondary Data

The problem of adaptive radar detection in compound-Gaussian clutter without secondary data is considered in this paper.In most practical applications,the number of training data is limited.To overcome the lack of training data,an autoregressive（AR）-process-based covariance matrix estimator is proposed.Then,with the estimated covariance matrix the one-step generalized likelihood ratio test（GLRT） detector is designed without training data.Finally,detection performance of our proposed detector is assessed.

Adaptive detection in the presence of signal mismatch

The problem of adaptive detection in the situation of signal mismatch is considered; that is, the actual signal steering vector is not aligned with the nominal one. Two novel tunable detectors are proposed. They can control the degree to which the mismatched signals are rejected. Remarkably, it is found that they both cover existing famous detectors as their special cases. More importantly, they possess the constant false alarm rate（CFAR）property and achieve enhanced mismatched signal rejection or improved robustness than their natural competitors. Besides, they can provide slightly better matched signals detection performance than the existing detectors.

A vector inserting TPG for BIST design with low peak power consumption

A test pattern generator （TPG） which can highly reduce the peak power consumption during built-in self-test （BIST） application is proposed. The proposed TPG, called LPpe-TPG, consists of a linear feedback shift register （LFSR） and some control circuits. A procedure is presented firstly to make compare vectors between pseudorandom test patterns by adding some circuits to the original LFSR and secondly to insert some vectors between two successive pseudorandom test patterns according to the ordinal selection of every two bits of the compare vector. Then the changes between any successive test patterns of the test set generated by the LPpe-TPG are not more than twice. This leads to a decrease of the weighted switching activity （WSA） of the circuit under test （CUT） and therefore a reduction of the power consumption. Experimental results based on some ISCAS＇ 85 benchmark circuits show that the peak power consumption has been reduced by 25.25% to 64.46%. Also, the effectiveness of our approach to reduce the total and average power consumption is kept, without losing stuck-at fault coverage.

Numerical verification of similar Cam-clay model based on generalized potential theory

From the mathematical principles, the generalized potential theory can be employed to create constitutive model of geomaterial directly. The similar Cam-clay model, which is created based on the generalized potential theory, has less assumptions,clearer mathematical basis, and better computational accuracy. Theoretically, it is more scientific than the traditional Cam-clay models. The particle flow code PFC3 D was used to make numerical tests to verify the rationality and practicality of the similar Cam-clay model. The verification process was as follows: 1) creating the soil sample for numerical test in PFC3 D, and then simulating the conventional triaxial compression test, isotropic compression test, and isotropic unloading test by PFC3D; 2)determining the parameters of the similar Cam-clay model from the results of above tests; 3) predicting the sample's behavior in triaxial tests under different stress paths by the similar Cam-clay model, and comparing the predicting results with predictions by the Cam-clay model and the modified Cam-clay model. The analysis results show that the similar Cam-clay model has relatively high prediction accuracy, as well as good practical value.

Fiducial generalized p-values for testing zero-variance components in linear mixed-effects models

Linear mixed-effects models are widely used in analysis of longitudinal data. However, testing for zero-variance components of random effects has not been well-resolved in statistical literature, although some likelihood-based procedures have been proposed and studied. In this article, we propose a generalized p-value based method in coupling with fiducial inference to tackle this problem. The proposed method is also applied to test linearity of the nonparametric functions in additive models. We provide theoretical justifications and develop an implementation algorithm for the proposed method. We evaluate its finite-sample performance and compare it with that of the restricted likelihood ratio test via simulation experiments. We illustrate the proposed approach using an application from a nutritional study.

Tests for nonparametric parts on partially linear single index models

Tests for nonparametric parts on partially linear single index models are considered in this paper. Based on the estimates obtained by the local linear method, the generalized likelihood ratio tests for the models are established. Under the null hypotheses the normalized tests follow asymptotically the χ2-distribution with the scale constants and the degrees of freedom being independent of the nuisance parameters, which is called the Wilks phenomenon. A simulated example is used to evaluate the performances of the testing procedures empirically.

A GENERATOR AND A SIMPLEX SOLVER FOR NETWORK PIECEWISE LINEAR PROGRAMS

This is a brief report on our recent work in network piecewise linear programming (NPLP),and it consists of two parts. In the first park, we describe a generator for NPLP problems which is derived from the classical network linear program generator NETGEN. The generator creates networks of the same topological structures as NETGEN, but each arc is associated with a convex piecewise linear cost. The purpose of this program is to provide a set of standard test problems which can be used to compare the performance of various algorithms for NPLP. In the second part,we introduce a network simplex method that directly solves a network piecewise linear program without reformulating it as a network linear program of higher dimension. Forty benchmark NPLP problems are solved by this method and a reformulation method. The computational results are in favor of the direct method and show that solving an NPLP problem is not much harder than solving a network linear program of the same dimension.

SMALL SAMPLE PROPERTIES OF THEPOWER FUNCTION OF F TESTS IN TWO-WAYERROR COMPONENT REGRESSION

In this paper we investigate properties of the power function of the generalized least squaresF ted for linear hypotheses under regression models with two-way error component model. Thecovariance structure of the model depends on the correlation coefficients ρ1 and ρ2 correspondingto the random effects. This model has been frequently applied to the analysis of panel data.In general, we show that the power is a monotonically increasing function of ρ1 (ρ2) in a regionwhich is ciO6e to the ρ1 (ρ2) axis, and a monotonically decreasing function of ρ1 (ρ2) in a regionclose to the ρ2 (ρ1) axis.

Statistical inference for the nonparametric and semiparametric hidden Markov model via the composite likelihood approach

In this paper, we propose a new estimation method for a nonparametric hidden Markov model(HMM), in which both the emission model and the transition matrix are nonparametric, and a semiparametric HMM, in which the transition matrix is parametric while emission models are nonparametric. The estimation is based on a novel composite likelihood method, where the pairs of consecutive observations are treated as independent bivariate random variables. Therefore, the model is transformed into a mixture model, and a modified expectation-maximization(EM) algorithm is developed to compute the maximum composite likelihood.We systematically study asymptotic properties for both the nonparametric HMM and the semiparametric HMM. We also propose a generalized likelihood ratio test to choose between the nonparametric HMM and the semiparametric HMM. We derive the asymptotic distribution and prove the Wilk’s phenomenon of the proposed test statistics. Simulation studies and an application in volatility clustering analysis of the volatility index in the Chicago Board Options Exchange(CBOE) are conducted to demonstrate the effectiveness of the proposed methods.

On some aspects of a bivariate alternative zero-inflated logarithmic series distribution

In this paper,we discuss some important aspects of the bivariate alternative zero inflated log-arithmic series distribution(BAZILSD)of which the marginals are the alternative zero-inflated logarithmic series ditributions of Kumar and Riyaz(2015.An alternative version of zero-inflated logarithmic series distribution and some of its applications.Journal of Statistical Computation and Simulation,85(6),1117-1127).We study some important properties of the distribution by deriving expressions for its probability mass function,factorial moments,conditional probabil-ity generating functions,and recursion formulae for its probilities,raw moments and factorial moments.The parameters of the BAZILSD are estimated by the method of maximum likelihood and certain test procedures are also considered.Further certain real-life data applications are cited for ilustrating the usefulness of the model.A simulation study is conducted for assessing the performance of the maximum likelihood estimators of the parameters of the BAZILSD.

A novel target detection approach based on adaptive radar waveform design

To resolve problems of complicated clutter, fast-varying scenes, and low signal-clutterratio （SCR） in application of target detection on sea for space-based radar （SBR）, a target detection approach based on adaptive waveform design is proposed in this paper. Firstly, complicated sea clutter is modeled as compound Gaussian process, and a target is modeled as some scatterers with Gaussian reflectivity. Secondly, every dwell duration of radar is divided into several sub-dwells. Regular linear frequency modulated pulses are transmitted at Sub-dwell 1, and the received signal at this sub-dwell is used to estimate clutter covariance matrices and pre-detection. Estimated matrices are updated at every following sub-dwell by multiple particle filtering to cope with fast-varying clutter scenes of SBR. Furthermore, waveform of every following sub-dwell is designed adaptively according to mean square optimization technique. Finally, principal component analysis and generalized likelihood ratio test is used for mitigation of colored interference and property of constant false alarm rate, respectively. Simulation results show that, considering configuration of SBR and condition of complicated clutter, 9 dB is reduced for SCR which reliable detection requires by this target detection approach. Therefore, the work in this paper can markedly improve radar detection performance for weak targets.

GLRT Detectors for Aircraft Wake Vortices in Clear Air

In this article, radar echoes of aircraft wake vortices are modeled as weighted sums of the frequency components of the echoes with a special covariance matrix for the weighted coefficients. With a proposed detection scheme, two generalized likelihood ratio test (GLRT) detectors are derived respectively for aircraft wake vortices with time-varying and time-invariant Doppler spectra. Then the analytical expressions for detection and false alarm probabilities of the detectors are derived and three factors are investigated which mainly influence the detection performance, i.e., the Doppler extension and uncertainty of the aircraft wake vortex, and the number of the detection cells. The results indicate that, the signal-to-noise ratio (SNR) loss induced by Doppler extension is generally several decibels. The SNR loss due to Doppler uncertainty is approximately proportional to the logarithm of the number of spectrum lines in the uncertain Doppler spectrum intervals. For a large number of detection cells, the SNR gain is approximately proportional to the square root of the number of the detection cells.

Polarimetric synthetic aperture radar change detection for specific land cover types

This paper presents a supervised polarimetric synthetic aperture radar(PolSAR)change detection method applied to specific land cover types.For each pixel of a PolSAR image,its target scattering vector can be modeled as having a complex multivariate normal distribution.Based on this assumption,the joint distribution of two corresponding vectors in a pair of PolSAR images is derived.Then,a generalized likelihood ratio test statistic for the equality of two likelihood functions of such joint distribution is considered and a maximum likelihood distance measure for specific land cover types is presented.Subsequently,the Kittler and Illingworth minimum error threshold segmenta-tion method is applied to extract the specific changed areas.Experiments on two repeat-pass Radarsat-2 fully polarimetric images of Suzhou,China,demonstrate that the proposed change detection method gives a good performance in determining the specific changed areas in PolSAR images,especially the areas that have changed to water.

Is There Excess Liquidity in China？

In this paper, we developed the recursive unit root tests proposed by Phillips et al. （2013） and used them to identify the beginning and the end of potential excess liquidity in the Chinese monetary market during the period from 1992 to 2013. The result indicates that excess liquidity existed from the third quarter of 2002 to 2013. The analysis shows that since 2003, the inflationary pressure of excess liquidity has remained high. We provide evidence supporting the money illusion hypothesis in China. The recursive unit root test is suited to practical implementation with time series and delivers a consistent date-stamping strategy for determining the origination and termination of multiple bubbles. Simulations show that the test significantly improves discriminatory power and leads to distinct power gains.