In geodesy and geophysics,many large-scale over-determined linear equations need to be solved which are often illconditioned. When the conjugate gradient method is used,their ill-conditioning effects to the solutions must be overcome,which is studied in this paper. Through the regularization ideas,the conjugate gradient method is improved,and the regularization iterative solution based on controlling condition number is put forward. Firstly by constructing the interference source vector,a new equation is derived with ill-condition diminished greatly,which has the same solution to the original normal equation. Then the new equation is solved by conjugate gradient method. Finally the effectiveness of the new method is verified by some numerical experiments of airborne gravity downward to the earth surface. In the numerical experiments the new method is compared with LS,CG and Tikhonov methods,and its accuracy is the highest.

A few of halide inorganic scintillation crystals have been applied as radiation detection materials and are playing important roles in nuclear medicine, high energy physics, security inspection, petroleum logging and so on, but most of them are on the way of research and development. In this paper, a series of novel halide scintillation crystals, LaBr3(Ce), LaCl3(Ce), SrI2(Eu), Cs2LiYCl6(Ce) and NaI(Tl) were studied using low energy 241Am radioactive source. The effect of reflective film thickness on low-energy ray transmittance and light output of encapsulated scintillators was investigated, Teflon thickness of 0.48 mm as reflective film is best choice to obtain higher light collection and better radiation transmittance. Among all these crystals, LaBr3(Ce) crystal has excellent energy resolution above 25keV gamma ray radiation, 9.3% at 26.34 keV, 8.4% at 59.54 keV and2.6% at 661.66 keV. Only NaI (Tl) crystal works fine below 25 keV X-rays radiation, with energy resolution of 17.68% at 13.9 keV, 14.16% at 17.8 keV and 13.42% at 20.8 keV.

In this paper, the relative light output, energy resolution and count rate of encapsulated LaBr3 (Ce) crystals were tested under the temperature from 25 °C to 175 °C using 137Cs γ radioactive source. The variation of high temperature scintillation performance of LaBr3 and NaI(Tl) crystal packages was measured and analyzed. The results show that the decline of light output of LaBr3(Ce) scintillation crystal is about 80% of that of NaI(Tl) at 175 °C. The energy resolution of LaBr3(Ce) at high temperature 175 °C is approximately 8%, which is better than the 9.9% energy resolution of NaI(Tl) scintillation crystals at room temperature 25 °C. The count rate of LaBr3(Ce) is about 5-6 times more than that of the NaI(Tl) crystal.

应用Bayesian统计思想,提出一种针对平稳、可逆ARMA模型AO类和IO类异常值同时探测的方法.首先综合考虑时间序列数据中AO类异常值和IO类异常值同时出现的复杂情况,在模型参数未知的情况下,建立基于识别变量标记的异常值探测模型,将异常值探测问题归纳为多重假设检验问题;其次使用Openbugs软件执行Gibbs抽样程序获得样本对多重假设检验问题进行Bayesian统计推断,确定异常值的位置、类型以及异常扰动的具体大小;最后通过模拟实验与已有的异常值探测方法进行比较.提出的方法对时间序列ARMA模型中同时出现的AO类和IO类异常值具有良好的探测效果.

顾及钟差的物理特性,提出了一种新的卫星钟差时间序列异常值探测方法.利用二次多项式模型将卫星钟差分解为钟差、钟速、钟漂三个物理意义明确的分量,然后对每个分量通过ARIMA模型异常值探测的Bayesian方法进行异常值探测与估计.最后,采用IGS钟差数据进行实验,验证了该方法的有效性.

The method of time series analysis is widely used in many fields of science, engineering, finance and economics etc, and fitting a time series model accurately is the important basis of time series analysis. Based on the Bayesian statistical theory, this paper presents a Bayesian method which can identify an ARMA (autoregressive moving-average) model and estimate the model parameters simultaneously. Firstly, in order to determine the orders of the ARMA model, an identification model with the recognition variables is constructed. Moreover, the problem of determining the orders of the ARMA model is transformed into two sets of hypothesis tests. By the principle of Bayesian hypothesis testing, it is suggested to solve the above hypothesis test problems by calculating the posterior probabilities of the hypotheses. However, due to the large number of the unknown parameters in the identification model, this paper proposes to obtain the samples by Gibbs sampling and then calculate the posterior probabilities of the hypotheses, the AR coefficients, the MA coefficients and the variance of the random errors to fit the ARMA model. Finally, in order to illustrate the good performance of the method proposed in this article, we design three simulation examples and compare the results of our method with two existing methods: RJMCMC method and EACF method. It can be found clearly that the method proposed in this paper has more accurate results for fitting an ARMA model.

Based on the time series analysis method, this article develops a Bayesian method of detecting and repairing the cycle slips in the GNSS carrier-phase data. Firstly, this article analyses the characteristics of the cycle slips in the GNSS carrier-phase observations and establishes the relationships between the cycle slips and the additive outliers (AOs) in the stationary time series. When the ARMA (autoregressive moving-average) model is used to fit the stationary time series obtained by differencing the GNSS carrier-phase observations, the detection of cycle slips in the GNSS carrier-phase observations can be transformed to the detection of AOs in the ARMA model. Then, this article proposes a Bayesian method of detecting the AOs in the ARMA model, and the implementation of detecting the cycle slips in the GNSS carrier-phase observations is also developed. Finally, the new Bayesian method of detecting the cycle slips is used to the real GNSS carrier-phase data. From the comparison among the Bayesian method, the high-order differences method and ionospheric residual method, we can find that the Bayesian method has a better detection efficiency for several kinds of cycle slips in the GNSS carrier-phase observations than other methods.

The computation of weighted total least squares (WTLS) estimate of partial EIV model requires more iterations and more computation burden.Therefore,the study has proposed a new algorithm for computing the WTLS estimate of partial EIV model by improving objective function based on the weighted LS principle and applying the differential and inversion transformation of matrix.The results of numerical examples show that the new algorithm requires less iterations and more superior in the sense of computational efficiency.

The weighed total least square (WTLS) estimate is very sensitive to the outliers in the partial EIV model. A new procedure for detecting outliers based on the data-snooping is presented in this paper. Firstly, a two-step iterated method of computing the WTLS estimates for the partial EIV model based on the standard LS theory is proposed. Secondly, the corresponding w-test statistics are constructed to detect outliers while the observations and coefficient matrix are contaminated with outliers, and a specific algorithm for detecting outliers is suggested. When the variance factor is unknown, it may be estimated by the least median squares (LMS) method. At last, the simulated data and real data about two-dimensional affine transformation are analyzed. The numerical results show that the new test procedure is able to judge that the outliers locate in x component, y component or both components in coordinates while the observations and coefficient matrix are contaminated with outliers.

Considering that the independent component is sensitive to outliers, we propose an algorithm for faults detection in multivariate pseudorange time series based on independent component analysis (ICA). The threshold for outlier detection is determined through the Chebyshev inequality. Then we introduce the interventional model of time series to estimate the magnitudes of the potential satellite faults, and finally the satellite faults are identified based on the 3σ principle. In order to meet the real time requirement of receiver autonomous integrity monitoring (RAIM), a sliding window is used to transform the fault detection algorithm of the batch process into a real time one. Furthermore, a new algorithm for on line detection and identification of multiple faults is designed, and then the implementation process of the new RAIM algorithm is given. We validate the new algorithm by the civil data from 5 iGMAS monitoring stations of BeiDou in China. Examples illustrate that the new algorithm is effective in handling multiple satellite faults in real time, and the correct detection probability of faults is higher than that of the existed RANCO algorithm.

Negatively charged nitrogen-vacancy (NV−) center ensembles in diamond have proved to have great potential for use in highly sensitive, small-package solid-state quantum sensors. One way to improve sensitivity is to produce a high-density NV− center ensemble on a large scale with a long coherence lifetime. In this work, the NV− center ensemble is prepared in type-Ib diamond using high energy electron irradiation and annealing, and the transverse relaxation time of the ensemble—T2—was systematically investigated as a function of the irradiation electron dose and annealing time. Dynamical decoupling sequences were used to characterize T2. To overcome the problem of low signal-to-noise ratio in T2 measurement, a coupled strip lines waveguide was used to synchronously manipulate NV− centers along three directions to improve fluorescence signal contrast. Finally, NV− center ensembles with a high concentration of roughly 1015 mm−3 were manipulated within a ~10 µs coherence time. By applying a multi-coupled strip-lines waveguide to improve the effective volume of the diamond, a sub-femtotesla sensitivity for AC field magnetometry can be achieved. The long-coherence high-density large-scale NV− center ensemble in diamond means that types of room-temperature micro-sized solid-state quantum sensors with ultra-high sensitivity can be further developed in the near future.

Kalman filter is one of the most common ways to deal with dynamic data and has been widely used in project fields. However, the accuracy of Kalman filter for discrete dynamic system is poor when the observation matrix is ill-conditioned. Therefore, the method for overcoming the harmful effect caused by ill-conditioned observation matrix in discrete dynamic system is studied in this paper. Firstly, Tikhonov regularized Kalman filter (TRKF) and its algorithm are proposed by combining Tikhonov regularization method and Kalman filter. Meanwhile, some excellent properties of TRKF are proved. Secondly, the methods of choosing regularization parameter and regularization matrix in TRKF are given. Thirdly, simulated examples are designed to evaluate the performance of TRKF and comparisons between TRKF and Ordinary Ridge-type Kalman Filter (ORKF) are given. Finally, TRKF is applied in autonomous orbit determination of BeiDou Navigation Satellite System (BDS) with cross-link ranging observations and ground tracking observations so as to prevent filter divergent which is caused by ill-conditioned observation matrix. Simulations and applications illustrate that TRKF can overcome the harmful effect caused by ill-conditioned observation matrix in discrete dynamic system and the accuracy is improved effectively

Clock offset measurements of satellite-ground time transfer are usually affected by outliers due to the impact of ionosphere errors,tropospheric errors,and muhipath effects.Therefore,in this paper,we propose an autoregressive model based on Bayesian methods for detecting outliers in the clock offset measurements with the classification variables.Furthermore,the model for estimating the magnitude of outliers is given to correct the clock offset measurements,and solves the problem of outlier estimation by transforming it into a simple least square problem.Different schemes based on the real BDS data were designed to evaluate the performance of the new Bayesian method.We applied the new method ito the fast recovery of the clock offset prediction.Test examples illustrate that the Bayesian methods can detect the outliers effectively and estimate the magnitudes of outliers accurately.

The weighted total least-squares (WTLS)estimate for the partial errors-in-variables (EIV) model is very susceptible to outliers.Because the observations and coefficient matrix in the partial EIV model may be contaminated with outliers simultaneously,a totalrobustified least squares (TRLS) estimation for the partial EIV model is proposed by combining a two-step iterated algorithm of the WTLS estimate with the equivalent weight method of robust M-estimation.And the uniformly most powerful test statistics are constructed to determine the down-weighting factors.For the characteristics of the two-step iterated method,two different down-weighting schemes are presented.In the first scheme down-weighting is only implemented for the coefficient matrix and not for the observations when some elements of the coefficient matrix are estimated,and the second scheme is contrary.A simulated two-dimensional affine transformation and a linear fitting with real data are analyzed.The results show that the TRLS with the first scheme is superior to one with the second scheme,and it outperforms the existing robust methods with residual and posterior estimate of variance of unit weight and existing robust methods for the general EIV model.

According to a puzzling probability theory exercise for student, the distribution law of random variable is given by multiplication formula and full probability formula respectively. By analysis, the reason that the probability theory exercises make student confused is that the exercise does not conform to real life.

病态EIV模型的病灶源于设计矩阵的部分数据列之间存在复共线性关系.针对病灶特点制定正则化策略,在克服病态性的同时尽量减小正则化过程所引起的副作用,提出靶向病灶的正则化方法.通过数值试验,与总体最小二乘方法、病态总体正则化方法等进行比较,结果表明靶向病灶的正则化方法最优.

从理论角度分析了观测矩阵的复共线性对卡尔曼滤波的影响,并在均方误差最小意义下,给出了一种有偏卡尔曼滤波算法.分别对观测矩阵和观测量施加扰动进行了试验和分析,证明观测矩阵的病态性会对卡尔曼滤波估计造成严重危害.数值模拟结果表明,本文算法能够有效改善观测矩阵病态性对卡尔曼滤波估计的影响,提高解算质量.

The weighted total least-squares (WTLS) estimate is sensitive to outliers and will be strongly disturbed if there are outliers in the observations and coefficient matrix of the partial errors-in-variables (EIV) model. The L 1 norm minimization method is a robust technique to resist the bad effect of outliers. Therefore, the computational formula of the L 1 norm minimization for the partial EIV model is developed by employing the linear programming theory. However, the closed-form solution cannot be directly obtained since there are some unknown parameters in constrained condition equation of the presented optimization problem. The iterated procedure is recommended and the proper condition for stopping iteration is suggested. At the same time, by treating the partial EIV model as the special case of the non-linear Gauss–Helmert (G–H) model, another iterated method for the L 1 norm minimization problem is also developed. At last, two simulated examples and a real data of 2D affine transformation are conducted. It is illustrated that the results derived by the proposed L 1 norm minimization methods are more accurate than those by the WTLS method while the observations and elements of the coefficient matrix are contaminated with outliers. And the two methods for the L 1 norm minimization problem are identical in the sense of robustness. By comparing with the data-snooping method, the L 1 norm minimization method may be more reliable for detecting multiple outliers due to masking. But it leads to great computation burden.