Equivalence between the internal observability and equation

This paper is concerned with a third order in time linear Moore-Gibson-Thompson equation which describes the acoustic velocity potential in ultrasound wave program.Influenced by the work of Kaltenbacher,Lasiecka and Marchand(Control Cybernet.2011,40:971-988),we establish an observability inequality of the conservative problem,and then discuss the equivalence between the exponential stabilization of a dissipative system and the internal observational inequality of the corresponding conservative system.

A STRONG POSITIVITY PROPERTY AND A RELATED INVERSE SOURCE PROBLEM FOR MULTI-TERM TIME-FRACTIONAL DIFFUSION EQUATIONS

In this article,we consider the diffusion equation with multi-term time-fractional derivatives.We first derive,by a subordination principle for the solution,that the solution is positive when the initial value is non-negative.As an application,we prove the uniqueness of solution to an inverse problem of determination of the temporally varying source term by integral type information in a subdomain.Finally,several numerical experiments are presented to show the accuracy and efficiency of the algorithm.

Using Residual Estimators to Detect Outliers and Potential Controlling Observations in Structural Equation Modelling: QQ Plot Approach

The structural equation model (SEM) concept is generally influenced by the presence of outliers and controlling variables. To a very large extent, this could have consequential effects on the parameters and the model fitness. Though previous researches have studied outliers and controlling observations from various perspectives including the use of box plots, normal probability plots, among others, the use of uniform horizontal QQ plot is yet to be explored. This study is, therefore, aimed at applying uniform QQ plots to identifying outliers and possible controlling observations in SEM. The results showed that all the three methods of estimators manifest the ability to identify outliers and possible controlling observations in SEM. It was noted that the Anderson-Rubin estimator of QQ plot showed a more efficient or visual display of spotting outliers and possible controlling observations as compared to the other methods of estimators. Therefore, this paper provides an efficient way identifying outliers as it fragments the data set.

Bayesian analysis of nuclear equation of state at high baryon density

Bayesian analysis was employed to constrain the equation of state(EoS)of nuclear matter with a baryon density of up to six times the nuclear saturation density,using data from heavy-ion collisions at beam energies√S_(NN)=2-10GeV.The resulting EoS excellently agrees with that constrained by astrophysical observations.

An Observational Study of the 30-50 Day Atmospheric Oscillations Part II: Temporal Evolution and Hemispheric Interaction across the Equator

In this part, the temporal evolution and interaction across the equator of 30-50 day oscillation in the atmosphere are investigated further. The annual variation of 30-50 day oscillation is quite obvious in the mid-high latitudes. In the tropical atmosphere, the obvious interannual variation is an important property for temporal evolution of 30-50 day oscillation. The low-frequency wavetrain across the equator over the central Pacific and central Atlantic area, the movement of the long-lived low-frequency system across the equator and the meridional wind component across the equator will obviously show the interaction of 30-50 day oscillation in the atmosphere across the equator.

Data-Driven Modeling of Partially Observed Biological Systems

We present a numerical approach for modeling unknown dynamical systems using partially observed data,with a focus on biological systems with(relatively)complex dynamical behavior.As an extension of the recently developed deep neural network(DNN)learning methods,our approach is particularly suitable for practical situations when(i)measurement data are available for only a subset of the state variables,and(ii)the system parameters cannot be observed or measured at all.We demonstrate that,with a properly designed DNN structure with memory terms,effective DNN models can be learned from such partially observed data containing hidden parameters.The learned DNN model serves as an accurate predictive tool for system analysis.Through a few representative biological problems,we demonstrate that such DNN models can capture qualitative dynamical behavior changes in the system,such as bifurcations,even when the parameters controlling such behavior changes are completely unknown throughout not only the model learning process but also the system prediction process.The learned DNN model effectively creates a“closed”model involving only the observables when such a closed-form model does not exist mathematically.

Parallelizable Calculation of Observables Values on Analog Quantum Computer

The superiority of hypothetical quantum computers is not due to faster calculations but due to different schemes of calculations running on special hardware. The core of quantum computing follows the way a state of a quantum system is defined when basic things interact with each other. In conventional approach it is implemented through tensor product of qubits. In the geometric algebra formalism simultaneous availability of all the results for non-measured observables is based on the definition of states as points on three-dimensional sphere.

Discrete Quantum Transitions, Duality: Emergence of Physical Structures and Occurrence of Observed Formations (Hidden Properties of Mathematical Physics Equations)

With the help of skew-symmetric differential forms, the hidden properties of the mathematical physics equations that describe discrete quantum transitions and emergence the physical structures are investigated. It is shown that the mathematical physics equations possess a unique property. They can describe discrete quantum transitions, emergence of physical structures and occurrence observed formations. However, such a property possesses only equations on which no additional conditions, namely, the conditions of integrability, are imposed. The intergrability conditions are realized from the equations themselves. Just under realization of integrability conditions double solutions to the mathematical physics equations, which describe discrete transitions and so on, are obtained. The peculiarity consists in the fact that the integrability conditions do not directly follow from the mathematical physics equations;they are realized under the description of evolutionary process. The hidden properties of differential equations were discovered when studying the integrability of differential equations of mathematical physics that depends on the consistence between the derivatives in differential equations along different directions and on the consistence of equations in the set of equations. The results of this work were obtained with the help of skew-symmetric differential forms that possess a nontraditional mathematical apparatus such as nonidentical relations, degenerate transformations and the transition from nonintegrable manifolds to integrable structures. Such results show that mathematical physics equations can describe quantum processes.

Asymptotic Behavior of the Drift Coefficient Estimator of Stochastic Differential Equations Driven by Small Noises

The parametric estimation problem for diffusion processes with small white noise based on continuous time observations is well developed. However,in parametric inference,it is more realistic and interesting to consider asymptotic estimation for diffusion processes based on discrete observations. The least squares method is used to obtain the estimator of the drift parameter for stochastic differential equations( SDEs) driven by general Lévy noises when the process is observed discretely. Its strong consistency and the rate of convergence of the squares estimator are studied under some regularity conditions.

Stability analysis for an Euler-Bernoulli beam under local internal control and boundary observation

An Euler-Bernoulli beam system under the local internal distributed control and boundary point observation is studied. An infinite-dimensional observer for the open-loop system is designed. The closed-loop system that is non- dissipative is obtained by the estimated state feedback. By a detailed spectral analysis, it is shown that there is a set of generalized eigenfunctions, which forms a Riesz basis for the state space. Consequently, both the spectrum-determined growth condition and exponential stability are concluded.

Parameterized Solution to a Class of Sylvester Matrix Equations

A class of formulas for converting linear matrix mappings into conventional linear mappings are presented. Using them, an easily computable numerical method for complete parameterized solutions of the Sylvester matrix equation AX - EXF = BY and its dual equation XA - FXE = YC are provided. It is also shown that the results obtained can be used easily for observer design. The method proposed in this paper is universally applicable to linear matrix equations.

基于观测方程重构滤波算法的锂离子电池荷电状态估计

滤波算法中观测方程的准确性在电池状态评估中起着决定性作用。然而,该文通过试验发现,由于温度、工作电流和荷电状态(SOC)的影响,即使使用精度较高的电池模型,扩展卡尔曼滤波(EKF)算法中观测方程的输出值与实际电压之间仍会存在较大误差,即产生了较大的新息。该文提出一种基于观测方程重组的增强型扩展卡尔曼滤波(E-EKF)算法。该算法的核心思想是利用具有温度、SOC和电流自适应能力的误差修正策略对观测方程进行重组,实现算法中新息的降低,进而提高SOC估计的准确性。使用两种不同温度下的典型工况试验对E-EKF算法的性能进行了验证。试验结果表明,该算法能够适应不同的温度和工况,并具有较高的SOC估计精度。

无迹卡尔曼滤波估计空间目标特征信息

为了加强对空间目标,尤其是非合作目标的探测监视,空间目标的各种特性正受到越来越多的关注。通过无迹卡尔曼滤波对空间目标的位置、速度、姿态、角速度和材料复折射率5种状态参数进行了反演估计。利用观测角度、光度和偏振度数据作为观测值估计目标的状态,基于位置与速度运动学模型和姿态与角速度动态模型,完成5种状态的时间演化,实现了对5种状态参数的联合估计。仿真结果表明,设置合理的状态初始值、状态方程和测量方程噪声,5种状态参数误差均能合理收敛,无迹卡尔曼滤波能够较好地预测空间目标的5种特征参数,同时也验证了观测角度、光度和偏振度数据可以用于反演空间运动目标的5种非直接观测特征信息。

NADARAYA-WATSON ESTIMATORS FOR REFLECTED STOCHASTIC PROCESSES

We study the Nadaraya-Watson estimators for the drift function of two-sided reflected stochastic differential equations.The estimates,based on either the continuously observed process or the discretely observed process,are considered.Under certain conditions,we prove the strong consistency and the asymptotic normality of the two estimators.Our method is also suitable for one-sided reflected stochastic differential equations.Simulation results demonstrate that the performance of our estimator is superior to that of the estimator proposed by Cholaquidis et al.(Stat Sin,2021,31:29-51).Several real data sets of the currency exchange rate are used to illustrate our proposed methodology.

顾及观测空间信息的CPⅢ网多维粗差可区分能力分析

高铁轨道控制网(CPⅢ网)是一个自由测站、自动观测的边角同测后方交会测量网,其观测值间的粗差可区分性除了与控制网设计空间有关外,还会受到全站仪自动观测等观测空间因素的影响.为此,在由粗差判断方程得到CPⅢ网多维观测值粗差可区分能力的设计空间相关关系基础上,考虑CPⅢ网数据采集中全站仪自动观测特点,引入观测值时序相关性,将观测值间的可靠性关系由传统只考虑设计空间影响扩展到综合评价设计空间和观测空间影响,挖掘得到符合CPⅢ网测量实际的多维粗差可区分能力的规律;然后,采用蒙特卡罗方法验证顾及观测空间信息的CPⅢ网多维粗差可区分能力的正确性.研究结果表明:CPⅢ网观测值可靠性会受到观测空间的影响,在粗差探测实践中应予以考虑;CPⅢ网中每个测量边观测值均有粗差发现与定位能力;观测同一个目标点的3个测量边中最多可发现并定位1个测量边中的2个粗差;当测站点无错误时,1个测站观测n个目标点的n个测量边中,最多可以发现并定位└n/2┘个测量边中的2└n/2┘个粗差.

基于数字可量测影像组合定位算法在地图测绘当中的应用

针对地图测绘过程当中测量精度较低,测绘还原度不高等问题,对数字可量测影像组合定位算法在地图测绘当中的应用进行研究。地图测绘通过移动测量站对路网数据、地理背景以及立体影像的地图数据信息进行采集。同时建立数字可量测影像的观测方程以及组合定位框架,以减小地图测绘误差。经过对比实验验证,数字可量测影像组合定位算法在地图测绘中应用的可行度高,相比其他地图测绘方式具有更小的轴向误差,且波动幅度较小。该方法能够进行更加精准、全面的地图测绘工作。

北斗三频约束在多模数据基线解算质量中的应用

针对多模系统基线解算时波长较长、解算过程相对较为复杂的问题,本文提出以北斗三频约束为基础的多模系统基线解算方式。该方式首先对中长基线对无电离层的模糊度进行计算,而后在求出的组合模糊度中分离基础模糊度。通过将北斗三频的基础模糊度代入GPS进行基线解算,求得GPS对应的模糊度,并将求解结果代入观测值方程。改进办法使基线解算在更短的历元内解算完成,同时保证解算质量。经过验证,该方法在保证足够精确度的同时,能够大幅缩短基线解算时间,提高解算质量。

The solutions of navigation observation equations for CAPS

Chinese scientists invent the navigation and positioning system based on commercial communications satellites and develop them successfully into China Area Positioning System (CAPS). In principle, this system is different from the GPS broadcasting satellite navigation class, where the propagation epoch of original navigation signals for pseudo-range measurement is from a ground master control station rather than from satellite transponders. This paper addresses the establishment of the three observation equation models for the navigation and positioning system based on communications satellites, and expresses them identically to operator equations and optimized models. Furthermore, both algorithms of the linear solution for the observable characteristic equation and the least-squares solution for the condition number more than 4 are discussed, with several methods for the exact solution, such as improving the behavior of coefficient matrices, right estimation for the weighted right hand side and selection of iteration forms of solutions, and the influence of the condition number on improving navigation and positioning accuracy is also analyzed carefully. Hopefully, all the works would be contributive to further development of the navigation and positioning system based on communications satellites, and be potentially valuable to other satellite navigation and positioning systems.

Parametric Approach for the Normal Luenberger Function Observer Design in Second-order Descriptor Linear Systems

In this paper, the normal Luenberger function observer design for second-order descriptor linear systems is considered. It is shown that the main procedure of the design is to solve a so-called second-order generalized Sylvester-observer matrix equation. Based on an explicit parametric solution to this equation, a parametric solution to the normal Luenberger function observer design problem is given. The design degrees of freedom presented by explicit parameters can be further utilized to achieve some additional design requirements.

PEAK COVARIANCE STABILITY OF A RANDOM RICCATI EQUATION ARISING FROM KALMAN FILTERING WITH OBSERVATION LOSSES

We consider the stability of a random Riccati equation with a Markovian binary jump coefficient. More specifically, we are concerned with the boundedness of the solution of a random Riccati difference equation arising from Kalman filtering with measurement losses. A sufficient condition for the peak covariance stability is obtained which has a simpler form and is shown to be less conservative in some cases than a very recent result in existing literature. Furthermore, we show that a known sufficient condition is also necessary when the observability index equals one.