基于手机的随机误差统计规律实验数据处理方法

大学物理教学中包含的随机误差统计规律实验项目要涉及大量的数据处理,本文介绍了如何基于智能手机的节拍器、秒表以及WPS软件,加快时间测量中随机误差的统计规律实验进程。针对经典的数据处理软件Origin和Excel大多只能够在PC端运行的限制,结合自身的教学实践,利用智能手机中WPS软件,对手动采集的大量时间测量实验数据进行自动处理,快速得到实验结果。学生无需到实验室进行实验,实验效果明显,实验效率显著提升,激发了学生学习兴趣。在移动学习模式广泛应用于教学,且智能手机普及的今天,具有较强的推广价值。     

随机误差条件下置信区间与置信概率的函数关系

通过对随机误差分布规律的理论分析,利用数理统计和数值计算方法,得到了置信区间与置信概率的函数关系,给出了实用的计算数据。     

两种多光谱高温计无源温区标定方法抗随机误差能力研究

两种多光谱高温计无源温区标定方法,即依据图形相似性原理的标定方法和依据高温计传递函数的标定方法。为验证两种方法的实用性,通过对黑体辐射出度加入不同大小的随机误差模拟不同测量精度的多光谱高温测量系统,对这两种方法的抗干扰能力进行了研究。实验结果证明,依据图形相似原理的标定方法具有强抗随机误差能力,适用于随机误差较大的测量系统。当随机误差很小时,其精度低于依据传递函数的标定方法,但当随机误差增加到一定范围,其精度远高于后者。基于高温计传递函数的标定方法虽在一定的随机误差范围内具有高的外推标定精度,但抗随机误差能力较弱,适用于随机误差小的测量系统。     

光纤陀螺信号的小波包去噪及改进

光纤陀螺经过确定性误差补偿后,各种随机噪声成为其误差的主要来源。为了减小光纤陀螺的随机误差,研究基于小波包分析的滤波方法,分析了小波包滤波的原理以及滤波过程中阈值及阈值函数的选取问题,并进行了相应的改进。然后分别采用Allan方差法和功率谱密度(PSD)方法分析滤波前后光纤陀螺的随机误差特性,对滤波的效果进行理论上的分析。最后,选取光纤陀螺VG951的漂移数据进行仿真验证,结果表明,基于改进的小波包滤波方法能够有效地减小光纤陀螺的随机误差,从而提高测试的精度。     

根据性质对误差进行分类的一种新观点

根据误差的性质，针对仍广泛使用的“偶然误差和系统误差”、“随机误差和系统误差”等分类方法，本文提出了新的“随机误差和非随机误差”的误差分类方法     

基于速度平滑距离的高精度测量方法研究

随着卫星定位以及测定轨精度的提高，需要研究厘米量级的高精度测距系统。针对现有测控系统测量距离值存在较大随机误差的问题，提出了一种基于速度对距离值进行平滑的方法，以减小测距随机误差。为了保证速度的解算精度，给出了一种基于三阶锁相环路的跟踪接收方案，并对环路跟踪精度、速度平滑时间选择及优化等进行分析和仿真。仿真结果表明，新提出的接收方案和速率平滑距离方法能够实现对不同动态目标信号的有效跟踪，有效降低距离测量的随机误差，可为高精度航天测控系统提供一种解决思路。     

激光雷达信号随机误差的估算

在分析随机误差来源和激光雷达数据特点的基础上,介绍一种新的随机误差计算方法--噪音比例因子方法.该方法用一次测量数据列中远处背景信号算出噪音比例因子,再由噪音比例因子求出任一距离上有用信号的随机误差.用实测的激光雷达信号进行检验,结果表明,这种方法是可靠且可行的.     

激光雷达信号随机误差的估算

在分析随机误差来源和激光雷达数据特点的基础上,介绍一种新的随机误差计算方法——噪音比例因子方法.该方法用一次测量数据列中远处背景信号算出噪音比例因子,再由噪音比例因子求出任一距离上有用信号的随机误差.用实测的激光雷达信号进行检验,结果表明,这种方法是可靠且可行的.     

基于Allan方差的MEMS陀螺随机误差建模

针对由于MEMS陀螺随机误差较大而影响MEMS惯性测量系统测量精度的问题,提出一种利用Allan方差分析随机误差并建模的方法。在分析Allan方差原理的基础上,通过Allan方差分析法分离和辨识了MEMS陀螺仪的各项随机误差以及误差系数,并利用随机误差系数进行了数学建模。通过与ARMA模型比较,表明利用Allan方差建立的模型更加精确。该方法为MEMS惯性导航系统中姿态测量的误差补偿和滤波提供了新的思路,对提高MEMS惯性测量系统的测量精度具有一定的实际应用价值。     

利用数字傅里叶变换方法讨论噪声对测量OTF的影响

测量OTF时所产生的误差,可分为系统误差和随机误差。前者误差是有一定规律的,例如探测器的非线性或扫描狭缝的有限宽度。后者误差是随机性的。例如探测器的噪声引起的,或者在测量中由于系统受振动或干扰引起的。如果我们知道误差产生的原因,则可采取措施,对其进行修正或避免,但对误差进行完全修正或避免实际上是难以实现的。所以为改善测量OTF的精度,重点研究统计误差是很重要的。     

Analysis of random laser scattering pulse signals with lognormal distribution

The statistical distribution of natural phenomena is of great significance in studying the laws of nature. In order to study the statistical characteristics of a random pulse signal, a random process model is proposed theoretically for better studying of the random law of measured results. Moreover, a simple random pulse signal generation and testing system is designed for studying the counting distributions of three typical objects including particles suspended in the air, standard particles, and background noise. Both normal and lognormal distribution fittings are used for analyzing the experimental results and testified by chi-square distribution fit test and correlation coefficient for comparison. In addition, the statistical laws of three typical objects and the relations between them are discussed in detail. The relation is also the non-integral dimension fractal relation of statistical distributions of different random laser scattering pulse signal groups.     

Derivation of quantum statistics from Gauss's principle and the second law

Quantum statistical laws are derived from bona fide stationary probability distributions of physical stochastic processes. These distributions are shown to be the laws of error for which the average occupation numbers are the most probable values. They determine uniquely the statistical entropy functions and the second law gives the quantum statistical distributions.     

二元线性回归分析法在牛顿第二定律验证实验中的应用

回归分析法是对一定的测量数据,寻找出隐藏在随机性中的统计规律性．在考虑滑块和导轨之间空气黏性阻力的情况下,利用二元线性回归分析法直接验证牛顿第二定律,改进了牛顿第二定律的传统实验验证方法．结果表明,在实验误差允许的范围内牛顿第二定律均能得到较好地直接验证．     

Occurrence, Repetition and Matching of Patterns in the Low-temperature Ising Model

We continue our study of the exponential law for occurrences and returns of patterns in the context of Gibbsian random fields. For the low-temperature plus-phase of the Ising model, we prove exponential laws with error bounds for occurrence, return, waiting and matching times. Moreover we obtain a Poisson law for the number of occurrences of large cylindrical events and a Gumbel law for the maximal overlap between two independent copies. As a by-product, we derive precise fluctuation results for the logarithm of waiting and return times. The main technical tool we use, in order to control mixing, is disagreement percolation     

Limitations on the precision of atomic meanlife measurements

Uncertainty estimates in atomic meanlife measurements are usually obtained by statistical inference based on the hypothesis that the exponential decay law is exact and the distribution of random errors about it is Gaussian. At some level of precision these parameter evaluation methods must be accompanied by additional hypothesis testing. Possible limitations on these accuracies are examined in the light of recent measurements and calculations, and are quantitatively studied through the simulation and fitting of several alternative models.     

On the probability distribution of the stochastic saturation scale in QCD

It was recently noticed that high-energy scattering processes in QCD have a stochastic nature. An event-by-event scattering amplitude is characterised by a saturation scale which is a random variable. The statistical ensemble of saturation scales formed with all the events is distributed according to a probability law whose cumulants have been recently computed. In this work, we obtain the probability distribution from the cumulants. We prove that it can be considered as Gaussian over a large domain that we specify and our results are confirmed by numerical simulations.     

Analytical derivation of the stationarity and the ergodicity of a field scattered by a slightly rough random surface

In the framework of the small perturbation method, we present a new theoretical derivation of the statistical and spatial properties of a field scattered by a one-dimensional slightly rough random surface. The work concerns the intermediate field zone where the scattered field is reduced to the contribution of the progressive plane waves. The surface is assumed to be stationary, ergodic and Gaussian. First, from a statistical point of view, we demonstrate that under oblique incidence the scattered field is not stationary while it is strictly stationary under normal incidence. For an infinite surface, the scattered field modulus obeys to Hoyt law and the phase is not uniform. Second, from a spatial point of view, for a given altitude and under all incidences, we show that the scattered field is ergodic. Under oblique incidence, the phase is spatially uniform and the modulus is given by a Rayleigh law. Under normal incidence, the phase is not uniform and the modulus is given by a Hoyt law. Third, from a practical point of view, we show that the field measured by a directional antenna is ergodic and stationary if the angular transfer function of the antenna does not contain the specular direction.     

A comparative study of two phenomenological models of dephasing in series and parallel resistors

We compare two recent phenomenological models of dephasing using a double barrier and a quantum ring geometry. While the stochastic absorption model generates controlled dephasing leading to Ohm's law for large dephasing strengths, a Gaussian random phase based statistical model shows many inconsistencies.     

A unified statistical treatment for the multi-variate joint probability expression of general random processes in the form of finite expansion terms

In this paper, for a multi-variate random process of arbitrary distribution type which can be considered to be a sum of two different random processes as a result of the natural internal mechanism of the fluctuation, or of an artificial analytical classification of the fluctuation, a unified statistical treatment for the multi-variate joint probability distribution and the multi-variate joint moment with arbitrary order of the resultant random process is introduced exactly in the form of finite expansion terms. The validity of the present theory has been experimentally confirmed not only by means of digital simulation but also by Hiroshima City street noise data. The experimental results clearly show the usefulness of the theory, and also the importance of the exact correction to the truncation error of the expansion expression.