Data Association for Multiple Sensor Types Using Fuzzy Logic

This paper provides a fortran algorithm that can be used to compute the cdf of the product of two normal distribution random variables. We also give references that provide mathematical properties, tables, and applications of this distribution

Determining distributions of the functions of random variables is a very important problem with a wide range of applications in Risk Management, Finance, Economics, Science, and many other areas. This paper develops the theory on both density and distribution functions for the quotient Y = X 1 X 2 and the ratio of one variable over the sum of two variables Z = X 1 X 1 + X 2 of two dependent or independent random variables X 1 and X 2 by using copulas to capture the structures between X 1 and X 2 . Thereafter, we extend the theory by establishing the density and distribution functions for the quotients Y = X 1 X 2 and Z = X 1 X 1 + X 2 of two dependent normal random variables X 1 and X 2 in the case of Gaussian copulas. We then develop the theory on the median for the ratios of both Y and Z on two normal random variables X 1 and X 2 . Furthermore, we extend the result of median for Z to a larger family of symmetric distributions and symmetric copulas of X 1 and X 2 . Our results are the foundation of any further study that relies on the density and cumulative probability functions of ratios for two dependent or independent random variables. Since the densities and distributions of the ratios of both Y and Z are in terms of integrals and are very complicated, their exact forms cannot be obtained. To circumvent the difficulty, this paper introduces the Monte Carlo algorithm, numerical analysis, and graphical approach to efficiently compute the complicated integrals and study the behaviors of density and distribution. We illustrate our proposed approaches by using a simulation study with ratios of normal random variables on several different copulas, including Gaussian, Student-t, Clayton, Gumbel, Frank, and Joe Copulas. We find that copulas make big impacts from different Copulas on behavior of distributions, especially on median, spread, scale and skewness effects. In addition, we also discuss the behaviors via all copulas above with the same Kendall’s coefficient. The approaches developed in this paper are flexible and have a wide range of applications for both symmetric and non-symmetric distributions and also for both skewed and non-skewed copulas with absolutely continuous random variables that could contain a negative range, for instance, generalized skewed-t distribution and skewed-t Copulas. Thus, our findings are useful for academics, practitioners, and policy makers.

The literature is replete with acknowledgments that spatial autocorrelation (SA) inflates the variance of a random variable (RV), and that it also may alter other RV distributional properties. In most studies, impacts of SA have been examined only for the three most commonly used distributions: the normal, Poisson (and its negative binomial counterpart), and binomial distributions; much less is known about its effects on two other RVs that are utilized in GIScience research: the beta and the multinomial. The beta distribution—which is considered to be very flexible because it can mimic a uniform, exponential, sinusoidal, and normal RV—can be utilized to analyze the radiance of a remotely sensed image, for example. The multinomial distribution, a generalization of the binomial distribution, has been widely used for land use classification, and to describe land use change. The literature also suggests that RV impacts of negative SA, a neglected topic in spatial analysis, may differ from those of positive SA, at least for some RVs (e.g., the Poisson RV). The purpose of this article is to extend the investigation of effects of SA to beta and multinomial RVs, with both positive SA and negative SA assessed and contrasted with each other, using simulation experiments. The simulation experiments are designed to support this assessment. One of the major discoveries is that impacts of positive SA and negative SA behave similarly when a RV conforms to a normal distribution; however, maximum negative SA is unable to materialize for asymmetric RV, whereas positive SA always converges upon its maximum.

The multilevel Monte Carlo (MLMC) method has been used for a wide variety of stochastic applications. In this paper we consider its use in situations in which input random variables can be replaced by similar approximate random variables which can be computed much more cheaply. A nested MLMC approach is adopted in which a two-level treatment of the approximated random variables is embedded within a standard MLMC application. We analyse the resulting nested MLMC variance in the specific context of an SDE discretisation in which Normal random variables can be replaced by approximately Normal random variables, and provide numerical results to support the analysis.

This tutorial paper provides a short introduction to selected aspects of sensor data fusion by discussing characteristic examples. We consider three cases when fusion of sensor data is important: when emphasis is placed on data produced at different instants of time (i.e., target tracking), when data being collected from different sensor sources are important, and when we have data with background information on the sensor performance as well as data with nonsensor context information. The feedback from data processing to the data acquisition process is illustrated by a sensor management example.

Thermal/power issues have become increasingly important with more and more transistors being placed on a single chip. Many dynamic thermal/power management techniques have been proposed to address such issues but they all depend heavily on accurate knowledge of the chip's thermal state during runtime. In this paper, we describe a unified statistical framework for designing an on-chip thermal sensing infrastructure that can be used to track the chip's thermal state at runtime. Specifically, we address the following problems in this statistical framework: 1) sensor placement; 2) sensor data compression; 3) sensor data fusion; and 4) overall interplay. Our methods exploit the correlations between temperatures in different parts of the chip to drive sensor placement, data compression, and data fusion in both noiseless and noisy sensor cases. Our framework is also capable of choosing the appropriate degree of compression for each sensor while accounting for their local space constraints during deployment. The experimental results show that the root-mean-square error of the thermal estimates produced by our sensing infrastructure is on average 35% better than an equivalent system that uses a range-based placement scheme and a uniform compression scheme. It took our methods at most about 9 s to decide the overall solution for placement, compression, and data fusion at the design stage. This demonstrates the effectiveness and applicability of our unified statistical design methodology.

Target tracking plays an important role in the construction, operation, and maintenance of the space station by the robot, which puts forward high requirements on the accuracy of target tracking. However, the special space environment may cause complex non-Gaussian noise in target tracking data. And the performance of traditional Kalman Filter will deteriorate seriously when the error signals are non-Gaussian, which may lead to mission failure. In the paper, a novel Kalman Filter algorithm with Generalized Maximum Correntropy Criterion (GMCKF) is proposed to improve the tracking accuracy with non-Gaussian noise. The GMCKF algorithm, which replaces the default Gaussian kernel with the generalized Gaussian density function as kernel, can adapt to multi-type non-Gaussian noises and evaluate the noise accurately. A parameter automatic selection algorithm is proposed to determine the shape parameter of GMCKF algorithm, which helps the GMCKF algorithm achieve better performance for complex non-Gaussian noise. The performance of the proposed algorithm has been evaluated by simulations and the ground experiments. Then, the algorithm has been applied in the maintenance experiments in TianGong-2 space laboratory of China. The results validated the feasibility of the proposed method with the target tracking precision improved significantly in complex non-Gaussian environment.

In this paper we give the solution of Bessis–Moussa–Villani (BMV) conjecture for the generalized Gaussian random variables [Formula: see text] where f is in the real Hilbert space [Formula: see text].The main examples of generalized Gaussian random variables are q-Gaussian random variables, (-1 ≤ q ≤ 1), related to q-CCR relation and other commutation relations. We will prove that BMV conjecture is true for all operators A = G(f), B = G(g); i.e. we will show that the function [Formula: see text] is positive-definite function on the real line. The case q = 0, i.e. when G(f) are the free Gaussian (Wigner) random variables and the operators A and B are free with respect to the vacuum trace was proved by Fannes and Petz.23

<p indent="0mm">The insulation failure of key equipment in power systems caused by gas-solid interface flashover of basin insulators is a key scientific problem that must be solved urgently. The time and space scales of gas electron multiplication and solid-surface charge evolution span multiple orders of magnitude, resulting in an unclear physical mechanism of the gas-solid coupling interface discharge of a basin insulator. A gas-solid coupling surface flashover model was established considering three junction point charge injection, solid surface charge transport, and gas collision ionization. The violent collision ionization in the gas caused by electrons emitted from the solid was taken as the surface flashover criterion. The key parameters characterizing surface charge transport and gas collision ionization were extracted based on gas-solid coupling surface flashover, and a model considering random variables was established to simulate the flashover voltage distribution of epoxy resin. The flashover voltage obeys the Weibull distribution when the charge transport parameters are Gaussian random variables, and the simulation results are consistent with the experimental results. By comparing the simulation and experimental results, it is found that the characteristic flashover voltage and distribution parameter are mainly controlled by the gas and solid media, respectively, and each charge transport random variable has a different effect on the distribution shape parameter. The Weibull distribution of flashover voltage consistent with the experimental results can be obtained by adjusting the standard deviation of charge transport random variables. This research explains the relationship between the Weibull distribution of flashover voltage and the charge transport and gas collision ionization parameters, providing an effective method to simulate the probability distribution characteristics of flashover voltage, which can also be used to evaluate the failure probability of the gas-solid interface under a certain voltage.

In the reliability analysis of safety critical complex engineering structures, a very large number of the system parameters can be considered as random variables. The difficulty in computing the failure probability using the classical first- and second-order reliability methods (FORM and SORM) increases rapidly with the number of variables or ‘dimension’. There are mainly two reasons behind this. The first is the increase in computational time with the increase in the number of random variables. In principle, this problem can be handled with superior computational tools. The second reason, which is perhaps more fundamental, is that there are some conceptual difficulties typically associated with high dimensions. This means that even when one manages to carry out the necessary computations, the application of existing FORM and SORM may still lead to incorrect results in high dimensions. This paper is aimed at addressing this issue. Based on the asymptotic distribution of quadratic form in Gaussian random variables, two formulations for the case when the number of random variables n →∞ is provided. The first is called ‘strict asymptotic formulation’ and the second is called ‘weak asymptotic formulation’. Both approximations result in simple closed-form expressions for the probability of failure of an engineering structure. The proposed asymptotic approximations are compared with existing approximations and Monte Carlo simulations using numerical examples.

ABSTRACTConvolutions of normal random variables often arise in engineering problems, and the probability densities of the sums of these random variables are known in the literature. There are practical situations where specification limits on a process are imposed externally, and the product is typically scrapped if its performance does not fall in the specification range. As such, the actual distribution after inspection is truncated. Despite the practical importance of the role of truncated distributions, there has been little work on the theoretical foundation of convolutions associated with truncated random variables. This is paramount, since convolutions are often used as an important standard in statistical tolerance analysis. In this article, the convolutions of the combinations of truncated normal and truncated skew normal random variables on double and triple truncations are developed. The successful completion of this research task on convolution could help obtain a better understanding of integ...

The state of technical objects can be checked by comparing the average values ​​of samples of measurements of their parameters. Non-parametric statistics allow you to draw statistical conclusions, in particular, to evaluate distribution characteristics and test statistical hypotheses, without, as a rule, weakly justified assumptions that the distribution function of the sample elements belongs to one or another parametric family. For example, it is widely believed that statistical data often follow a normal distribution. Meanwhile, the analysis of practical results, in particular, measurement errors, always leads to the same conclusion - in the vast majority of cases, real distributions differ significantly from normal ones. In the tasks of non-destructive testing, technical diagnostics and monitoring of the state of objects, non-parametric statistics are the basis for research and decision-making about suitability or quality. Despite the large number of publications dedicated to research on specific issues of the use of non-parametric statistics methods, the internal structure of this scientific direction remains an actual problem even at the present time. Most often, in practice, the problem of belonging of samples to one general population is solved. One of the main verification criteria is the Student criterion. But, in order to use them, it is necessary to check samples for "normality". Uncritical use of the normality hypothesis often leads to significant errors, for example, when rejecting the results of observations (outliers), during statistical quality control, and in other cases. If the samples are short (n⩽20), and the measurements are normal random variables, then classical mathematical statistics suggests solving this problem with a modified Student's test [1]. The power of this criterion is no worse than the classic Student's criterion. This is especially evident with short samples (n≤20). In this article, by conducting computational experiments, the informativeness of the modified and classic Student's criterion was compared. The study was conducted for samples of random variables with three distribution laws - logistic, exponential and Rayleigh. The result showed that the modified Student's test has more power than the classical test. But, as expected, both criteria are sensitive to the symmetry of the distribution law - the greater its asymmetry, the greater the error of accepting the null hypothesis.

ABSTRACTLikelihood ratio tests for a change in mean in a sequence of independent, normal random variables are based on the maximum two-sample t-statistic, where the maximum is taken over all possible changepoints. The maximum t-statistic has the undesirable characteristic that Type I errors are not uniformly distributed across possible changepoints. False positives occur more frequently near the ends of the sequence and occur less frequently near the middle of the sequence. In this paper we describe an alternative statistic that is based upon a minimum p-value, where the minimum is taken over all possible changepoints. The p-value at any particular changepoint is based upon both the two-sample t-statistic at that changepoint and the probability that the maximum two-sample t-statistic is achieved at that changepoint. The new statistic has a more uniform distribution of Type I errors across potential changepoints and it compares favorably with respect to statistical power, false discovery rates, and the mean square error of changepoint estimates.

The tracking of objects using distributed multiple sensors is an important field of work in the application areas of autonomous robotics, military applications, and mobile systems. In this survey, we review a number of computationally intelligent methods that are used for developing robust tracking schemes through sensor data fusion. The survey discusses the application of the various algorithms at different layers of the JDL model and highlights the weaknesses and strengths of the approaches in the context of different applications

In the domain of intelligent driving vehicles, radar and camera sensors play a crucial role, and their fusion has been widely acknowledged to enhance sensing range and accuracy. This article delves into the challenge of asynchronous information fusion for object detection between radar and camera, taking into consideration different sampling frequencies of radar and camera. Initially, different state observation and prediction models for radar and camera are formulated, leading to the proposal of a comprehensive target tracking model. Subsequently, the matching and fusion process of detection results is undertaken, yielding an optimal estimation as the output of the sensor information fusion system. Furthermore, the article introduces the intelligent vehicle sensor fusion task and describes the stepwise approach to sensor fusion in traffic scenarios, including coordinate transform, sensor data preprocessing, and target track. To validate the proposed sensor asynchronous fusion algorithm, a simulation experiment and a road test are conducted focusing on interaction between ego and environment vehicles. The simulation results underscore the effectiveness of the algorithm, with an average lateral error reduction of 32% and an average longitudinal error reduction of 63%. Road test shows that effective fusion can expand the detection range of sensor system and improve the detection performance.