The Probability hypothesis density (PHD) filter sequentially computes the first-order multi-target moment for the full multi-target Probability density function and dramatically reduces the computational expense of tracking problem. In this paper، we propose an improved implementation of the PHD using the notion of auxiliary particle filter to enhance the effectiveness of the Sequential Monte Carlo (SMC) implementation of the PHD filter. The proposed method differs from traditional SMC implementations because it demonstrates an ability to simultaneously search in an effective way for persistent and newborn targets where the birth intensity is uniform and noninformative. Simulation results indicate that our novel method dramatically improves the accuracy of PHD approximation when compared to traditional SMC implementation methods for the same number of particles.

The PHD filter recursion is introduced to enable the implementation of expensive computational algorithms of multitarget Bayesian filtering. The goal of this recursion is to update and propagate the posterior intensity of a Random Finite Set during time steps. To that end, Cardinalized PHD is introduced as an extension of PHD filter to overcome the PHD’s weakness in estimating the number of targets. In the CPHD filter, the posterior intensity function and the cardinality distribution are updating at the same time. In this paper, we use auxiliary particle filter to implement the CPHD filter. The benefit of the proposed algorithm is to sample at the higher dimensional space compared to the dimensional of the target space in order to generate approximating samples of the CPHD filter and this will improve the estimation accuracy.To that end, we first reformulize the CPHD recursion in a way which is suitable for auxiliary particle filter. Then, to sample in a higher dimensional space, we first use an auxiliary variable which is the index of previously generated samples and then we apply another auxiliary variable which is the index of current measurements to improve the estimation of the number and position of multiple targets. Comparison between mean and variance of estimated cardinality and error of multitarget position estimation obtained from simulation results indicate the superiority of our proposed algorithm compared to the current implementation method of the CPHD filter by using SIR particle filter.

Probability density functions of the involved random variables are essential for the reliability-based design of offshore structures. The objective of present research was the derivation of Probability density function (PDF) for the local joint flexibility (LJF) factor, fLJF, in two-planar tubular DK-joints commonly found in jacket-type offshore structures. A total of 162 finite element (FE) analyses were carried out on 81 FE models of DK-joints subjected to two types of axial loading. Generated FE models were validated using available experimental data, FE results, and design formulas. Based on the results of parametric FE study, a sample database was prepared for the fLJF values and density histograms were generated for respective samples based on the Freedman-Diaconis rule. Nine theoretical PDFs were fitted to the developed histograms and the maximum likelihood (ML) method was applied to evaluate the parameters of fitted PDFs. In each case, the Kolmogorov-Smirnov and chi-squared tests were used to evaluate the goodness of fit. Finally, the Inverse Gaussian model was proposed as the governing Probability distribution function for the fLJF. After substituting the values of estimated parameters, two fully defined PDFs were presented for the fLJF in tubular DK-joints subjected to two types of axial loading.

Membership function based on Probability density functionچندین روش به منظور برآورد تابع چگالی احتمال وجود دارد. از سوی دیگر، در نظریه مجموعه هایفازی یکی از روش های ساختن تابع عضویت بر پایه ی مجموعه داده، روش مبتنی بر تابع چگالی احتمال است.با توجه به روش های متداول در برآورد تابع چگالی، این مسئله می تواند به محاسبه انواع تابع عضویت بر پایهیک مجموعه داده منجر شود. در این مقاله، برخی از این روش ها بیان و با مثال عددی تشریح می شوند..

Although knowing the time of the occurrence of the earthquakes is vital and helpful, unfortunately it is still unpredictable. By the way there is an urgent need to find a method to foresee this catastrophic event. There are a lot of methods for forecasting the time of earthquake occurrence. Another method for predicting that is to know Probability density function of time interval between earthquakes. In this paper a new Probability density function (PDF) for the time interval between earthquakes is found out. The parameters of the PDF will be estimated, and ultimately, the PDF will be tested by the earthquakes data about Iran.

In the last two decades, many researchers have focused on the problem of automation of vehicles, and many research has been devoted to solving the challenges posed by this area. One of the important aspects in this area is the problem of localizing the vehicle and mapping the environment simultaneously in an unknown environment, which is briefly referred to as SLAM. So far, many methods have been proposed to solve this problem, but few of these researches have been implemented on the platform of collaborative robots. In this paper, SLAM problem is extended to multi robot platform by employing extended kalman filter. Due to lack of knowledge about the measurement noise covariance, the elements of this matrix adapted according to the actual data received from the sensor by employing particle swarm optimization technique. Then, to solve this problem in the dynamic environment, Probability hypothesis density filter is used to track the dynamic objects in the field of view of sensors. Finally, the performance of the algorithm is evaluated in a MATLAB environment.

Distance-based clustering methods categorize samples by optimizing a global criterion, finding ellipsoid clusters with roughly equal sizes. In contrast, density-based clustering techniques form clusters with arbitrary shapes and sizes by optimizing a local criterion. Most of these methods have several hyper-parameters, and their performance is highly dependent on the hyper-parameter setup. Recently, a Gaussian density Distance (GDD) approach was proposed to optimize local criteria in terms of distance and density properties of samples. GDD can find clusters with different shapes and sizes without any free parameters. However, it may fail to discover the appropriate clusters due to the interfering of clustered samples in estimating the density and distance properties of remaining unclustered samples. Here, we introduce Adaptive GDD (AGDD), which eliminates the inappropriate effect of clustered samples by adaptively updating the parameters during clustering. It is stable and can identify clusters with various shapes, sizes, and densities without adding extra parameters. The distance metrics calculating the dissimilarity between samples can affect the clustering performance. The effect of different distance measurements is also analyzed on the method. The experimental results conducted on several well-known datasets show the effectiveness of the proposed AGDD method compared to the other well-known clustering methods.

In this paper, the two-observational  percentile, percentile and maximum likelihood estimation of the Probability density function of  Inverse Weibull random variable are studied. Finally, these estimates are compared using simulation studies and a real data.