Probability density function

About: Probability density function is a research topic. Over the lifetime, 22321 publications have been published within this topic receiving 422885 citations. The topic is also known as: probability function & PDF.

An Importance Sampling Method for TDOA-Based Source Localization

Abstract: We consider the source localization problem using time-difference-of-arrival (TDOA) measurements in sensor networks. The maximum likelihood (ML) estimation of the source location can be cast as a nonlinear/nonconvex optimization problem, and its global solution is hardly obtained. In this paper, we resort to the Monte Carlo importance sampling (MCIS) technique to find an approximate global solution to this problem. To obtain an efficient importance function that is used in the technique, we construct a Gaussian distribution and choose its probability density function (pdf) as the importance function. In this process, an initial estimate of the source location is required. We reformulate the problem as a nonlinear robust least squares (LS) problem, and relax it as a second-order cone programming (SOCP), the solution of which is used as the initial estimate. Simulation results show that the proposed method can achieve the Cramer-Rao bound (CRB) accuracy and outperforms several existing methods.

Atomic Displacements in One‐ and Two‐Dimensional Diffusion

Abstract: The statistics of surface diffusion phenomena are developed for the conditions appropriate to measurements in the field‐ion microscope. Examined in detail are: (1) The effect of boundaries (lattice steps) on the mean‐square displacement in a random walk; (2) the probability density for distances traversed in a two‐dimensional walk along nonorthogonal surface channels; (3) the distribution of distances for random walks in which the number of jumps is subject to fluctuation, as it is in real systems. Both reflecting and adsorbing boundaries are found to diminish the mean‐square displacement in the same fashion. The effect of nonorthogonality, and even more so of fluctuations, is to enhance the frequency of small displacements when compared with a Rayleigh distribution.

Dimensionless score function for multiple hypothesis tracking

Abstract: This paper discusses several theoretical issues related to the score function for the measurement-to-track association/assignment decision in the track-oriented version of the multiple hypothesis tracker (MHT). This score function is the likelihood ratio: the ratio of the probability density function (pdf) of a measurement having originated from a track, to the pdf of this measurement having a different origin. The likelihood ratio score is derived rigorously starting from the fully Bayesian MHT (hypothesis oriented, based on combinatorial analysis of the general multitarget problem), which is shown to be amenable under some (reasonable) assumptions to the track-oriented MHT (TOMHT). The latter can be implemented efficiently using multidimensional assignment (MDA). The main feature of a likelihood ratio is the fact that it is a (physically) dimensionless quantity and, consequently, can be used for the association of different numbers of measurements and/or measurements of different dimension. The explicit forms of the likelihood ratio are discussed both for the commonly used Kalman tracking filter, as well as for the interacting multiple model (IMM) estimator. The issues of measurements of different dimension and different coordinate systems together with the selection of certain MHT design parameters - the spatial densities of the false measurements and new targets - are also discussed.

Exact analysis of postdetection combining for DPSK and NFSK systems over arbitrarily correlated Nakagami channels

Abstract: Postdetection combining is a popular means to improve the bit error performance of DPSK and noncoherent FSK (NFSK) systems over fading channels. Nevertheless, the error performance of such systems in an arbitrarily correlated Nakagami environment is not available in the literature. The difficulty arises from inherent nonlinearity in noncoherent detection and from attempts to determine explicitly the probability density function of the total signal-to-noise ratio at the combiner output. We directly determine the error probability from the characteristic function of decision variables, resulting in closed-form solutions involving matrix differentiation. The performance calculation is further simplified by developing a recursive technique. The theory is illustrated by analyzing two feasible antenna arrays used in base stations for diversity reception, ending up with some findings of interest to system design.

Performance Analysis of Free-Space Optical Links Over M\'{a}laga ($\mathcal{M}$) Turbulence Channels with Pointing Errors

Abstract: In this work, we present a unified performance analysis of a free-space optical (FSO) link that accounts for pointing errors and both types of detection techniques (i.e. intensity modulation/direct detection (IM/DD) as well as heterodyne detection). More specifically, we present unified exact closed-form expressions for the cumulative distribution function, the probability density function, the moment generating function, and the moments of the end-to-end signal-to-noise ratio (SNR) of a single link FSO transmission system, all in terms of the Meijer's G function except for the moments that is in terms of simple elementary functions. We then capitalize on these unified results to offer unified exact closed-form expressions for various performance metrics of FSO link transmission systems, such as, the outage probability, the scintillation index (SI), the average error rate for binary and $M$-ary modulation schemes, and the ergodic capacity (except for IM/DD technique, where we present closed-form lower bound results), all in terms of Meijer's G functions except for the SI that is in terms of simple elementary functions. Additionally, we derive the asymptotic results for all the expressions derived earlier in terms of Meijer's G function in the high SNR regime in terms of simple elementary functions via an asymptotic expansion of the Meijer's G function. We also derive new asymptotic expressions for the ergodic capacity in the low as well as high SNR regimes in terms of simple elementary functions via utilizing moments. All the presented results are verified via computer-based Monte-Carlo simulations.