Nonlinear Gaussian Model Research Articles

Optimizing ethephon application timing for ‘Meyer’ zoysiagrass seedhead suppression

AbstractZoysiagrass (Zoysia spp. Willd.) is a desirable, low‐input turfgrass species used on golf courses. However, prolific zoysiagrass seedhead production in the spring can increase golf course maintenance costs and reduce aesthetics. Previous research demonstrates that a single autumn ethephon application can suppress zoysiagrass seedhead production the following spring, but the optimum application timing is not well‐defined. The objective of this research was to determine the optimum window for an effective ethephon application for ‘Meyer’ zoysiagrass seedhead suppression. Small‐plot field research was conducted in Indiana, Kansas, Arkansas, and Tennessee. Seedheads were suppressed up to 99% depending on application timing. In Indiana, applications made on September 19 provided 99% seedhead suppression. In Kansas, applications between August 30 and September 18 yielded >64% seedhead suppression. In Arkansas, applications between October 3 and October 17 yielded >52% seedhead suppression. In Tennessee, applications between September 19 and October 23 provided >78% seedhead suppression. Applications made outside these windows resulted in more seedhead production at each respective location. Interestingly, optimum application timing was approximately 2 weeks later in Arkansas and Tennessee compared to Indiana and Kansas. Using growing degree days, a nonlinear Gaussian model was fit to predict the optimum ethephon application timing. In addition to data from this research, the proposed model accurately predicted observed zoysiagrass seedhead suppression in previously published research. This research better characterizes the optimum autumn application timing for Meyer zoysiagrass seedhead suppression across the transition zone.

Trajectory PHD Filter for Adaptive Measurement Noise Covariance Based on Variational Bayesian Approximation

In order to solve the problem that the measurement noise covariance may be unknown or change with time in actual multi-target tracking, this paper brings the variational Bayesian approximation method into the trajectory probability hypothesis density (TPHD) filter and proposes a variational Bayesian TPHD (VB-TPHD) filter to obtain measurement noise covariance adaptively. By modeling the unknown covariance as the random matrix that obeys the inverse gamma distribution, VB-TPHD filter minimizes the Kullback–Leibler divergence (KLD) and estimates the sequence of multi-trajectory states with noise covariance matrices simultaneously. We propose the Gaussian mixture VB-TPHD (AGM-VB-TPHD) filter under adaptive newborn intensity for linear Gaussian models and also give the extended Kalman (AEK-VB-TPHD) filter and unscented Kalman (AUK-VB-TPHD) filter in nonlinear Gaussian models. The simulation results prove the effectiveness of the idea that the VB-TPHD filter can form robust and stable trajectory filtering while learning adaptive measurement noise statistics. Compared with the tag-VB-PHD filter, the estimated error of the VB-TPHD filter is greatly reduced, and the estimation of the trajectory number is more accurate.

Image Reconstruction for Limited-Angle Electron Beam X-Ray Computed Tomography With Energy-Integrating Detectors for Multiphase Flows

We propose a new iterative X-ray computed tomography (CT) reconstruction algorithm for electron beam X-ray tomography of multiphase flows in metal pipes. This application uses limited-angle projections due to the fixed configuration, and semiconductor-type energy-integrating detectors. For the data-fitting objective function, the proposed method incorporates a nonlinear Gaussian model with object-dependent variance to approximate the compound Poisson distribution, and a dual material decomposition based on images of the volume fractions of metal (titanium) and liquid (water). The volume fraction-based material decomposition enables us to use a maximum sum constraint that helps address the ill-posed nature of the problem. Two different regularizers, $\ell _0$ norm and edge-preserving hyperbola regularizers, are applied differently on each volume fraction image based on the characteristics of objects in each image. A synthetic phantom simulation illustrates that the proposed algorithm enables the aforementioned CT system to achieve high quality images by minimizing artifacts induced by limited-angle data and beam hardening.

Robust Multitarget Tracking Scheme Based on Gaussian Mixture Probability Hypothesis Density Filter

The Gaussian mixture probability hypothesis density (GM-PHD) filter has been widely adopted to track multiple targets, because it can effectively handle target birth/death without the track-to-measurement data association process. However, the GM-PHD filter is known to have serious problems related to birth intensity generation and target tractability. In addition, weight underestimation/overestimation may occur if there are missing detections or measurement clutters. Since these problems may lead to severe estimation errors, many researchers have tried to find solutions. However, none of the researchers have been successful at solving these problems simultaneously. In this paper, we propose a robust multitarget tracking scheme based on the GM-PHD filter to improve estimation accuracy, even if there are many false detections. The proposed scheme includes the processing step of evaluating multiple states/measurements, which is designed to overcome the weight underestimation/overestimation problems. Furthermore, it includes generating the birth intensity for the next iteration using measurements not associated with any tracked states. We also show that the proposed method can be extended to nonlinear Gaussian models. The simulation results demonstrate that the proposed scheme can provide relatively accurate multitarget estimates compared with the previous approaches when the measurements include many false positives/negatives.

Approximations of the Optimal Importance Density Using Gaussian Particle Flow Importance Sampling

ABSTRACTRecently developed particle flow algorithms provide an alternative to importance sampling for drawing particles from a posterior distribution, and a number of particle filters based on this principle have been proposed. Samples are drawn from the prior and then moved according to some dynamics over an interval of pseudo-time such that their final values are distributed according to the desired posterior. In practice, implementing a particle flow sampler requires multiple layers of approximation, with the result that the final samples do not in general have the correct posterior distribution. In this article we consider using an approximate Gaussian flow for sampling with a class of nonlinear Gaussian models. We use the particle flow within an importance sampler, correcting for the discrepancy between the target and actual densities with importance weights. We present a suitable numerical integration procedure for use with this flow and an accompanying step-size control algorithm. In a filtering context, we use the particle flow to sample from the optimal importance density, rather than the filtering density itself, avoiding the need to make analytical or numerical approximations of the predictive density. Simulations using particle flow importance sampling within a particle filter demonstrate significant improvement over standard approximations of the optimal importance density, and the algorithm falls within the standard sequential Monte Carlo framework.

Two implementations of marginal distribution Bayes filter for nonlinear Gaussian models

The marginal distribution Bayes (MDB) filter is an efficient approach for tracking an unknown and time-varying number of targets in the presence of clutter, noise, data association uncertainty, and detection uncertainty. This filter propagates the marginal distributions and existence probabilities of each target in the filter recursion, and it admits a closed-form solution for a linear Gaussian multi-target model. However, this closed-form solution is not general enough to accommodate nonlinear multi-target models. In this paper, we propose two implementations of the MDB filter to accommodate nonlinear multi-target models. The first is the first-order Taylor approximation MDB (FTA-MDB) filter which is based on the linearization technique of nonlinear function, and the second is the unscented transform MDB (UT-MDB) filter which is based on the unscented transform technique. Simulation results demonstrate that the proposed implementations are better on multiple targets tracking than the UK-PHD filter.

A feasibility study of temperature rise measurement in a tissue phantom as an alternative way for characterization of the therapeutic high intensity focused ultrasonic field

The feasibility that temperature field measurements in vitro as an alternative way to characterize the high intensity focused ultrasound (HIFU) field used in therapeutic applications has been explored in a phantom study. Thermocouples (copper-constantan, diameter 0.125 mm) are embedded in a phantom filled with tissue mimicking material that simulates the thermal and acoustic properties of soft-tissue. The temperature rises as a function of ultrasound exposure time near the focus of a HIFU transducer (1.1 MHz, active radius a = 32 mm, geometric focal length = 62 mm) of various acoustic powers up to 30 W are measured and compared with predicted values using a simple nonlinear Gaussian model. The experimental results can be explained well by the model if no acoustic cavitation takes place. When the acoustic power become higher (>5 W) and the local temperature elevation >15 °C and the local temperature is >40 °C at the focal point, cavitation vapor bubbles appear. The presence of the cavitation bubbles may increase the temperature rise rate initially. The bubble aggregates may form along the beam axis under sonication and then eventually makes the temperature elevation reach a saturated value. When acoustic cavitation occurs, the bubble-assisted enhancement of the initial temperature rise (exposure time t < 2 s) can still be predicted by the theory.

Active Fault Detection for Neural Network Based Control of Non-linear Stochastic Systems

This paper deals with design of active fault detection of non-linear stochastic systems. As general solution of the problem is extremely difficult, a special case of active detector design for a given set of controllers for jump Markov non-linear Gaussian models is considered. The optimal active detector for a given set of controllers is intractable and therefore, the rolling horizon technique will be used to reduce computational costs. The system is modelled using a multi-layer perceptron neural network where structure and unknown parameters are obtained by means of an off-line training process based on the extended Kalman filter estimation method and structure optimization using pruning of the insignificant connections. The proposed active detector is compared with a passive one based on open-loop feedback strategy and the performance is illustrated in an example by simulation and Monte Carlo analysis.

A self-organizing state space model and simplex initial distribution search

This paper proposes a method to seek initial distributions of parameters for a self-organizing state space model proposed by Kitagawa (J Am Stat Assoc 93:1203---1215, 1998). Our method is based on the simplex Nelder---Mead algorithm for solving nonlinear and discontinuous optimization problems. We show the effectiveness of our method by applying it to a linear Gaussian model, a linear non-Gaussian model, a nonlinear Gaussian model, and a stochastic volatility model.

A Self-organizing State Space Model and Simplex Initial Distribution Search

This paper proposes a method to seek initial distributions of parameters for a self-organizing state space model proposed by Kitagawa (1998). Our method is based on the simplex Nelder-Mead algorithm for solving nonlinear and discontinuous optimization problems. We show the effectiveness of our method by applying it to a linear Gaussian model, a linear non-Gaussian model, a nonlinear Gaussian model, and a stochastic volatility model.

Consistency conditions for random-walk models of turbulent dispersion

Random-walk models have long been used to calculate the dispersion of passive contaminants in turbulence. When applied to nonstationary and inhomogeneous turbulence, the model coefficients are functions of the Eulerian turbulence statistics. More recently the same random-walk models have been used as turbulence closures in the evolution equation for the Eulerian joint probability density function (pdf) of velocity. There are, therefore, consistency conditions relating the coefficients specified in a random-walk model of dispersion and the Eulerian pdf calculated using the same random-walk model. It is shown that even if these conditions are not satisfied, the dispersion model does not violate the second law of thermodynamics: all that is required to avoid a second-law violation is that the mean pressure gradient be properly incorporated. It is also shown that for homogeneous turbulence the consistency conditions are satisfied by a linear Gaussian model; and that for inhomogeneous turbulence they are satisfied by a nonlinear Gaussian model.