Adaptive Smoothing for Trajectory Reconstruction

Trajectory reconstruction is the process of inferring the path of a moving object between successive observations. In this paper, we propose a smoothing spline -- which we name the V-spline -- that incorporates position and velocity information and a penalty term that controls acceleration. We introduce a particular adaptive V-spline designed to control the impact of irregularly sampled observations and noisy velocity measurements. A cross-validation scheme for estimating the V-spline parameters is given and we detail the performance of the V-spline on four particularly challenging test datasets. Finally, an application of the V-spline to vehicle trajectory reconstruction in two dimensions is given, in which the penalty term is allowed to further depend on known operational characteristics of the vehicle.Comment: 25 pages, submitte

Adaptive Smoothing Spline for Trajectory Reconstruction

Trajectory reconstruction is the process of inferring the path of a moving object between successive observations. In this paper, we propose a smoothing spline -- which we name the V-spline -- that incorporates position and velocity information and a penalty term that controls acceleration. We introduce a particular adaptive V-spline designed to control the impact of irregularly sampled observations and noisy velocity measurements. A cross-validation scheme for estimating the V-spline parameters is given and we detail the performance of the V-spline on four particularly challenging test datasets. Finally, an application of the V-spline to vehicle trajectory reconstruction in two dimensions is given, in which the penalty term is allowed to further depend on known operational characteristics of the vehicle

El defensor de Córdoba : diario católico: Año IV Número 928 - 1902 octubre 31

Copia digital. Madrid : Ministerio de Cultura. Subdirección General de Coordinación Bibliotecaria, 200

V-Splines and Bayes Estimate

Smoothing splines can be thought of as the posterior mean of a Gaussian process regression in a certain limit. By constructing a reproducing kernel Hilbert space with an appropriate inner product, the Bayesian form of the V-spline is derived when the penalty term is a fixed constant instead of a function. An extension to the usual generalized cross-validation formula is utilized to find the optimal V-spline parameters

Adaptive Sequential MCMC for Combined State and Parameter Estimation

In the case of a linear state space model, we implement an MCMC sampler with two phases. In the learning phase, a self-tuning sampler is used to learn the parameter mean and covariance structure. In the estimation phase, the parameter mean and covariance structure informs the proposed mechanism and is also used in a delayed-acceptance algorithm. Information on the resulting state of the system is given by a Gaussian mixture. In on-line mode, the algorithm is adaptive and uses a sliding window approach to accelerate sampling speed and to maintain appropriate acceptance rates. We apply the algorithm to joined state and parameter estimation in the case of irregularly sampled GPS time series data

Bayesian inference of spatially correlated random parameters for on-farm experiment

Accounting for spatial variability is crucial while estimating treatment effects in large on-farm trials. It allows to determine the optimal treatment for every part of a paddock, resulting in a management strategy that improves sustainability and profitability of the farm. We specify a model with spatially correlated random parameters to account for the spatial variability in large on-farm trials. A Bayesian framework has been adopted to estimate the posterior distribution of these parameters. By accounting for spatial variability, this framework allows the estimation of spatially-varying treatment effects in large on-farm trials. Several approaches have been proposed in the past for assessing spatial variability. However, these approaches lack an adequate discussion of the potential problem of model misspecification. Often the Gaussian distribution is assumed for the response variable, and this assumption is rarely investigated. Using Bayesian post sampling tools, we show how to diagnose the problem of model misspecification. To illustrate the applicability of our proposed method, we analysed a real on-farm strip trial from Las Rosas, Argentina, with the main aim of obtaining a spatial map of locally-varying optimal nitrogen rates for the entire paddock. The analysis of these data revealed that the assumption of Gaussian distribution for the response variable is unsatisfactory; the Student-t distribution provides a more robust inference. We finish the paper by discussing the difference between the proposed Bayesian approach and geographically weighted regression, and comparing the results of these two approaches

V-Spline: An Adaptive Smoothing Spline for Trajectory Reconstruction

Trajectory reconstruction is the process of inferring the path of a moving object between successive observations. In this paper, we propose a smoothing spline—which we name the V-spline—that incorporates position and velocity information and a penalty term that controls acceleration. We introduce an adaptive V-spline designed to control the impact of irregularly sampled observations and noisy velocity measurements. A cross-validation scheme for estimating the V-spline parameters is proposed, and, in simulation studies, the V-spline shows superior performance to existing methods. Finally, an application of the V-spline to vehicle trajectory reconstruction in two dimensions is given, in which the penalty term is allowed to further depend on known operational characteristics of the vehicle

Statistical analysis of comparative experiments based on large strip on-farm trials

Statistical methods used for small plot analyses are unsuitable for large-scale on-farm experiments because they fail to take into account the spatial variability in treatment effects within paddocks. Several new methods have recently been proposed that are inspired by geostatistical analyses of spatially-varying treatment effects, which are typical for site-specific crop management trials with quantitative treatments. However, these methods do not address the objective of comparative experiments, where the overall assessment of treatments’ performance is of interest. Moreover, most biometricians, who routinely analyse data from field trials, are either unfamiliar with the new geostatistical techniques or reluctant to include these in their regular analytical toolkits due to the unavailability of easy-to-use software tools. The linear mixed model is widely used for analysing small plot field trials because it is extremely versatile in modelling spatial and extraneous variability and is accessible through user-friendly software implementation. Motivated by comparative experiments, conducted in large strip trials using qualitative treatment factors, and yield data obtained from harvest monitor, we propose a linear mixed effects model for determining the best treatment at both local and global spatial scales within a paddock, based on yield predictions and profit estimates. To account for the large spatial variation in on-farm strip trials, we divide the trial into smaller regions or pseudo-environments (PEs), each containing at least two replicates. We propose two approaches for creating these PEs. In the presence of appropriate spatial covariates, a clustering method is proposed; otherwise, the trial area is stratified into equal-sized rectangular blocks using a systematic partitioning scheme. PEs are used to estimate the treatment effects by incorporating treatment-by-PE interactions in linear mixed effects models. The optimum treatment within each PE is found by either comparing the best linear unbiased predictions solely or incorporating profit and comparing economic performance. To illustrate the applicability of our method, we have analysed two large strip trials conducted in Western Australia

The socio-economic impact of fungicide resistance in West Australia's Wheatbelt

Farming is a risky business, demanding daily decisions on farm input expenditure and best practices while operating in an uncertain climate. One of these decisions regards agro-chemical inputs for disease control, a decision increasingly challenged by fungicide resistance for many pathogens of agricultural significance. To understand disease management decision-making and the importance of fungicide resistance, we surveyed 137 barley growers from West Australia's Wheatbelt. On average, this group spent AU$42/ha on fungicide application. Our survey found that growers were willing to invest an additional AU$18/ha to delay resistance of the pathogen to fungicides. Qualitative data show that barley growers perceive fungicide resistance as a growing issue in the region with a significant economic and emotional impact. Growers also expressed concern that fungicide resistance could become a long-term threat to the sustainability of their agribusiness. This study demonstrates that understanding growers' financial motivations and the economics of plant diseases is vital