Long-term exploration and tours for energy constrained robots with online proprioceptive traversability estimation

This paper is concerned with how a localised and energy-constrained robot can maximise its time in the field by taking paths and tours that minimise its energy expenditure. A significant component of a robot's energy is expended on mobility and is a function of terrain traversability. We estimate traversability online from data sensed by the robot as it moves, and use this to generate maps, explore and ultimately converge on minimum energy tours of the environment. We provide results of detailed simulations and parameter studies that show the efficacy of this approach for a robot moving over terrain with unknown traversability as well as a number of a priori unknown hard obstacles.

Online estimation of Allan variance parameters

A new online method is presented for estimation of the angular randomwalk and rate randomwalk coefficients of inertial measurement unit gyros and accelerometers. In the online method, a state-space model is proposed, and recursive parameter estimators are proposed for quantities previously measured from offline data techniques such as the Allan variance method. The Allan variance method has large offline computational effort and data storage requirements. The technique proposed here requires no data storage and computational effort of approximately 100 calculations per data sample.

On-line estimation of Allan variance parameters

A new online method is presented for estimation of the angular random walk and rate random walk coefficients of IMU (inertial measurement unit) gyros and accelerometers. The online method proposes a state space model and proposes parameter estimators for quantities previously measured from off-line data techniques such as the Allan variance graph. Allan variance graphs have large off-line computational effort and data storage requirements. The technique proposed here requires no data storage and computational effort of O(100) calculations per data sample.

Solid volume fraction estimation of bone:marrow replica models using ultrasound transit time spectroscopy

The acceptance of broadband ultrasound attenuation (BUA) for the assessment of osteoporosis suffers from a limited understanding of both ultrasound wave propagation through cancellous bone and its exact dependence upon the material and structural properties. It has recently been proposed that ultrasound wave propagation in cancellous bone may be described by a concept of parallel sonic rays; the transit time of each ray defined by the proportion of bone and marrow propagated. A Transit Time Spectrum (TTS) describes the proportion of sonic rays having a particular transit time, effectively describing the lateral inhomogeneity of transit times over the surface aperture of the receive ultrasound transducer. The aim of this study was to test the hypothesis that the solid volume fraction (SVF) of simplified bone:marrow replica models may be reliably estimated from the corresponding ultrasound transit time spectrum. Transit time spectra were derived via digital deconvolution of the experimentally measured input and output ultrasonic signals, and compared to predicted TTS based on the parallel sonic ray concept, demonstrating agreement in both position and amplitude of spectral peaks. Solid volume fraction was calculated from the TTS; agreement between true (geometric calculation) with predicted (computer simulation) and experimentally-derived values were R2=99.9% and R2=97.3% respectively. It is therefore envisaged that ultrasound transit time spectroscopy (UTTS) offers the potential to reliably estimate bone mineral density and hence the established T-score parameter for clinical osteoporosis assessment.

Improved estimation of size-transition matrices using tag-recapture data

We derive a new method for determining size-transition matrices (STMs) that eliminates probabilities of negative growth and accounts for individual variability. STMs are an important part of size-structured models, which are used in the stock assessment of aquatic species. The elements of STMs represent the probability of growth from one size class to another, given a time step. The growth increment over this time step can be modelled with a variety of methods, but when a population construct is assumed for the underlying growth model, the resulting STM may contain entries that predict negative growth. To solve this problem, we use a maximum likelihood method that incorporates individual variability in the asymptotic length, relative age at tagging, and measurement error to obtain von Bertalanffy growth model parameter estimates. The statistical moments for the future length given an individual's previous length measurement and time at liberty are then derived. We moment match the true conditional distributions with skewed-normal distributions and use these to accurately estimate the elements of the STMs. The method is investigated with simulated tag-recapture data and tag-recapture data gathered from the Australian eastern king prawn (Melicertus plebejus).

Estimation for the general sample selection models

Consider a general regression model with an arbitrary and unknown link function and a stochastic selection variable that determines whether the outcome variable is observable or missing. The paper proposes U-statistics that are based on kernel functions as estimators for the directions of the parameter vectors in the link function and the selection equation, and shows that these estimators are consistent and asymptotically normal.

Maximum likelihood estimation of mortality and growth with individual variability from multiple length-frequency data

We consider estimation of mortality rates and growth parameters from length-frequency data of a fish stock and derive the underlying length distribution of the population and the catch when there is individual variability in the von Bertalanffy growth parameter L-infinity. The model is flexible enough to accommodate 1) any recruitment pattern as a function of both time and length, 2) length-specific selectivity, and 3) varying fishing effort over time. The maximum likelihood method gives consistent estimates, provided the underlying distribution for individual variation in growth is correctly specified. Simulation results indicate that our method is reasonably robust to violations in the assumptions. The method is applied to tiger prawn data (Penaeus semisulcatus) to obtain estimates of natural and fishing mortality.

Working correlation structure misspecification, estimation and covariate design: Implications for generalised estimating equations performance

The method of generalised estimating equations for regression modelling of clustered outcomes allows for specification of a working matrix that is intended to approximate the true correlation matrix of the observations. We investigate the asymptotic relative efficiency of the generalised estimating equation for the mean parameters when the correlation parameters are estimated by various methods. The asymptotic relative efficiency depends on three-features of the analysis, namely (i) the discrepancy between the working correlation structure and the unobservable true correlation structure, (ii) the method by which the correlation parameters are estimated and (iii) the 'design', by which we refer to both the structures of the predictor matrices within clusters and distribution of cluster sizes. Analytical and numerical studies of realistic data-analysis scenarios show that choice of working covariance model has a substantial impact on regression estimator efficiency. Protection against avoidable loss of efficiency associated with covariance misspecification is obtained when a 'Gaussian estimation' pseudolikelihood procedure is used with an AR(1) structure.

Effect of individual variability on estimation of population parameters from length-frequency data

We consider estimation of mortality rates and growth parameters from length-frequency data of a fish stock when there is individual variability in the von Bertalanffy growth parameter L-infinity and investigate the possible bias in the estimates when the individual variability is ignored. Three methods are examined: (i) the regression method based on the Beverton and Holt's (1956, Rapp. P.V. Reun. Cons. Int. Explor. Mer, 140: 67-83) equation; (ii) the moment method of Powell (1979, Rapp. PV. Reun. Int. Explor. Mer, 175: 167-169); and (iii) a generalization of Powell's method that estimates the individual variability to be incorporated into the estimation. It is found that the biases in the estimates from the existing methods are, in general, substantial, even when individual variability in growth is small and recruitment is uniform, and the generalized method performs better in terms of bias but is subject to a larger variation. There is a need to develop robust and flexible methods to deal with individual variability in the analysis of length-frequency data.

ESTIMATION OF EVAPOTRANSPIRATION IN AN EXPERIMENTAL WATERSHED IN A DECIDUOUS FOREST OF SOUTH INDIA

Forested areas play a dominant role in the global hydrological cycle. Evapotranspiration is a dominant component most of the time catching up with the rainfall. Though there are sophisticated methods which are available for its estimation, a simple reliable tool is needed so that a good budgeting could be made. Studies have established that evapotranspiration in forested areas is much higher than in agricultural areas. Latitude, type of forests, climate and geological characteristics also add to the complexity of its estimation. Few studies have compared different methods of evapotranspiration on forested watersheds in semi arid tropical forests. In this paper a comparative study of different methods of estimation of evapotranspiration is made with reference to the actual measurements made using all parameter climatological station data of a small deciduous forested watershed of Mulehole (area of 4.5 km2 ), South India. Potential evapotranspiration (ETo) was calculated using ten physically based and empirical methods. Actual evapotranspiration (AET) has been calculated through computation of water balance through SWAT model. The Penman-Montieth method has been used as a benchmark to compare the estimates arrived at using various methods. The AET calculated shows good agreement with the curve for evapotranspiration for forests worldwide. Error estimates have been made with respect to Penman-Montieth method. This study could give an idea of the errors involved whenever methods with limited data are used and also show the use indirect methods in estimation of Evapotranspiration which is more suitable for regional scale studies.

Improved estimation of size-transition matrices using tag-recapture data

We derive a new method for determining size-transition matrices (STMs) that eliminates probabilities of negative growth and accounts for individual variability. STMs are an important part of size-structured models, which are used in the stock assessment of aquatic species. The elements of STMs represent the probability of growth from one size class to another, given a time step. The growth increment over this time step can be modelled with a variety of methods, but when a population construct is assumed for the underlying growth model, the resulting STM may contain entries that predict negative growth. To solve this problem, we use a maximum likelihood method that incorporates individual variability in the asymptotic length, relative age at tagging, and measurement error to obtain von Bertalanffy growth model parameter estimates. The statistical moments for the future length given an individual’s previous length measurement and time at liberty are then derived. We moment match the true conditional distributions with skewed-normal distributions and use these to accurately estimate the elements of the STMs. The method is investigated with simulated tag–recapture data and tag–recapture data gathered from the Australian eastern king prawn (Melicertus plebejus).

Estimation of cosmological parameters using adaptive importance sampling

We present a Bayesian sampling algorithm called adaptive importance sampling or population Monte Carlo (PMC), whose computational workload is easily parallelizable and thus has the potential to considerably reduce the wall-clock time required for sampling, along with providing other benefits. To assess the performance of the approach for cosmological problems, we use simulated and actual data consisting of CMB anisotropies, supernovae of type Ia, and weak cosmological lensing, and provide a comparison of results to those obtained using state-of-the-art Markov chain Monte Carlo (MCMC). For both types of data sets, we find comparable parameter estimates for PMC and MCMC, with the advantage of a significantly lower wall-clock time for PMC. In the case of WMAP5 data, for example, the wall-clock time scale reduces from days for MCMC to hours using PMC on a cluster of processors. Other benefits of the PMC approach, along with potential difficulties in using the approach, are analyzed and discussed.

Theoretical Estimation of Length Dependent In-Plane Stiffness of Single Walled Carbon Nanotubes Using the Nonlocal Elasticity Theory

In the present paper, Eringen's nonlocal elasticity theory is employed to evaluate the length dependent in-plane stiffness of single-walled carbon nanotubes (SWCNTs). The SWCNT is modeled as an Euler-Bernoulli beam and is analyzed for various boundary conditions to evaluate the length dependent in-plane stiffness. It has been found that the nonlocal scaling parameter has a significant effect on the length dependent in-plane stiffness of SWCNTs. It has been observed that as the nonlocal scale parameter increases the stiffness ratio of SWCNT decreases. In nonlocality, the cantilever SWCNT has high in-plane stiffness as compared to the simply-supported and the clamped cases.

Methods and applications for improving parameter prediction models for stand structures in Finland

This thesis report attempts to improve the models for predicting forest stand structure for practical use, e.g. forest management planning (FMP) purposes in Finland. Comparisons were made between Weibull and Johnson s SB distribution and alternative regression estimation methods. Data used for preliminary studies was local but the final models were based on representative data. Models were validated mainly in terms of bias and RMSE in the main stand characteristics (e.g. volume) using independent data. The bivariate SBB distribution model was used to mimic realistic variations in tree dimensions by including within-diameter-class height variation. Using the traditional method, diameter distribution with the expected height resulted in reduced height variation, whereas the alternative bivariate method utilized the error-term of the height model. The lack of models for FMP was covered to some extent by the models for peatland and juvenile stands. The validation of these models showed that the more sophisticated regression estimation methods provided slightly improved accuracy. A flexible prediction and application for stand structure consisted of seemingly unrelated regression models for eight stand characteristics, the parameters of three optional distributions and Näslund s height curve. The cross-model covariance structure was used for linear prediction application, in which the expected values of the models were calibrated with the known stand characteristics. This provided a framework to validate the optional distributions and the optional set of stand characteristics. Height distribution is recommended for the earliest state of stands because of its continuous feature. From the mean height of about 4 m, Weibull dbh-frequency distribution is recommended in young stands if the input variables consist of arithmetic stand characteristics. In advanced stands, basal area-dbh distribution models are recommended. Näslund s height curve proved useful. Some efficient transformations of stand characteristics are introduced, e.g. the shape index, which combined the basal area, the stem number and the median diameter. Shape index enabled SB model for peatland stands to detect large variation in stand densities. This model also demonstrated reasonable behaviour for stands in mineral soils.

Estimation of soil hydraulic properties and their uncertainty: comparison between laboratory and field experiment

Often the soil hydraulic parameters are obtained by the inversion of measured data (e.g. soil moisture, pressure head, and cumulative infiltration, etc.). However, the inverse problem in unsaturated zone is ill-posed due to various reasons, and hence the parameters become non-unique. The presence of multiple soil layers brings the additional complexities in the inverse modelling. The generalized likelihood uncertainty estimate (GLUE) is a useful approach to estimate the parameters and their uncertainty when dealing with soil moisture dynamics which is a highly non-linear problem. Because the estimated parameters depend on the modelling scale, inverse modelling carried out on laboratory data and field data may provide independent estimates. The objective of this paper is to compare the parameters and their uncertainty estimated through experiments in the laboratory and in the field and to assess which of the soil hydraulic parameters are independent of the experiment. The first two layers in the field site are characterized by Loamy sand and Loamy. The mean soil moisture and pressure head at three depths are measured with an interval of half hour for a period of 1 week using the evaporation method for the laboratory experiment, whereas soil moisture at three different depths (60, 110, and 200 cm) is measured with an interval of 1 h for 2 years for the field experiment. A one-dimensional soil moisture model on the basis of the finite difference method was used. The calibration and validation are approximately for 1 year each. The model performance was found to be good with root mean square error (RMSE) varying from 2 to 4 cm(3) cm(-3). It is found from the two experiments that mean and uncertainty in the saturated soil moisture (theta(s)) and shape parameter (n) of van Genuchten equations are similar for both the soil types. Copyright (C) 2010 John Wiley & Sons, Ltd.