Background:A new variance estimator is derived and tested for big BAF(Basal Area Factor)sampling which is a forest inventory system that utilizes Bitterlich sampling(point sampling)with two BAF sizes,a small BAF for t...Background:A new variance estimator is derived and tested for big BAF(Basal Area Factor)sampling which is a forest inventory system that utilizes Bitterlich sampling(point sampling)with two BAF sizes,a small BAF for tree counts and a larger BAF on which tree measurements are made usually including DBHs and heights needed for volume estimation.Methods:The new estimator is derived using the Delta method from an existing formulation of the big BAF estimator as consisting of three sample means.The new formula is compared to existing big BAF estimators including a popular estimator based on Bruce’s formula.Results:Several computer simulation studies were conducted comparing the new variance estimator to all known variance estimators for big BAF currently in the forest inventory literature.In simulations the new estimator performed well and comparably to existing variance formulas.Conclusions:A possible advantage of the new estimator is that it does not require the assumption of negligible correlation between basal area counts on the small BAF factor and volume-basal area ratios based on the large BAF factor selection trees,an assumption required by all previous big BAF variance estimation formulas.Although this correlation was negligible on the simulation stands used in this study,it is conceivable that the correlation could be significant in some forest types,such as those in which the DBH-height relationship can be affected substantially by density perhaps through competition.We derived a formula that can be used to estimate the covariance between estimates of mean basal area and the ratio of estimates of mean volume and mean basal area.We also mathematically derived expressions for bias in the big BAF estimator that can be used to show the bias approaches zero in large samples on the order of 1n where n is the number of sample points.展开更多
The problem of trajectory optimization of an unmanned aerial vehicle(UAV)for static target localization with biased bearing measurements is considered.The angular bias in sensor measurements is modeled as an additive ...The problem of trajectory optimization of an unmanned aerial vehicle(UAV)for static target localization with biased bearing measurements is considered.The angular bias in sensor measurements is modeled as an additive constant in the observation model and jointly estimated with the position of the target.The necessary conditions for system observability of this estimation problem is first derived analytically with geometrical interpretations provided.The trajectory of UAV is designed based on the Fisher Information Matrix(FIM)considering physical constraints to enhance the system observability.Simulation results with Monte-Carlo runs are presented to demonstrate the improvement in target localization with biased measurements by UAV trajectory optimization.展开更多
基金Support was provided by Research Joint Venture Agreement 17-JV-11242306045,“Old Growth Forest Dynamics and Structure,”between the USDA Forest Service and the University of New HampshireAdditional support to MJD was provided by the USDA National Institute of Food and Agriculture McIntire-Stennis Project Accession Number 1020142,“Forest Structure,Volume,and Biomass in the Northeastern United States.”+1 种基金supported by the USDA National Institute of Food and Agriculture,McIntire-Stennis project OKL02834the Division of Agricultural Sciences and Natural Resources at Oklahoma State University.
文摘Background:A new variance estimator is derived and tested for big BAF(Basal Area Factor)sampling which is a forest inventory system that utilizes Bitterlich sampling(point sampling)with two BAF sizes,a small BAF for tree counts and a larger BAF on which tree measurements are made usually including DBHs and heights needed for volume estimation.Methods:The new estimator is derived using the Delta method from an existing formulation of the big BAF estimator as consisting of three sample means.The new formula is compared to existing big BAF estimators including a popular estimator based on Bruce’s formula.Results:Several computer simulation studies were conducted comparing the new variance estimator to all known variance estimators for big BAF currently in the forest inventory literature.In simulations the new estimator performed well and comparably to existing variance formulas.Conclusions:A possible advantage of the new estimator is that it does not require the assumption of negligible correlation between basal area counts on the small BAF factor and volume-basal area ratios based on the large BAF factor selection trees,an assumption required by all previous big BAF variance estimation formulas.Although this correlation was negligible on the simulation stands used in this study,it is conceivable that the correlation could be significant in some forest types,such as those in which the DBH-height relationship can be affected substantially by density perhaps through competition.We derived a formula that can be used to estimate the covariance between estimates of mean basal area and the ratio of estimates of mean volume and mean basal area.We also mathematically derived expressions for bias in the big BAF estimator that can be used to show the bias approaches zero in large samples on the order of 1n where n is the number of sample points.
文摘The problem of trajectory optimization of an unmanned aerial vehicle(UAV)for static target localization with biased bearing measurements is considered.The angular bias in sensor measurements is modeled as an additive constant in the observation model and jointly estimated with the position of the target.The necessary conditions for system observability of this estimation problem is first derived analytically with geometrical interpretations provided.The trajectory of UAV is designed based on the Fisher Information Matrix(FIM)considering physical constraints to enhance the system observability.Simulation results with Monte-Carlo runs are presented to demonstrate the improvement in target localization with biased measurements by UAV trajectory optimization.
