An approximate point-based alternative for the estimation of variance under big BAF sampling

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.

A Polynomial Prediction Filter Method for Estimating Multisensor Dynamically Varying Biases

The estimation of the sensor measurement biases in a multisensor system is vital for the sensor data fusion. A solution is provided for the estimation of dynamically varying multiple sensor biases without any knowledge of the dynamic bias model parameters. It is shown that the sensor bias pseudomeasurement can be dynamically obtained via a parity vector. This is accomplished by multiplying the sensor uncalibrated measurement equations by a projection matrix so that the measured variable is eliminated from the equations. Once the state equations of the dynamically varying sensor biases are modeled by a polynomial prediction filter, the dynamically varying multisensor biases can be obtained by Kalman filter. Simulation results validate that the proposed method can estimate the constant biases and dynamic biases of multisensors and outperforms the methods reported in literature.

Robust Sensor Bias Estimation for Ill-Conditioned Scenarios

Sensor bias estimation is an inherent problem in multi-sensor data fusion systems. Classical methods such as the Generalized Least Squares （GLS） method can have numerical problems with ill-conditioned sets which are common in practical applications. This paper describes an azimuth-GLS method that provides a solution to the ill-conditioning problem while maintaining reasonable accuracy com- pared with the classical GLS method. The mean square error is given for both methods as a criterion to de- termine when to use this azimuth-GLS method. Furthermore, the separation boundary between the azi- muth-GLS favorable region and that of the GLS method is explicitly plotted. Extensive simulations show that the azimuth-GLS approach is preferable in most scenarios.

A closed-form solution for moving source localization using LBI changing rate of phase difference only

Due to the deficiencies in the conventional multiple-receiver localization syste,.ns based on direction of arrival （DOA） such as system complexity of interferometer or array and ampli- tude/phase unbalance between multiple receiving channels and constraint on antenna configuration, a new radiated source localization method using the changing rate of phase difference （CRPD） measured by a long baseline interferometer （LBI） only is studied. To solve the strictly nonlinear problem, a two-stage closed-form solution is proposed. In the first stage, the DOA and its changing rate are estimated from the CRPD of each observer by the pseudolinear least square （PLS） method, and then in the second stage, the source position and velocity are found by another PLS minimiza- tion. The bias of the algorithm caused by the correlation between the measurement matrix and the noise in the second stage is analyzed. To reduce this bias, an instrumental variable （IV） method is derived. A weighted IV estimator is given in order to reduce the estimation variance. The proposed method does not need any initial guess and the computation is small. The Cramer-Rao lower bound （CRLB） and mean square error （MSE） are also analyzed. Simulation results show that the proposed method can be close to the CRLB with moderate Gaussian measurement noise.

Convergence and error bounds of adaptive filtering under model structure and regressor uncertainties

Adaptive filtering algorithms are investigated when system models are subject to model structure errors and regressor signal perturbations. System models for practical applications are often approximations of high-order or nonlinear systems, introducing model structure uncertainties. Measurement and actuation errors cause signal perturbations, which in turn lead to uncertainties in regressors of adaptive filtering algorithms. Employing ordinary differential equation （ODE） methodologies, we show that convergence properties and estimation bias can be characterized by certain differential inclusions. Conditions to ensure algorithm convergence and bounds on estimation bias are derived. These findings yield better understanding of the robustness of adaptive algorithms against structural and signal uncertainties.

Trajectory Optimization for Target Localization and Sensor Bias Calibration with Bearing-Only Information

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.