This report describes algorithms for fitting certain curves and surfaces to points in three dimensions. All fits are based on orthogonal distance regression. The algorithms were developed as reference software for the National Institute of Standards and Technology's Algorithm Testing System, which has been used for 5 years by NIST and by members of the American Society of Mechanical Engineers' ...

Simultaneous Localization and Mapping (SLAM) has focused on noisy but unique data associations resulting in linear Gaussian uncertainty models. However, a unique decision is often not possible using only local information, giving rise to ambiguities that have to be resolved globally during optimization. To solve this problem, the pose graph data structure is extended here by multimodal constrai...

We compare the two well-known global optimization methods, simulated annealing and genetic optimization, to a local gradient-based optimization technique. We rate the applicability of each method in terms of the minimal achievable target value for a given number of simulation runs in an inverse modeling application. The gradient-based optimizer used in the experiment is based on the Levenberg-M...

We propose a new self-adaptive Levenberg-Marquardt algorithm for the system of nonlinear equations F(x) = 0. The Levenberg-Marquardt parameter is chosen as the product of ‖Fk‖ with δ being a positive constant, and some function of the ratio between the actual reduction and predicted reduction of the merit function. Under the local error bound condition which is weaker than the nonsingularity, w...

Retrieving information from remotely sensed data is an important task. In the present work, data of L band microwave radiometer has been used to collect the brightness temperature over bare and vegetated fields in two polarizations at different moisture levels. Artificial neural network (ANN) trained with Levenberg-Marquardt algorithm has been used to determine soil moisture from brightness tem...

A novel hybrid method for tracking multiple indistinguishable maneuvering targets using a wireless sensor network is introduced in this paper. The problem of tracking the location of targets is formulated as a Maximum Likelihood Estimation. We propose a hybrid optimization method, which consists of an iterative and a heuristic search method, for finding the location of targets simultaneously. T...

A novel algorithm is proposed for CANDECOMP/PARAFAC tensor decomposition to exploit best rank-1 tensor approximation. Different from the existing algorithms, our algorithm updates rank-1 tensors simultaneously in-parallel. In order to achieve this, we develop new all-at-once algorithms for best rank-1 tensor approximation based on the Levenberg-Marquardt method and the rotational update. We sho...

An advanced operational semi-empirical algorithm for processing satellite remote sensing data in the visible region is described. Based on the Levenberg-Marquardt multivariate optimization procedure, the algorithm is developed for retrieving major water colour producing agents: chlorophyll-a, suspended minerals and dissolved organics. Two assurance units incorporated by the algorithm are intend...

We present an algorithm based on maximum likelihood for the estimation and renormalization (marginalization) of exponential densities. The moment-matching problem resulting from the maximization of the likelihood is solved as an optimization problem using the Levenberg-Marquardt algorithm. In the case of renormalization, the moments needed to set up the moment-matching problem are evaluated usi...