A Special Homotopy Continuation Method For A Class of Polynomial Systems

A special homotopy continuation method, as a combination of the polyhedral homotopy and the linear product homotopy, is proposed for computing all the isolated solutions to a special class of polynomial systems. The root number bound of this method is between the total degree bound and the mixed volume bound and can be easily computed. The new algorithm has been implemented as a program called LPH using C++. Our experiments show its efficiency compared to the polyhedral or other homotopies on such systems. As an application, the algorithm can be used to find witness points on each connected component of a real variety

Implicit sampling for path integral control, Monte Carlo localization, and SLAM

The applicability and usefulness of implicit sampling in stochastic optimal control, stochastic localization, and simultaneous localization and mapping (SLAM), is explored; implicit sampling is a recently-developed variationally-enhanced sampling method. The theory is illustrated with examples, and it is found that implicit sampling is significantly more efficient than current Monte Carlo methods in test problems for all three applications

Sensor Networks TDOA Self-Calibration: 2D Complexity Analysis and Solutions

Given a network of receivers and transmitters, the process of determining their positions from measured pseudo-ranges is known as network self-calibration. In this paper we consider 2D networks with synchronized receivers but unsynchronized transmitters and the corresponding calibration techniques,known as TDOA techniques. Despite previous work, TDOA self-calibration is computationally challenging. Iterative algorithms are very sensitive to the initialization, causing convergence issues.In this paper, we present a novel approach, which gives an algebraic solution to three previously unsolved scenarios. Our solvers can lead to a position error <1.2% and are robust to noise