Niilo Sirola

Closed-form algorithms in mobile positioning: Myths and misconceptions

The iterative least squares method, or Gauss-Newton method, is a standard algorithm for solving general nonlinear systems of equations, but it is often said to be unsuited for mobile positioning with e.g. ranges or range differences or angle-of-arrival measurements. Instead, various closed-form methods have been proposed and are constantly being reinvented for the problem, claiming to outperform Gauss-Newton. We list some common conceptual and computation pitfalls for closedform solvers, and present an extensive comparison of different closed-form solvers against a properly implemented Gauss-Newton solver. We give all the algorithms in similar notations and implementable form and a couple of novel closed-form methods and implementation details. The Gauss-Newton method strengthened with a regularisation term is found to be as accurate as any of the closed-form methods, and to have comparable computation load, while being simpler to implement and avoiding most of the pitfalls.

Exhaustive global grid search in computing receiver position from modular satellite range measurements

A global grid search algorithm with an application in weak signal satellite positioning is implemented and tested numerically. The algorithm consists of local Gauss-Newton search and a global starting point chooser, and it can be generalized as a global optimization method for functions with an attraction basin of computable minimum radius. The method is shown to .nd the global minimum in a bounded region in predictable time.

Benchmarking Nonlinear Filters

Algorithm developers need relevant and practical criteria to evaluate and compare the performance of different discrete-time filters or filter variants. This paper discusses some pit-falls in different approaches and proposes a combination of criteria on which to base comparisons. A comparison of eight filters for a class of hybrid personal positioning problems is presented as an example.

A motion model for articulated vehicles and a distributed acceleration measurement system

A motion model is developed for a trailer-truck combination that fuses the differential equations governing the motion of the trailer with the dynamics model of the truck. Three different parametrisations of the vehicle state are proposed. The resulting model is a stepping stone for a filtering solution for tracking the position and attitude of articulated vehicles, such as trailer-trucks, articulated buses or work machines, or even trains.

PNaFF: A modular software platform for testing hybrid position estimation algorithms

PNaFF (personal navigation filter framework) is a comprehensive simulation and filtering test bench that is being developed within the Personal Positioning Research Group at the Department of Mathematics of Tampere University of Technology. Hybrid positioning is a process where measurements from different sources are used to obtain position estimate. PNaFF provides tools for comparison and visualization of the performance of hybrid positioning filters that estimate the current state from measurements and the previous state estimate. New filters can be added to PNaFF easily and the performance of the new filter can be assessed instantly. Different kinds of measurements can be used in estimation, and it is simple to add new measurement types.