Robert Piché

A comparative survey of WLAN location fingerprinting methods

The term “location fingerprinting” covers a wide variety of methods for determining receiver position using databases of radio signal strength measurements from different sources. In this work we present a survey of location fingerprinting methods, including deterministic and probabilistic methods for static estimation, as well as filtering methods based on Bayesian filter and Kalman filter. We present a unified mathematical formulation of radio map database and location estimation, point out the equivalence of some methods from the literature, and present some new variants. A set of tests in an indoor positioning scenario using WLAN signal strengths is performed to determine the influence of different calibration and location method parameters. In the tests, the probabilistic method with the kernel function approximation of signal strength histograms was the best static positioning method. Moreover, all filters improved the results significantly over the static methods.

SO-MI: A surrogate model algorithm for computationally expensive nonlinear mixed-integer black-box global optimization problems

This paper introduces a surrogate model based algorithm for computationally expensive mixed-integer black-box global optimization problems with both binary and non-binary integer variables that may have computationally expensive constraints. The goal is to find accurate solutions with relatively few function evaluations. A radial basis function surrogate model (response surface) is used to select candidates for integer and continuous decision variable points at which the computationally expensive objective and constraint functions are to be evaluated. In every iteration multiple new points are selected based on different methods, and the function evaluations are done in parallel. The algorithm converges to the global optimum almost surely. The performance of this new algorithm, SO-MI, is compared to a branch and bound algorithm for nonlinear problems, a genetic algorithm, and the NOMAD (Nonsmooth Optimization by Mesh Adaptive Direct Search) algorithm for mixed-integer problems on 16 test problems from the literature (constrained, unconstrained, unimodal and multimodal problems), as well as on two application problems arising from structural optimization, and three application problems from optimal reliability design. The numerical experiments show that SO-MI reaches significantly better results than the other algorithms when the number of function evaluations is very restricted (200-300 evaluations).

Rank based fingerprinting algorithm for indoor positioning

A novel Received Signal Strength (RSS) rank based fingerprinting algorithm for indoor positioning is presented. Because RSS rank is invariant to bias and scaling, the algorithm provides the same accuracy for any receiver device, without the need for RSS calibration. Similarity measures to compare ranked vectors are introduced and their impact on positioning accuracy is investigated in experiments. Experimental results shown that proposed algorithm can achieve better accuracy than commonly used NN and WKNN fingerprinting algorithms.

Robust Extended Kalman Filtering in Hybrid Positioning Applications

The Kalman filter and its extensions has been widely studied and applied in positioning, in part because its low computational complexity is well suited to small mobile devices. While these filters are accurate for problems with small nonlinearities and nearly Gaussian noise statistics, they can perform very badly when these conditions do not prevail. In hybrid positioning, large nonlinearities can be caused by the geometry and large outliers (blunder measurements) can arise due to multipath and non line-of-sight signals. It is therefore of interest to find ways to make positioning algorithms based on Kalman-type filters more robust. In this paper two methods to robustify the Kalman filter are presented. In the first method the variances of the measurements are scaled according to weights that are calculated for each innovation, thus giving less influence to measurements that are regarded as blunder. The second method is a Bayesian filter that approximates the density of the innovation with a non-Gaussian density. Weighting functions and innovation densities are chosen using Hubers min-max approach for the epsilon contaminated normal neighborhood, the p-point family, and a heuristic approach. Six robust extended Kalman filters together with the classical extended Kalman filter (EKF) and the second order extended Kalman filter (EKF2) are tested in numerical simulations. The results show that the proposed methods outperform EKF and EKF2 in cases where there is blunder measurement or considerable linearization errors present.

Mixture surrogate models based on Dempster-Shafer theory for global optimization problems

Recent research in algorithms for solving global optimization problems using response surface methodology has shown that it is in general not possible to use one surrogate model for solving different kinds of problems. In this paper the approach of applying Dempster-Shafer theory to surrogate model selection and their combination is described. Various conflict redistribution rules have been examined with respect to their influence on the results. Furthermore, the implications of the surrogate model type, i.e. using combined, single or a hybrid of both, have been studied. The suggested algorithms were applied to several well-known global optimization test problems. The results indicate that the used approach leads for all problems to a thorough exploration of the variable domain, i.e. the vicinities of global optima could be detected, and that the global minima could in most cases be approximated with high accuracy.

Fluid Transmission Line Modeling Using a Variational Method

A variational method is used to derive numerical models for transient flow simulation in fluid transmission lines. These are generalizations of models derived using the more traditional modal method. Three different transient compressible laminar pipe flow models are considered (inviscous, one-dimensional linear viscous, and two-dimensional dissipative viscous flow), and a model for transient turbulent pipe flow is given. The (model) equations in the laminar case are given in the form of a set of constant coefficient ordinary differential equations, and for the turbulent case (model) in the form of a set of nonlinear ordinary differential equations. Explicit equations are given for various end conditions. Attenuation factors, similar to the window functions used in spectral analysis, are used to attenuate Gibbs phenomenon oscillations.

Particle filter and smoother for indoor localization

We present a real-time particle filter for 2D and 3D hybrid indoor positioning. It uses wireless local area network (WLAN) based position measurements, step and turn detection from a hand-held inertial sensor unit, floor plan restrictions, altitude change measurements from barometer and possibly other measurements such as occasional GNSS fixes. We also present a particle smoother, which uses future measurements to improve the position estimate for non-real-time applications. A light-weight fallback filter is run in the background for initialization, divergence monitoring and possibly re-initialization. In real-data tests the particle filter is more accurate and consistent than the methods that do not use floor plans. An example is shown on how smoothing helps to improve the filter estimate. Moreover, a floor change case is presented, in which the filter is capable of detecting the floor change and improving the 2D accuracy using the floor change information.

Recursive outlier-robust filtering and smoothing for nonlinear systems using the multivariate student-t distribution

Nonlinear Kalman filter and Rauch-Tung-Striebel smoother type recursive estimators for nonlinear discrete-time state space models with multivariate Students t-distributed measurement noise are presented. The methods approximate the posterior state at each time step using the variational Bayes method. The nonlinearities in the dynamic and measurement models are handled using the nonlinear Gaussian filtering and smoothing approach, which encompasses many known nonlinear Kalman-type filters. The method is compared to alternative methods in a computer simulation.

Statistical path loss parameter estimation and positioning using RSS measurements in indoor wireless networks

A Bayesian method for dynamical off-line estimation of the position and path loss model parameters of a WLAN access point is presented. Two versions of three different on-line positioning methods are tested using real data. The tests show that the methods that use the estimated path loss parameter distributions with finite precisions outperform the methods that only use point estimates for the path loss parameters. They also outperform the coverage area based positioning method and are comparable in accuracy with the fingerprinting method. Taking the uncertainties into account is computationally demanding, but the Gauss-Newton optimization method is shown to provide a good approximation with computational load that is reasonable for many real-time solutions.

Variable step size time integration methods for transient eddy current problems

For transient eddy current problems modelled as differential-algebraic equations (DAEs), a time integration method suitable for ordinary differential equations (ODEs) will not necessarily work. We present two Runge-Kutta methods that are suitable for the time integration of the classes of DAEs to which eddy current problems belong. Both methods have error estimators and hence allow variable step sizes. In tests our variable step size integrators were competitive with fixed step size integrators, in particular with Crank-Nicolson.