There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Data Mining - Concepts and Techniques.

On robust estimation of the location parameter

Filtering and smoothing methods are used to produce an accurate estimate of the state of a time-varying system based on multiple observational inputs (data). Interest in these methods has exploded in recent years, with numerous applications emerging in fields such as navigation, aerospace engineering, telecommunications, and medicine. This compact, informal introduction for graduate students and advanced undergraduates presents the current state-of-the-art filtering and smoothing methods in a unified Bayesian framework. Readers learn what non-linear Kalman filters and particle filters are, how they are related, and their relative advantages and disadvantages. They also discover how state-of-the-art Bayesian parameter estimation methods can be combined with state-of-the-art filtering and smoothing algorithms. The book’s practical and algorithmic approach assumes only modest mathematical prerequisites. Examples include MATLAB computations, and the numerous end-of-chapter exercises include computational assignments. MATLAB/GNU Octave source code is available for download at www.cambridge.org/sarkka, promoting hands-on work with the methods.

贝叶斯滤波与平滑 (Bayesian filtering and smoothing)

The growing commercial interest in indoor location-based services (ILBS) has spurred recent development of many indoor positioning techniques. Due to the absence of global positioning system (GPS) signal, many other signals have been proposed for indoor usage. Among them, Wi-Fi (802.11) emerges as a promising one due to the pervasive deployment of wireless LANs (WLANs). In particular, Wi-Fi fingerprinting has been attracting much attention recently because it does not require line-of-sight measurement of access points (APs) and achieves high applicability in complex indoor environment. This survey overviews recent advances on two major areas of Wi-Fi fingerprint localization: advanced localization techniques and efficient system deployment. Regarding advanced techniques to localize users, we present how to make use of temporal or spatial signal patterns, user collaboration, and motion sensors. Regarding efficient system deployment, we discuss recent advances on reducing offline labor-intensive survey, adapting to fingerprint changes, calibrating heterogeneous devices for signal collection, and achieving energy efficiency for smartphones. We study and compare the approaches through our deployment experiences, and discuss some future directions.

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Wi-Fi Fingerprint-Based Indoor Positioning: Recent Advances and Comparisons

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.

A comparative survey of WLAN location fingerprinting methods

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.

Particle filter and smoother for indoor localization

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.

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

This paper investigates the similarities and differences of the signal strength fluctuations and positioning accuracy in indoor scenarios for three types of wireless area networks: two Wireless Local Area Networks (WLANs) at 24 GHz and 5 GHz frequency, respectively, and one Wireless Personal Area Network (WPAN), namely the Bluetooth Low Energy (BLE) Two path-loss models based on weighted centroids and non-negative least squares estimation are presented: one including a floor loss factor, and the other one ignoring the floor losses, and the three signal types are compared in terms of the path-loss parameters, channel fluctuations and positioning accuracy, namely the distance errors and floor detection probabilities The comparison is done based on real-field measurement data collected from a university building in Tampere, Finland It is shown that all these three signal types have similar shadowing variances and close path-loss parameter values, and that a path-loss model considering floor losses gives the best floor detection probability, but not necessarily the smallest distance error

Received signal strength models for WLAN and BLE-based indoor positioning in multi-floor buildings

In this paper, we present a new filter, the Fingerprint Kalman Filter (FKF), and apply it to indoor positioning. FKF enables sequential position estimation using WLAN RSSI measurements and fingerprint data. Fingerprints that are collected beforehand in a calibration phase contain samples of the radio map in certain points, namely, calibration points. This means that FKF does not need an analytic formula of the measurement equation like conventional Kalman-type filters do (e.g. the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF)). Like EKF and UKF, FKF is based on the recursive computation of the Best Linear Unbiased Estimator (BLUE) and has small computational and memory requirements. An often-used Kalman-type filter for this problem is so-called Position Kalman Filter (PKF) that uses static position solutions as measurements for the conventional Kalman filter. In the test part of the paper, we compare FKF, PKF and different static location estimation methods, namely, the Nearest Neighbor (NN) and the Kernel method. The test data is real WLAN RSSI measurement data. The results indicate that the filters give more accurate position estimates than the static methods. FKF performs better than PKF with NN as the static estimator, and the computational load of FKF is smaller than PKF with the Kernel method.

Simo Ali-Loytty

Papers

A comparative survey of WLAN location fingerprinting methods

Particle filter and smoother for indoor localization

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

Received signal strength models for WLAN and BLE-based indoor positioning in multi-floor buildings

Fingerprint Kalman Filter in indoor positioning applications