Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

This document provides a survey of the mathematical methods currently used for position estimation in indoor local positioning systems (LPS), particularly those based on radiofrequency signals. The techniques are grouped into four categories: geometry-based methods, minimization of the cost function, fingerprinting, and Bayesian techniques. Comments on the applicability, requirements, and immunity to nonline-of-sight (NLOS) propagation of the signals of each method are provided.

http://www.car.upm-csic.es/lopsi/static/publicaciones/Congreso%20Internacional/WISP2009Seco.pdf

A survey of mathematical methods for indoor localization

A common technical difficulty in target tracking in a wireless sensor network is that individual homogeneous sensors only measure their distances to the target whereas the state of the target composes of its position and velocity in the Cartesian coordinates. That is, the senor measurements are nonlinear in the target state. Extended Kalman filtering is a commonly used method to deal with the nonlinearity, but this often leads to unsatisfactory or even unstable tracking performances. In this paper, we present a new target tracking approach which avoids the instability problem and offers superior tracking performances. We first propose an improved noise model which incorporates both additive noises and multiplicative noises in distance sensing. We then use a maximum likelihood estimator for prelocalization to remove the sensing nonlinearity before applying a standard Kalman filter. The advantages of the proposed approach are demonstrated via experimental and simulation results.

Target Tracking in Wireless Sensor Networks Based on the Combination of KF and MLE Using Distance Measurements

The advances in photonic device technologies are bringing ultra-high-bit-rate networking-at speeds towards 100 Gb/s and beyond-much closer to practical reality. It is increasingly likely that in the longer term ultrafast optical time-division techniques-together with wavelength multiplexing-will be used in networks at all levels, from the transcontinental backbone to the desktop. Examples of devices include a subpicosecond clock source packaged inside a laptop personal computer and an OTDM switch on a single semiconductor chip, both produced at HHI. Advances similar to these make it possible now to envisage the use of OTDM techniques, not just in the highest layers of national and international networks, but also much closer to the user-such as the world-first demonstrations at BT Laboratories of a 40 Gb/s TDMA LAN and a 100 Gb/s packet self-routing switch for multiprocessor interconnection. Ultrafast networks might even provide the interconnection backplane inside future desktop routers and servers with massive throughput.

Ultra-high-bit-rate networking : From the transcontinental backbone to the desktop : Optical networks technology in Europe

In this paper, we develop a novel robust optimization approach to source localization using time-difference-of-arrival (TDOA) measurements that are collected under non-line-of-sight (NLOS) conditions. A key feature of our approach is that it does not require knowledge of the distribution or statistics of the NLOS errors, which are often difficult to obtain in practice. Instead, it only assumes that the NLOS errors have bounded supports. Based on this assumption, we formulate the TDOA-based source localization problem as a robust least squares (RLS) problem, in which a location estimate that is robust against the NLOS errors is sought. Since the RLS problem is non-convex, we propose two efficiently implementable convex relaxation-based approximation methods to tackle it. We then conduct a thorough theoretical analysis of the approximation quality and computational complexity of these two methods. In particular, we establish conditions under which they will yield a unique localization of the source. Simulation results on both synthetic and real data show that the performance of our approach under various NLOS settings is very stable and is significantly better than that of several existing non-robust approaches.

Robust Convex Approximation Methods for TDOA-Based Localization Under NLOS Conditions

In cellular communication systems where non-line-of-sight (NLOS) channels are dominant as compared to line-of-sight (LOS) channels, a time difference of arrival (TDOA) localization method can outperform a time of arrival (TOA) localization method, although the TDOA method loses one degree of freedom in the number of usable range estimates when selecting a range estimate as the reference and doubles the variance of range sampling error when subtracting the reference range estimate. In this paper, we first show the computer simulation result on the localization performance of conventional TOA and TDOA methods in mixed LOS/NLOS environments, and then validate it by theoretical analysis. Here, we analyze the root mean square localization error by decomposing it into two factors; for one factor, which is the contribution from range sampling error, we evaluate it by the Cramer-Rao lower-bound, whereas for the other factor, which is the contribution from positively biased NLOS range error, we analyze it by perturbation method. We show that the theoretical result can well explain the localization performance by computer simulation for both the TOA and TDOA methods, and furthermore, we derive a simple condition among the number of cells, the average and variance of NLOS range error distribution which can correctly predict whether the TDOA method outperforms the TOA method or not for the case of all NLOS channels.

A Perturbation Analysis on the Performance of TOA and TDOA Localization in Mixed LOS/NLOS Environments

Many target localization techniques based on received signal strength indicator (RSSI) assume a prior knowledge of a channel model and its parameters for an area where a target node is localized. This is a limiting factor since an intensive pre- measurement campaign is required to determine the model and its parameters. Basing on channel measurement campaigns in different areas we confirmed that the variation in the RSSIs of the IEEE 802.15.4 signal can be described by a two-layer model. We therefore propose a novel target localization method with no prior knowledge of model parameter values. The method is based on a joint maximum likelihood target localization and channel model parameters estimation. The proposed method was experimentally verified in real environments and the results show that the location estimation accuracy outperforms the accuracy of the conventional method where the values of the channel model parameters are known in advance.

A Joint Estimation of Target Location and Channel Model Parameters in an IEEE 802.15.4-based Wireless Sensor Network

In target node localization problem, conventional methods based on received signal strength indicator (RSSI) assume a prior knowledge of a channel model and values of its parameters specific for an environment. This limits the conventional localization system to be set up quickly and effectively due to a necessary pre-measurement step to determine both the channel model and the values of its parameters. To address the limitation, a two-stage iterative algorithm which allows to localize a target node without any prior knowledge of the parameter values has been propose. Each stage of the algorithm can be implemented using different estimation methods, such as maximum likelihood (ML) and least square (LS) estimation which provides four different combinations. To determine the best combination, the location estimation performance for all four combinations is evaluated using experimental data collected in measurement campaigns on various indoor locations. The results reveal that the combination of ML estimation method implemented in both stages provides the best location estimation accuracy and the fastest convergence rate.

RSSI-based Localization without a Prior Knowledge of Channel Model Parameters

Many indoor localisation and tracking techniques in wireless sensor networks assume placing anchor nodes on a ceiling. However, placing the nodes on the ground can improve target localisation estimation accuracy based on received signal strength indicator as we show in this work. The presented results are based on an experiment conducted in a hall under two sets of conditions. In one case, people were present in the hall and in the other one, the hall was empty. For the case when people were present in the hall, the location estimation performance improved from 3.7 meters root-mean square error (RMSE) when using only the anchor nodes fixed to the ceiling to 2.2 meters RMSE when using only the anchor nodes placed on the ground. For the case when the hall was empty, the location estimation performance improved from 4.1 meters RMSE when using only the anchor nodes fixed to the ceiling to 2.4 meters RMSE when using only the anchor nodes placed on the ground. The target location estimation accuracy improved by 40% for both conditions.

An Effect of Anchor Nodes Placement on a Target Location Estimation Performance

In a computer simulation result on the location estimation for a cellular system, we found that a Time Difference Of Arrival (TDOA) method outperforms a Time Of Arrival (TOA) method when Non-Line-Of-Sight (NLOS) channels are dominant, whereas the TOA method outperforms the TDOA method when LOS channels are dominant. We could not easily accept the result, because TDOA method loses one degree of freedom in the number of usable range estimates when selecting a range estimate as a reference and doubles the variance of range error when subtracting the reference range estimate. In this paper, we try to theoretically prove the interesting result by the computer simulation. We divide the root mean square location estimation error into two factors, such as the error variance contributed from range sampling error and the error bias contributed from positive NLOS range error. For the error variance, we evaluate it by the Cramer-Rao lower bound, whereas for the error bias, we analyze it by perturbation method.

Radim Zemek

Papers

A Perturbation Analysis on the Performance of TOA and TDOA Localization in Mixed LOS/NLOS Environments

A Joint Estimation of Target Location and Channel Model Parameters in an IEEE 802.15.4-based Wireless Sensor Network

RSSI-based Localization without a Prior Knowledge of Channel Model Parameters

An Effect of Anchor Nodes Placement on a Target Location Estimation Performance

Analysis on TOA and TDOA Location Estimation Performances in a Cellular System