On Timing Based Localization In Cellular Radio Networks
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On Timing-Based Localization in Cellular Radio Networks
Author: Kamiar Radnosrati
language: en
Publisher: Linköping University Electronic Press
Release Date: 2018-08-29
The possibilities for positioning in cellular networks has increased over time, pushed by increased needs for location based products and services for a variety of purposes. It all started with rough position estimates based on timing measurements and sector information available in the global system for mobile communication (gsm), and today there is an increased standardization effort to provide more position relevant measurements in cellular communication systems to improve on localization accuracy and availability. A first purpose of this thesis is to survey recent efforts in the area and their potential for localization. The rest of the thesis then investigates three particular aspects, where the focus is on timing measurements. How can these be combined in the best way in long term evolution (lte), what is the potential for the new narrow-band communication links for localization, and can the timing measurement error be more accurately modeled? The first contribution concerns a narrow-band standard in lte intended for internet of things (iot) devices. This lte standard includes a special position reference signal sent synchronized by all base stations (bs) to all iot devices. Each device can then compute several pair-wise time differences that corresponds to hyperbolic functions. Using multilateration methods the intersection of a set of such hyperbolas can be computed. An extensive performance study using a professional simulation environment with realistic user models is presented, indicating that a decent position accuracy can be achieved despite the narrow bandwidth of the channel. The second contribution is a study of how downlink measurements in lte can be combined. Time of flight (tof) to the serving bs and time difference of arrival (tdoa) to the neighboring bs are used as measurements. From a geometrical perspective, the position estimation problem involves computing the intersection of a circle and hyperbolas, all with uncertain radii. We propose a fusion framework for both snapshot estimation and filtering, and evaluate with both simulated and experimental field test data. The results indicate that the position accuracy is better than 40 meters 95% of the time. A third study in the thesis analyzes the statistical distribution of timing measurement errors in lte systems. Three different machine learning methods are applied to the experimental data to fit Gaussian mixture distributions to the observed measurement errors. Since current positioning algorithms are mostly based on Gaussian distribution models, knowledge of a good model for the measurement errors can be used to improve the accuracy and robustness of the algorithms. The obtained results indicate that a single Gaussian distribution is not adequate to model the real toa measurement errors. One possible future study is to further develop standard algorithms with these models.
Timing-Based Localization using Multipath Information
Author: Andreas Bergström
language: en
Publisher: Linköping University Electronic Press
Release Date: 2020-01-09
The measurements of radio signals are commonly used for localization purposes where the goal is to determine the spatial position of one or multiple objects. In realistic scenarios, any transmitted radio signal will be affected by the environment through reflections, diffraction at edges and corners etc. This causes a phenomenon known as multipath propagation, by which multiple instances of the transmitted signal having traversed different paths are heard by the receiver. These are known as Multi-Path Components (MPCs). The direct path (DP) between transmitter and receiver may also be occluded, causing what is referred to as non-Line-of-Sight (non-LOS) conditions. As a consequence of these effects, the estimated position of the object(s) may often be erroneous. This thesis focuses on how to achieve better localization accuracy by accounting for the above-mentioned multipath propagation and non-LOS effects. It is proposed how to mitigate these in the context of positioning based on estimation of the DP between transmitter and receiver. It is also proposed how to constructively utilize the additional information about the environment which they implicitly provide. This is all done in a framework wherein a given signal model and a map of the surroundings are used to build a mathematical model of the radio environment, from which the resulting MPCs are estimated. First, methods to mitigate the adverse effects of multipath propagation and non-LOS conditions for positioning based on estimation of the DP between transmitter and receiver are presented. This is initially done by using robust statistical measurement error models based on aggregated error statistics, where significant improvements are obtained without the need to provide detailed received signal information. The gains are seen to be even larger with up-to-date real-time information based on the estimated MPCs. Second, the association of the estimated MPCs with the signal paths predicted by the environmental model is addressed. This leads to a combinatorial problem which is approached with tools from multi-target tracking theory. A rich radio environment in terms of many MPCs gives better localization accuracy but causes the problem size to grow large—something which can be remedied by excluding less probable paths. Simulations indicate that in such environments, the single best association hypothesis may be a reasonable approximation which avoids the calculation of a vast number of possible hypotheses. Accounting for erroneous measurements is crucial but may have drawbacks if no such are occurring. Finally, theoretical localization performance bounds when utilizing all or a subset of the available MPCs are derived. A rich radio environment allows for good positioning accuracy using only a few transmitters/receivers, assuming that these are used in the localization process. In contrast, in a less rich environment where basically only the DP/LOS components are measurable, more transmitters/receivers and/or the combination of downlink and uplink measurements are required to achieve the same accuracy. The receiver’s capability of distinguishing between multiple MPCs arriving approximately at the same time also affects the localization accuracy.
On Complexity Certification of Active-Set QP Methods with Applications to Linear MPC
Author: Daniel Arnström
language: en
Publisher: Linköping University Electronic Press
Release Date: 2021-03-03
In model predictive control (MPC) an optimization problem has to be solved at each time step, which in real-time applications makes it important to solve these efficiently and to have good upper bounds on worst-case solution time. Often for linear MPC problems, the optimization problem in question is a quadratic program (QP) that depends on parameters such as system states and reference signals. A popular class of methods for solving such QPs is active-set methods, where a sequence of linear systems of equations is solved. The primary contribution of this thesis is a method which determines which sequence of subproblems a popular class of such active-set algorithms need to solve, for every possible QP instance that might arise from a given linear MPC problem (i.e, for every possible state and reference signal). By knowing these sequences, worst-case bounds on how many iterations, floating-point operations and, ultimately, the maximum solution time, these active-set algorithms require to compute a solution can be determined, which is of importance when, e.g, linear MPC is used in safety-critical applications. After establishing this complexity certification method, its applicability is extended by showing how it can be used indirectly to certify the complexity of another, efficient, type of active-set QP algorithm which reformulates the QP as a nonnegative least-squares method. Finally, the proposed complexity certification method is extended further to situations when enhancements to the active-set algorithms are used, namely, when they are terminated early (to save computations) and when outer proximal-point iterations are performed (to improve numerical stability).