33 research outputs found

    The Complete Analytical Solution of the TDOA Localization Method

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    This article is focused on the analytical solution of a TDOA (Time Difference of Arrival) localization method, including analysis of accuracy and unambiguity of a target position estimation in 2D space. The method is processed under two conditions - sufficiently determined localization system and an overdetermined localization system. It is assumed that the TDOA localization system operates in a LOS (Line of Sight) situation and several time-synchronized sensors are placed arbitrarily across the area. The main contribution of the article is the complete description of the TDOA localization method in analytical form only. It means, this paper shows a geometric representation and an analytical solution of the TDOA localization technique model. In addition, analyses of unambiguity and solvability of the method algorithm are presented, together with accuracy analysis of this TDOA technique in analytical form. Finally, the description of this TDOA method is extended to an overdetermined TDOA system. This makes it possible to determine and subsequently optimize its computational complexity, for example increase its computational speed. It seems that such a description of the TDOA localization technique creates a simple and effective tool for technological implementation of this method into military localization systems

    Efficient closed-form estimators in multistatic target localization and motion analysis

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    Object localization is fast becoming an important research topic because of its wide applications. Often of the time, object localization is accomplished in two steps. The first step exploits the characteristics of the received signals and extracts certain localization information i.e. measurements. Some typical measurements include timeof-arrival (TOA), time-difference-of-arrival (TDOA), received signal strength (RSS) and angle-of-arrival (AOA). Together with the known receiver position information, the object location is then estimated in the second step from the obtained measurements. The localization of an object using a number of sensors is often challenged due to the highly nonlinear relationship between the measurements and the object location. This thesis focuses on the second step and considers designing novel and efficient localization algorithms to solve such a problem. This thesis first derives a new algebraic positioning solution using a minimum number of measurements, and from which to develop an object location estimator. Two measurements are sufficient in 2-D and three in 3-D to yield a solution if they are consistent. The derived minimum measurement solution is exact and reduces the computation to the roots of a quadratic equation. The solution derivation also leads to simple criteria to ascertain if the line of positions from two measurements intersects. By partitioning the overdetermined set of measurements first to obtain the individual minimum measurement solutions, we propose a best linear unbiased estimator to form the final location estimate. The analysis supports the proposed estimator in reaching the Cramer-Rao Lower Bound (CRLB) accuracy under Gaussian noise. A measurement partitioning scheme is developed to improve performance when the noise level becomes large. We mainly use elliptic time delay measurements for presentation, and the derived results apply to the hyperbolic time difference measurements as well. Both the 2-D and 3-D scenarios are considered. A multistatic system uses a transmitter to illuminate the object of interest and collects the reflected signal by several receivers to determine its location. In some scenarios such as passive coherent localization or for gaining flexibility, the position of the transmitter is not known. In this thesis, we investigate the use of the indirect path measurements reflected off the object alone, or together with the direct path measurements from the transmitter to receiver for locating the object in the absence of the transmitter position. We show that joint estimation of the object and transmitter positions from both the indirect and direct measurements can yield better object location estimate than using the indirect measurements only by eliminating the dependency of the transmitter position. An algebraic closed-form solution is developed for the nonlinear problem of joint estimation and is shown analytically to achieve the CRLB performance under Gaussian noise over the small error region. To complete the study and gain insight, the optimum receiver placement in the absence of transmitter position is derived, by minimizing the estimation confidence region or the estimation variance for the object location. The performance lost due to unknown transmitter position under the optimum geometries is quantified. Simulations confirm well with the theoretical developments. In practice, a more realistic localization scenario with the unknown transmitter is that the transmitter works non-cooperatively. In this situation, no timestamp is available in the transmitted signal so that the signal sent time is often not known. This thesis next considers the extension of the localization scenario to such a case. More generally, the motion potential of the unknown object and transmitter is considered in the analysis. When the transmitted signal has a well-defined pattern such as some standard synchronization or pilot sequence, it would still be able to estimate the indirect and direct time delays and Doppler frequency shifts but with unknown constant time delay and frequency offset added. In this thesis, we would like to estimate the object and transmitter positions and velocities, and the time and frequency offsets jointly. Both dynamic and partial dynamic localization scenarios based on the motion status of the object and the transmitter are considered in this thesis. By investigating the CRLB of the object location estimate, the improvement in position and velocity estimate accuracy through joint estimation comparing with the differencing approach using TDOA/FDOA measurements is evaluated. The degradation due to time and frequency offsets is also analyzed. Algebraic closed-form solutions to solve the highly nonlinear joint estimation problems are then proposed in this thesis, followed by the analysis showing that the CRLB performance can be achieved under Gaussian noise over the small error region. When the transmitted signal is not time-stamped and does not have a well-defined pattern such as some standard synchronization or pilot sequence, it is often impossible to obtain the indirect and direct measurements separately. Instead, a self-calculated TDOA between the indirect- and direct-path TOAs shall be considered which does not require any synchronization between the transmitter and a receiver, or among the receivers. A refinement method is developed to locate the object in the presence of the unknown transmitter position, where a hypothesized solution is needed for initialization. Analysis shows that the refinement method is able to achieve the CRLB performance under Gaussian noise. Three realizations of the hypothesized solution applying multistage processing to simplify the nonlinear estimation problem are derived. Simulations validate the effectiveness in initializing the refinement estimator

    Studies on Sensor Aided Positioning and Context Awareness

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    This thesis studies Global Navigation Satellite Systems (GNSS) in combination with sensor systems that can be used for positioning and obtaining richer context information. When a GNSS is integrated with sensors, such as accelerometers, gyroscopes and barometric altimeters, valuable information can be produced for several applications; for example availability or/and performance of the navigation system can be increased. In addition to position technologies, GNSS devices are integrated more often with different types of technologies to fulfil several needs, e.g., different types of context recognition. The most common integrated devices are accelerometer, gyroscope, and magnetometer but also other sensors could be used.More specifically, this thesis presents sensor aided positioning with two satellite signals with altitude assistance. The method uses both pseudorange and Doppler measurements. The system is required to be stationary during the process and a source of altitude information, e.g., a MEMS barometer, is needed in addition to a basic GNSS receiver. Authentic pseudorange and Doppler measurements with simulated altitude were used used to test the algorithm. Results showed that normally the accuracy of couple of kilometers is acquired. Thesis also studies on what kind of errors barometric altimeter might encounter especially in personal positioning. The results show that barometers in differential mode provide highly accurate altitude solution (within tens of centimeters), but local disturbances in pressure need to be acknowledged in the application design. For example, heating, ventilating, and air conditioning in a car can have effect of few meters. Thus this could cause problems if the barometer is used as a altimeter for under meter-level positioning or navigation.We also explore methods for sensor aided GNSS systems for context recognition. First, the activity and environment recognition from mobile phone sensor and radio receiver data is investigated. The aim is in activity (e.g., walking, running, or driving a vehicle) and environment (e.g., street, home, or restaurant) detection. The thesis introduces an algorithm for user specific adaptation of the context model parameters using the feedback from the user, which can provide a confidence measure about the correctness of a classification. A real-life data collection campaign validate the proposed method. In addition, the thesis presents a concept for automated crash detection to motorcycles. In this concept, three different inertial measurement units are attached to the motorist’s helmet, torso of the motorist, and to the rear of the motor cycle. A maximum a posteriori classifier is trained to classify the crash and normal driving. Crash dummy tests were done by throwing the dummy from different altitudes to simulate the effect of crash to the motorist and real data is collected by driving the motorcycle. Preliminary results proved the potential of the proposed method could be applicable in real situations. In all the proposed systems in this thesis, knowledge of the context can help the positioning system, but also positioning system can help in determining the context

    Accommodation of NLOS for Ultra-Wideband TDOA Localization in Single- and Multi-Robot Systems

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    Ultra-wideband (UWB) localization is one of the most promising indoor localization methods. Yet, non-line-ofsight (NLOS) positioning scenarios remain a challenge and can potentially cause significant localization errors. In this work, we leverage the utility of a group of mobile robots to test and validate our approach systematically in a real world setup. We use a particle filter based localization algorithm, which is wellsuited for accommodating arbitrary observation models, with the ultimate purpose of integrating various sensory information within a single framework. In particular, we propose a novel, probabilistic UWB TDOA error model which explicitly takes into account NLOS, and introduce it into our localization framework in combination with a standard motion model based on deadreckoning information. We subsequently extend our single-robot localization framework to a multi-robot, collaborative system by enabling the sharing of relative, inter-robot observations. Our experimental results show how the novel TDOA error model is able to improve localization performance when knowledge of the LOS/NLOS path condition is available. These results are complemented by additional experiments which show how a collaborative team of robots is able to significantly improve localization performance when poor knowledge of LOS/NLOS path condition is available

    RF signal sensing and source localisation systems using Software Defined Radios

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    Radio frequency (RF) source localisation is a critical technology in numerous location-based military and civilian applications. In this thesis, the problem of RF source localisation has been studied from the perspective of the system implementation for real-world applications. Commercial off-the-shelf Software Defined Radio (SDR) devices are used to demonstrate the practical RF source localisation systems. Compared to the conventional localisation systems, which rely on dedicated hardware, the SDR-based system is developed using general-purpose hardware and software-defined components, offering great flexibility and cost efficiency in system design and implementation. In this thesis, the theoretical results of source localisation are evaluated and put into practice. To be specific, the practical localisation systems using different measurement techniques, including received-signal-strength-indication (RSSI) measurements, time-difference-of-arrival (TDOA) measurements and joint TDOA and frequency-difference-of-arrival (FDOA) measurements, are demonstrated to localise the stationary RF signal sources using the SDRs. The RSSI-based localisation system is demonstrated in small indoor and outdoor areas with a range of several metres using the SDR-based transceivers. Furthermore, interests from the defence area motivated us to implement the time-based localisation systems. The TDOA-based source localisation system is implemented using multiple spatially distributed SDRs in a large outdoor area with the sensor-target range of several kilometres. Moreover, they are implemented in a fully passive way without prior knowledge of the signal emitter, so the solutions can be applied in the localisation of non-cooperative signal sources provided that emitters are distant. To further reduce the system cost, and more importantly, to deal with the situation when the deployment of multiple SDRs, due to geographical restrictions, is not feasible, a joint TDOA and FDOA-based localisation system is also demonstrated using only one stationary SDR and one mobile SDR. To improve the localisation accuracy, the methods that can reduce measurement error and obtain accurate location estimates are studied. Firstly, to obtain a better understanding of the measurement error, the error sources that affect the measurement accuracy are systematically analysed from three aspects: the hardware precision, the accuracy of signal processing methods, and the environmental impact. Furthermore, the approaches to reduce the measurement error are proposed and verified in the experiments. Secondly, during the process of the location estimation, the theoretical results on the pre-existing localisation algorithms which can achieve a good trade-off between the accuracy of location estimation and the computational cost are evaluated, including the weight least-squares (WLS)-based solution and the Extended Kalman Filter (EKF)-based solution. In order to use the pre-existing algorithms in the practical source localisation, the proper adjustments are implemented. Overall, the SDR-based platforms are able to achieve low-cost and universal localisation solutions in the real-world environment. The RSSI-based localisation system shows tens of centimetres of accuracy in a range of several metres, which provides a useful tool for the verification of the range-based localisation algorithms. The localisation accuracy of the TDOA-based localisation system and the joint TDOA and FDOA-based localisation system is several tens of metres in a range of several kilometres, which offers potential in the low-cost localisation solutions in the defence area

    Improved Localization Algorithms in Indoor Wireless Environment

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    Localization has been considered as an important precondition for the location-dependent applications such as mobile tracking and navigation.To obtain specific location information, we usually make use of Global Positioning System(GPS), which is the most common plat- form to acquire localization information in outdoor environments. When targets are in indoor environment, however, the GPS signal is usually blocked, so we also consider other assisted positioning techniques in order to obtain accurate position of targets. In this thesis, three different schemes in indoor environment are proposed to minimize localization error by placing refer- ence nodes in optimum locations, combining the localization information from accelerometer sensor in smartphone with Received Signal Strength (RSS) from reference nodes, and utilizing frequency diversity in Wireless Fidelity (WiFi) environment. Deployments of reference nodes are vital for locating nearby targets since they are used to estimate the distances from them to the targets. A reference nodes’ placement scheme based on minimizing the average mean square error of localization over a certain region is proposed in this thesis first and is applied in different localization regions which are circular, square and hexagonal for illustration of the flexibility of the proposed scheme. Equipped with accelerometer sensor, smartphone provides useful information which out- puts accelerations in three different directions. Combining acceleration information from smart- phones and signal strength information from reference nodes to prevent the accumulated error from accelerometer is studied in this thesis. The combined locating error is narrowed by as- signing different weights to localization information from accelerometer and reference nodes. In indoor environment, RSS technology based localization is the most common way to imply since it require less additional hardware compared to other localization technologies. However, RSS can be affected greatly by complex circumstance as well as carrier frequency. Utilization of diverse frequencies to improve localization performance is proposed in the end of this thesis along with some experiments applied on Software Defined Platform (SDR)

    New Approach of Indoor and Outdoor Localization Systems

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    Accurate determination of the mobile position constitutes the basis of many new applications. This book provides a detailed account of wireless systems for positioning, signal processing, radio localization techniques (Time Difference Of Arrival), performances evaluation, and localization applications. The first section is dedicated to Satellite systems for positioning like GPS, GNSS. The second section addresses the localization applications using the wireless sensor networks. Some techniques are introduced for localization systems, especially for indoor positioning, such as Ultra Wide Band (UWB), WIFI. The last section is dedicated to Coupled GPS and other sensors. Some results of simulations, implementation and tests are given to help readers grasp the presented techniques. This is an ideal book for students, PhD students, academics and engineers in the field of Communication, localization & Signal Processing, especially in indoor and outdoor localization domains

    Non-acyclicity of coset lattices and generation of finite groups

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    Efficient GPS Position Determination Algorithms

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    This research is aimed at improving the state of the art of GPS algorithms, namely, the development of a closed-form positioning algorithm for a standalone user and the development of a novel differential GPS algorithm for a network of users. The stand-alone user GPS algorithm is a direct, closed-form, and efficient new position determination algorithm that exploits the closed-form solution of the GPS trilateration equations and works in the presence of pseudorange measurement noise for an arbitrary number of satellites in view. A two-step GPS position determination algorithm is derived which entails the solution of a linear regression and updates the solution based on one nonlinear measurement equation. In this algorithm, only two or three iterations are required as opposed to five iterations that are normally required in the standard Iterative Least Squares (ILS) algorithm currently used. The mathematically derived stochastic model-based solution algorithm for the GPS pseudorange equations is also assessed and compared to the conventional ILS algorithm. Good estimation performance is achieved, even under high Geometric Dilution of Precision (GDOP) conditions. The novel differential GPS algorithm for a network of users that has been developed in this research uses a Kinematic Differential Global Positioning System (KDGPS) approach. A network of mobile receivers is considered, one of which will be designated the \u27reference station\u27 which will have known position and velocity information at the beginning of the time interval being examined. The measurement situation on hand is properly modeled, and a centralized estimation algorithm processing several epochs of data is developed. The effect of uncertainty in the reference receiver\u27s position and the level of the receiver noise are investigated. Monte Carlo simulations are performed to examine the ability of the algorithm to correctly estimate the non-reference mobile users\u27 position and velocity
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