Artikel and Buchkapitel
|||A new localization algorithm based on neural networks , In Proceedings of the 3rd KuVS/GI Expert Talk on Localization, 2018. [bib] [pdf] [abstract]|
Indoor localization plays a major role in a wide range of applications. To determine the location of a tag, localization algorithm is required. In the past, machine learning algorithms were difficult to implement in consumer hardware, but with the advent of tensor processing units, even smartphones are capable to use artificial intelligence to solve complex problems. In this paper, we investigate a machine learning algorithm based on neural networks and compare the result to a linear least squares estimator. We design and evaluate different neural networks. Based on our observation, the neural network delivers poor performance compared to the linear least squares estimator.
|||UWB-based Single Reference Point Positioning System , In ITG-Fachbericht-Mobilkommunikation VDE VERLAG GmbH, 2017. [bib] [abstract]|
Indoor positioning enables new applications, for instance monitoring of goods in smart factories. For such applications, indoor positioning requires cost-effective solutions with high accuracy. State-of-the-art positioning systems are expensive due to high infrastructure and maintenance costs. In this paper we suggest an accurate UWB-based single reference point positioning system using multiple antennas. We compare lateration and hyperbolic lateration as positioning methods and present efficient algorithms for UWB-based single reference point positioning systems. We present theoretical limits based on the Cramer-Rao lower bound and derive an error estimation as well as evaluation results. Our measurements indicate that decimeter accuracy is possible.
|||Survey of challenges and towards a unified architecture for location systems , In Journal of Network and Computer Applications, volume 67, 2016. [bib] [pdf] [abstract]|
Abstract Localization is a key aspect of emergent applications in the medical, industrial and consumer field. In this article we survey state of the art, identify current challenges and issues for localization systems and suggest a unified layered architecture. The analysis reveals that challenges cannot be addressed in an isolated manner for example, energy consumption is tied to the choice of algorithm and employed hardware. To separate various challenges and investigate them independently, we propose the concept of position providers. Position providers in the lower layers allow abstraction of positioning methods, positioning algorithms and positioning hardware. Thereby, a position provider encapsulates methods, algorithms and hardware. Furthermore, we suggest a classification of position providers inspired by related work. We propose a unified architecture for location systems which uses positioning and integration layers as main building blocks.
|||Iterative approach for anchor configuration of positioning systems , In ICT Express, volume 2, 2016. [bib] [pdf] [abstract]|
With anchor positions and measurements of distances between an object and anchors, positioning algorithms calculate the position of an object, e.g. via lateration. Positioning systems require calibration and configuration prior to operation. In the past, approaches employed reference nodes with GPS or other reference location systems to determine anchor positions. In this article, we propose an approach to determine anchor positions without prior knowledge. We evaluate our approach with simulations and real data based on the Decawave DW1000 radio and show that the error is proportional to the mean error of the distance estimation.
|||Höhenbestimmung mittels Luftdrucksensoren und differentieller Messung für Indoor-Anwendungen , In ImpulsE, volume 17, 2013. [bib]|
|||Development of an Electro Impedance Tomography-based Platform for Measurement of burial Depth of Cables in Subsea Sediments , In Oceans 2019, 2019. [bib] [abstract]|
Cables buried in the seabed are objects of interests especially as companies have to verify that the buried depth of the cables is in the expected range, typically $1~m$. Although several measurement systems have been designed in the past, there is no solution available that provides an accuracy of $pm10~cm$ for this purpose. In our approach we suggest to model and measure the electrical field and electrical impedance to determine the depth of a sea cable. In the first step we develop an electrical static field model for analytic investigations. We validate the model by a simulation tool and provide results for critical environmental parameters that affect our measurement accuracy.
|||On the Effective Length of Channel Impulse Responses in UWB Single Anchor Localization , In International Conference on Localization and GNSS, 2019. [bib] [abstract]|
Recently, single anchor localization evolves as a new research topic that exploits multipath propagation for calculation of tag positions. With a combination of movement information and particle filters, they provide a precision that is similar to multi-anchor systems. However, a systematic approach to the design and implementation of such systems is not yet available. The combination of theory and mathematical modeling for channel impulse responses is still an open research question that we address in this paper. Therefore, we propose a new representation of a channel impulse response targeted for single anchor localization systems. Based on this representation, we model the relationship between tag positions and channel impulse responses and evaluate the statistic properties of channel impulse responses in this application. In this paper, we introduce a new metric for the assessment of anchor positions, the effective length of CIRs. By the shortest effective length of a set of CIRs, we identify the best anchor position, since it indicates the position where requirements for the measurement of the channel impulse response are lowest.
|||Minimizing Indoor Localization Errors for Non-Line-of-Sight Propagation , In International Conference on Localization and GNSS, 2018. [bib] [abstract]|
Indoor Localization becomes more important, as it provides additional context for many applications for example in the Internet of Things (IoT). Time-of-flight measurements, as a basis for distance estimation, are susceptible for non-line-of-sight (NLOS) propagation, resulting in large distance errors. Standard least squares solutions to estimate the targets location do not account for NLOS propagation which results in large scale errors. We investigate the difference between L1- and L2-minimization and present a new framework based on a modified RANSAC approach. Additionally, we investigate a Support Vector Machine (SVM) to detect NLOS measurements.We present simulation and measurement results and evaluate our approach. We show that our framework delivers better performance in presence of NLOS propagation compared to plain L1- or L2-minimization.
|||RF-Based Safety-Critical Hybrid Localization , In The Ninth International Conference on Indoor Positioning and Indoor Navigation (IPIN), 2018. [bib] [abstract]|
In safety-critical environments, e.g. paint or machine shops, precise knowledge of positions of persons is important. If an emergency is detected, e.g. a fire or an intruder in the safety-critical area of heavy machinery, emergency shutdown procedures are activated. This requires fine-grained localization with a tag-based localization system, where the person carries a tag. Without a person carrying a tag, precise localization and detection is difficult. In this paper, we propose a RF-based hybrid localization system for safety-critical localization that consists of two major components: a tag-based and device-free subsystem. The device-free subsystem provides coarse-grained localization and monitors a gate area, serving as an entrance towards the safety-critical area where fine-grained localization is required. We propose an architecture of the system, discuss our setup and evaluate typical use cases. Our preliminary evaluation demonstrates that our system detects the correct state of the hybrid localization system with an accuracy of 90%.
|||TriClock – Clock Synchronization compensating Drift, Offset and Propagation Delay , In IEEE International Conference on Communications, 2018. [bib] [abstract]|
In wireless sensor networks (WSN) precise clock synchronization is still a challenge e.g. for synchronized medium access control (MAC). State of the art solutions require many messages or neglect clock drifts or propagation delay. In multi-hop networks synchronization errors increase with the number of hops because numerous messages increase latency. The latency and clock drift reduces synchronization accuracy. Finally, propagation delay introduces additional synchronization offsets. We introduce a novel synchronization protocol that requires a single message to compensate both clock offset and clock drift and one additional message to account for propagation delay. With this minimal amount of messages, an efficient multi-hop synchronization is practicable. We implement our approach on a DWM1000 hardware and evaluate the protocol in single-hop and multi-hop configuration. In our preliminary experiments, we achieved a synchronization accuracy of 0.46 ns in a single-hop configuration within 3.6 ms and 6 ns in a multi-hop configuration for 5 hops within 11 ms which is appropriate for MAC and time-division multiple access (TDMA) implementations.
|||Sundew: Design and Evaluation of a Model-based Device-free Localization System , In The Ninth International Conference on Indoor Positioning and Indoor Navigation (IPIN), 2018. [bib] [abstract]|
The state-of-the-art in device-free localization systems based on RF-measurements is fingerprinting. Fingerprinting requires reference measurements called fingerprints that are recorded during a training phase. Especially in device-free localization systems, recording of reference measurements for fingerprinting is a tedious, costly, and error-prone task. In this paper, we propose Sundew, a model-based device-free localization system that does not need fingerprinting in the sense of reference measurements but is able to calculate signal strength values at any position and compare it to actual measurements after a simple calibration phase. Sundew — as any device-free localization system — requires a metric for comparison of feature vectors. In this paper, we investigate the influence of nine different distance metrics on the positioning accuracy. Simulations and measurements show that our suggested model-based device-free localization system works best with the L 1 distance metric. Sundew estimates 90% of positions in a 2.5m x 2.5m grid correctly, independent of the orientation of the person in the target area.
|||S-TDoA - Sequential Time Difference of Arrival - A Scalable and Synchronization Free Approach for Positioning , In IEEE Wireless Communications and Networking Conference, 2016. [bib] [abstract]|
In the past various solutions for localization evolved to productive usage for wireless applications. These solutions are robust, precise and energy efficient. However, scalability, complexity and flexibility are still open issues. Especially, supported number of objects or update rates for localization are still limiting factors for the usage of the systems. In this work we suggest an approach called S-TDoA which stands for sequential Time Difference of Arrival that supports unlimited number of objects and high update rates. The key concept is a sequential triggering of anchors that send periodic messages. Tags determine their position by listening to the anchor messages and measuring time intervals. Additionally, this approach enhances security because tags are not visible as they do not send messages. We implement and evaluate S-TDoA in a localization system based on UWB-RF- Chips. The preliminary results demonstrate the advantages of our implementation regarding scalability and update rates as well as privacy.
|||Impact of Altitude Difference for Local Positioning Systems and Compensation with Two-Stage Filters , In 2016 International Conference on Localization and GNSS, 2016. [bib] [abstract]|
In range-based positioning systems, an altitude difference between tag and reference plane causes errors in two- and three-dimensional positioning. We analyze how these errors reduce accuracy of Local Positioning Systems (LPS) and show how compensation of the altitude difference improves performance of positioning. In this paper, we consider the availability of additional altitude information and transform the three-dimensional positioning problem into a two-dimensional problem. We provide algorithms for time-based positioning systems with a two-stage estimator for Two-Way Ranging and Time Difference of Arrival and incorporate additional altitude information. We simulate our approach for altitude difference compensation and provide an evaluation based on a Ultra-Wideband (UWB) radio with ranging capability and a barometric sensor for additional altitude information. A comparison is then made between our approach and standard solutions such as the Extended Kalman filter and the Unscented Kalman filter. Finally, the successful decrease in the positioning error for two- and three-dimensional positioning system, using the system disclosed herein, is illustrated. Based on our analysis, we derive practical solutions to deal with altitude differences for positioning systems.
|||Introduction, Discussion and Evaluation of Recursive Bayesian Filters for Linear and Nonlinear Filtering Problems in Indoor Localization , In The Seventh International Conference on Indoor Positioning and Indoor Navigation, 2016. [bib] [abstract]|
Linear and nonlinear filtering for state estimation (e.g. position estimation or sensor fusion) for indoor positioning and navigation applications is a challenging task. Sensor fusion becomes more important with cost-effective sensors being readily available. However, state estimation with recursive Bayesian filters for sensor fusion and filtering are difficult to apply. We present an overview for the general Bayesian filter and derive the most commonly used recursive Bayesian filters, namely the Kalman, extended Kalman and the unscented Kalman filter along with the particle filter. The later Kalman filters are extension of the original Kalman filter, which are able to solve nonlinear filtering problems. The particle filter is also able to solve nonlinear filtering problems. We evaluate the recursive Bayesian filters for linear and nonlinear filtering problems for sensor fusion from relative dead reckoning positioning data and absolute positioning data from an UWB positioning system. We discuss and evaluate performance and computational complexity and provide recommendations for the use case of the recursive Bayesian filters.
|||QRPos: Indoor Positioning System for Self-Balancing Robots based on QR Codes , In The Seventh International Conference on Indoor Positioning and Indoor Navigation, 2016. [bib]|
|||Investigation of Anomaly-based Passive Localization with Received Signal Strength for IEEE 802.15.4 , In The Seventh International Conference on Indoor Positioning and Indoor Navigation, 2016. [bib] [abstract]|
Localization has important applications, for instance intrusion detection and elderly care. Such applications benefit from Device-free passive (DfP) localization systems, which employ received signal strength measurements (RSSM) to detect and track entities that neither participate actively in the localization process nor emit signals actively. RSSMs include received signal strength indicator (RSSI), energy detection (ED) and link quality indicator (LQI) measurements. This paper compares different packet-based RSSMs for DfP localization and presents detection results of a DfP anomaly-based detection system employed by IEEE 802.15.4 compliant devices. Furthermore, we investigate techniques for anomaly detection with continuous RSSI measurements.
|||Indoor Localization based on Bi-Phase Measurements for Wireless Sensor Networks , In 2015 IEEE Wireless Communications and Networking Conference (WCNC): - Track 3: Mobile and Wireless Networks (IEEE WCNC 2015 - Track 3- Mobile and Wireless Networks), 2015. [bib] [abstract]|
Indoor localization is important for medical and industrial application as well as for wireless emergency and security systems. For such applications an accuracy within a few meters is desired. Available radio based systems within that accuracy are neither cost effective nor easy to deploy. In this work, we suggest an approach called biphase measurement based on phase measurements with two frequencies to determine the location of a tag. We design and build a complete indoor positioning system based on bi-phase measurements with easy to deploy wireless sensor nodes. The wireless sensor nodes shape anchors and tags and communicate results to a location engine of the indoor positioning system. Our implementation comprises lowcost IEEE802.15.4 radio chips with built-in support for phase measurements unit for both, anchor and tags. We compute the position of the tag based on distance estimation retrieved with bi-phase measurements. We evaluate our indoor positioning system providing first measurement results for accuracy and precision and discuss trade-off between scalability, real-time and accuracy.
|||Wireless Medical Sensors - Context, Robustness and Safety , In 49th annual conference of the German Society for Biomedical Engineering (BMT 2015), 2015. [bib]|
|||Accurate Radio Distance Estimation by Phase Measurements with Multiple Frequencies , In The Fifth International Conference on Indoor Positioning and Indoor Navigation 2014 (IPIN 2014), 2014. [bib] [abstract]|
Indoor localization is beneficial for logistics, industrial applications and for several consumer applications. In the area of logistics, e.g. warehouses, localization accuracy within a few meters is desired. Available radio based systems within that accuracy are neither cost effective nor easy to deploy. Distance estimations are one possible method for localization. In this work, we propose phase measurements between two wireless sensor nodes for distance estimation. We introduce a mathematical model to estimate distances from phase measurements with multiple frequencies and provide a systematic analysis of possible sources of errors. Additionally, we derive requirements, e.g. resolution and speed for a phase measurement unit to reach certain accuracy. To proof our theoretical results, we present evaluation results based on our implementation. Our implementation comprises a low cost IEEE 802.15.4 hardware with a built-in phase measurement unit. We implement the developed algorithm for distance estimation in our wireless sensor network and use two wireless sensor nodes to perform a phase measurement. The contribution of the paper comprises a new model for phase measurements to estimate distances and a preliminary evaluation with our hardware.
|||Experimental Evaluation & Optimization of a UWB Localization System for Medical Applications , In 48th annual conference of the German Society for Biomedical Engineering (BMT 2014), 2014. [bib]|
|||Evaluation of Radio Based, Optical and Barometric Localization for Indoor Altitude Estimation in Medical Applications , In The Fifth International Conference on Indoor Positioning and Indoor Navigation, 2014. [bib] [abstract]|
The advances of electronics provide options for improved monitoring of patients in clinical environment.Medical applications like blood pressure monitoring require precise and wireless altitude measurement in indoor environment. An error of only a few centimeters may lead to mistreatment of patients.Furthermore, user requirements like small form factor, usability and robust operation are important in the medical field.Existing evaluations of indoor localization systems focus on accuracy analysis of x- and y-coordinates and not on the z-coordinate (altitude). In this paper, we define evaluation criteria for altitude estimation in medical applications. We compare an Ultra-Wide-Band indoor localization system, an optical Microsoft Kinect camera system and our own development of a wireless barometric sensor against these criteria. We present a comparative measurement setup, results and a final evaluation of the three systems in an indoor environment.
|||Precise Indoor Altitude Estimation based on differential barometric Sensing for wireless Medical Applications , In Body Sensor Networks Conference 2013 (BSN2013), 2013. [bib] [abstract]|
Some medical applications require precise information of position and orientation of a patient as changes affect pressure condition inside the body. In this paper we focus on altitude estimation, where altitude is a distance, in vertical direction, between a reference and a point of a human body. We suggest equipping wireless sensor nodes with high resolution pressuresensors to calculate the altitude with the barometric formula. We implement a body sensor network based on IEEE 802.15.4 and synchronization mechanism with a reference. Pressure variations due to environmental effects are compensated by cancellation with this differential measurement setup. We demonstrate the need for differential measurements and show with a series of measurements that environmental pressure variations have no significant effect on the proposed altitude estimation. Compared to existing systems, our solution is cost effective, easy to deploy and provides a flexible tradeoff between precision and location lag by adjusting a filter constant.
|||Evaluation of time-based ranging methods: Does the choice matter? , In 14th Workshop on Positioning, Navigation and Communication, 2017. [bib] [abstract]|
Positioning is useful in a number of applications, for instance smart home, smart factory and health care applications. Time-based ranging methods for positioning are the state-of-the-art but require precise timestamping. Sophisticated ranging methods compensate sources of errors, for instance clock drift caused by a crystal or an asymmetrical measuring principle, to provide precise timestamping. So far, no comprehensive study of different time-based ranging methods using the same hardware and the same evaluation setup was carried out. Consequently, we discuss, implement and evaluate five time-based ranging methods, including Two-Way Ranging, Double Two-Way Ranging, Asymmetrical Double-Sided Two-Way Ranging, Symmetrical Double-Sided Two-Way Ranging and Burst Mode Symmetric Double-Sided Two-Way Ranging. We evaluate accuracy, precision, robustness and run time for the ranging methods and answer the question if the choice of the time-based ranging method matters.
|||Weighted Online Calibration for Odometry of Mobile Robots , In IEEE ICC Workshop on Advances in Network Localization and Navigation (ANLN), 2017. [bib]|
|||Anomaly-based Device-free Localization with Particle Filtering , In Workshop on Dependable Wireless Communications and Localization for the IoT, 2017. [bib] [abstract]|
In the Internet of Things (IoT), devices, e.g. sensors or actuators, transmit packets to transfer data. For the IoT localization information is crucial, as it provides additional context for the data. We envision that devices in the IoT know their position and on receipt of a packet, the received signal strength is measured. This measurement is used to build a device-free localization (DFL) system to improve the dependability of the IoT system. DFL systems are able to detect and track persons within a target area that neither wear a device nor participate actively in the process of localization. This work presents an anomaly-based DFL system that measures if a person affects the radio frequency (RF) propagation and determines the position with a particle filter. In our 65m 2 indoor testbed, we employ eight IEEE 802.15.4 compliant wireless transceivers and estimate the position of a person with a median localization error of 1.4m.
|||Modeling Received Signal Strength and Multipath Propagation Effects of Moving Persons , In 14th Workshop on Positioning, Navigation and Communication, 2017. [bib] [abstract]|
Device-free localization (DFL) systems detect and track persons without devices that participate in the localization process. A person moving within a target area affects the electromagnetic field that is measured by received signal strength (RSS) values. Consequently for DFL systems modeling of RSS is important and still an open issue. In this paper, we develop a simple model for prediction of RSS values in a setup with transmitter and receiver devices, a person and multipath propagation. We design and implement the model as a superposition of both, knife-edge diffraction to account for the change made by the person, and, propagation effects such as multipath propagation that result in reflection and path loss including the antenna characteristics. We evaluate our model in comparison with real measurements in various setups with and without multipath propagation. We achieve an accuracy that is close to our hardware limitations, which is the resolution of the measured RSS values of the receiver.
|||Comparison of wired and wireless synchronization with clock drift compensation suited for U-TDoA localization , In 13th Workshop on Positioning, Navigation and Communication, 2016. [bib] [abstract]|
Indoor localization with Uplink Time Difference of Arrival (U-TDoA) provides good scalability, high updates rates and high accuracy. However, clock errors lead to localization errors and synchronization is important. In this paper, we design and implement wired and wireless synchronization and provide a comparison between them. We design and implement a wireless synchronization with clock drift compensation. For wired and wireless synchronization, we discuss reasons for clock deviation that lead to localization errors. We evaluate both approaches in a U-TDoA measurement setup. Finally, we provide recommendations for wired and wireless synchronization.
|||Mobile Robot Seamless Localization with Localization Optimized QR Codes , In 12th Workshop on Positioning, Navigation and Communication, 2015. [bib] [abstract]|
Indoor navigation is a prerequisite for new emerging applications for autonomous mobile robots. Additionally to the location of a robot, the orientation is important for these applications. Furthermore, a solution to this localization problem should be inexpensive and easy extensible for new areas of a building. We propose inexpensive optical landmarks based on localization optimized Quick Response (QR) code for localization of the landmark within an image to reduce computational cost. We further specify the error correction level, border, and size of the QR code for optimal localization. The proposed QR code combines GPS coordinates and local coordinates which allows seamless integration of our approach. We perform image processing to estimate the distance and orientation of a mobile robot with respect to the localization optimized QR code. To evaluate our approach we implemented the approach in an Android application and measured the performance in experiments. Additionally, we suggest a method to retrieve more accurate GPS information based on the measured orientation and distances. Our implementation achieves update rates of up to 3 Hz and an accuracy of 1 cm
|||A Practical Toolbox for Getting Started with mmWave FMCW Radar Sensors , Technical report, Technische Universität Braunschweig, 2019. [bib] [pdf] [abstract]|
In this paper, we sum up our experience gathered working with mmWave FMCW radar sensors for localization problems. We give a glimpse of the foundations of radar that is necessary to understand the benefit and advantages of this technology. Moreover, we introduce our open-source software toolbox pymmw based on Python for Texas Instruments IWR1443 ES2.0 EVM sensors to provide students and researchers easy access to those radar sensors. In doing so, one can jump right into sensing with mmWave FMCW radar from a practical point of view and start doing experiments and developing own applications. Finally, pymmw is used for data acquisition of a scene illuminated by three virtual radars in three different states of occupancy showing the potential of mmWave FMCW radar for indoor and distance-based localization applications.
|||Impact of the antenna orientation for distance estimation , Technical report, Technische Universität Braunschweig, 2018. [bib] [pdf] [abstract]|
Indoor localization is important for a wide range of use cases including industrial, medical and scientific applications. The location accuracy is affected by the localization algorithm and the quality of the measurements as input for the algorithm. Many indoor localization systems employ ultra-wideband distance measurements, as they offer high accuracy and are cost effective. One of the methods for distance measurement is twoway ranging. This paper investigates the impact of the antenna orientation on the distance measurement based on symmetrical double-sided two-way ranging. We show that up to 0.25m of the measurement error is attributed to the orientation of the antennas. We provide explanations and suggest solutions to reduce the effect.
|||Lessons learned: Indoor Ultra-Wideband localization systems for an industrial IoT application , Technical report, Technische Universität Braunschweig, 2018. [bib] [pdf] [abstract]|
Since ultra-wideband (UWB) transceivers are available for wireless sensor networks, the usage in research and industry increased. Research efforts resulted in methods, measurement results, and solutions under laboratory conditions for a variety of indoor localization problems provided to the community. In this paper, we present an indoor positioning system (IPS) that is installed in a $mathbf1500 m^2$ real world production facility. In this real-world application, we faced some challenges that research has not addressed yet. For instance, challenges are receiving UWB signals from other floors in a multistory building through windows and multipath effects at walls like reflexions. We present solutions to increase the availability of such large-scale IPS, give a performance evaluation and recommendation for a modified NMEA sentence named iNMEA for IPS receivers.
|||Comparison of Antenna Types and Frequency Bands for Radio-based Device-free Localization , Technical report, Technische Universität Braunschweig, 2018. [bib] [pdf] [abstract]|
Radio-based device-free localization systems measure effects on radio signals e.g. signal strength variations to locate objects or persons in a target area. Such systems detect and track persons that do not participate in the localization process. Models for calculating the radio signal propagation are key for the performance in device-free localization systems. Received signal strength (RSS) is simple to measure. However, it is susceptible to changes in the environment and multipath propagation. In this paper, we compare PCB antennas to a circularly polarized cloverleaf antenna and measurements in the 2.4 GHz with measurements to the 868MHz ISM band. We investigate especially if a circularly polarized cloverleaf antenna is resilient against multipath propagation. Our preliminary results demonstrate that our model is suitable to the 868MHz band and the use of the 868MHz band increases the area where a person affects the RSS. The use of a circularly polarized cloverleaf antenna does not help to avoid multipath propagation.
|||Evaluation of Bluetooth Positioning for Medical Device Tracking , GRIN (T. M. Buzug et. al., ed.), 2017. [bib]|
|||Investigation of Anomaly-based Passive Localization with IEEE 802.15.4 , Technical report, RWTH Aachen University, 2016. [bib] [pdf]|
|||Position Calculation with Least Squares based on Distance Measurements , Technical report, Fachhochschule Lübeck, 2015. [bib] [pdf] [abstract]|
Position estimation based on distances is a well understood problem. This document describes a simple way to linearize the position equation. Based on the linearization the problem is solved step by step using least squares. This paper includes an example implementation in Matlab.
|||Comparison and Performance Evaluation of Indoor Localization Algorithms based on an Error Model for an Optical System , GRIN (T. M. Buzug et. al., ed.), 2015. [bib]|
|||Localization of Heart Reference Point of a Lying Patient with Microsoft Kinect Sensor , GRIN (T. M. Buzug et. al., ed.), 2014. [bib]|
Powered by bibtexbrowser