Dilution of precision in angle-of-arrival positioning systems

2006 ◽  
Vol 42 (5) ◽  
pp. 291 ◽  
Author(s):  
A.G. Dempster
Keyword(s):  
Angle Of Arrival ◽  
Positioning Systems ◽  
Dilution Of Precision

scholarly journals Accuracy Bounds for Array-Based Positioning in Dense Multipath Channels

Sensors ◽  
2018 ◽  
Vol 18 (12) ◽  
pp. 4249 ◽  
Author(s):  
Thomas Wilding ◽  
Stefan Grebien ◽  
Ulrich Mühlmann ◽  
Klaus Witrisal
Keyword(s):  
Error Bound ◽  
Antenna Arrays ◽  
Estimation Error ◽  
Position Estimation ◽  
Position Error ◽  
Time Of Arrival ◽  
Angle Of Arrival ◽  
Multipath Interference ◽  
Positioning Systems ◽  
Performance Loss

The accuracy of radio-based positioning systems will be limited by multipath interference in realistic application scenarios. This paper derives closed-form expressions for the Cramér–Rao lower bound (CRLB) on the achievable time-of-arrival (ToA) and angle-of-arrival (AoA) estimation-error variances, considering the presence of multipath radio channels, and extends these results to position estimation. The derivations are based on channel models comprising deterministic, specular multipath components as well as stochastic, diffuse/dense multipath. The derived CRLBs thus allow an evaluation of the influence of channel parameters, the geometric configuration of the environment, and system parameters such as signal bandwidth and array geometry. Our results quantify how the ToA and AoA accuracies decrease when the signal bandwidth is reduced, because more multipath will then interfere with the useful LoS component. Antenna arrays can (partly) compensate this performance loss, exploiting diversity among the multipath interference. For example, the AoA accuracy with a 16-element linear array at 1 MHz bandwidth is similar to a two-element array at 1 GHz , in the magnitude order of one degree. The ToA accuracy, on the other hand, still scales by a factor of 100 from the cm-regime to the m-regime because of the dominating influence of the signal bandwidth. The position error bound shows the relationship between the range and angle information under realistic indoor channel conditions and their different scaling behaviors as a function of the anchor–agent placement. Specular multipath components have a maximum detrimental influence near the walls. It is shown for an L-shaped room that a fairly even distribution of the position error bound can be achieved throughout the environment, using two anchors equipped with 2 × 2 -array antennas. The accuracy limit due to multipath increases from the 1–10-cm-range at 1 GHz bandwidth to the 0.5–1-m-range at 100 MHz .

scholarly journals Bluetooth 5.1: An Analysis of Direction Finding Capability for High-Precision Location Services

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3589
Author(s):  
Giovanni Pau ◽  
Fabio Arena ◽  
Yonas Engida Gebremariam ◽  
Ilsun You
Keyword(s):  
Indoor Localization ◽  
Direction Finding ◽  
Low Energy ◽  
Angle Of Arrival ◽  
Location Services ◽  
Positioning Systems ◽  
Future Developments ◽  
Direction Estimation ◽  
People First ◽  
Definition Of

This paper presents an in-depth overview of the Bluetooth 5.1 Direction Finding standard’s potentials, thanks to enhancing the Bluetooth Low Energy (BLE) firmware. This improvement allows producers to create location applications based on the Angle of Departure (AoD) and the Angle of Arrival (AoA). Accordingly, it is conceivable to design proper Indoor Positioning Systems (IPS), for instance, for the traceability of resources, assets, and people. First of all, Radio Frequency (RF) radiogoniometry techniques, helpful in calculating AoA and AoD angles, are introduced in this paper. Subsequently, the topic relating to signal direction estimation is deepened. The Bluetooth Core Specification updates concerning version 5.1, both at the packet architecture and prototyping levels, are also reported. Some suitable platforms and development kits for running the new features are then presented, and some basic applications are illustrated. This paper’s final part allows ascertaining the improvement made by this new definition of BLE and possible future developments, especially concerning applications related to devices, assets, or people’s indoor localization. Some preliminary results gathered in a real evaluation scenario are also presented.

scholarly journals Analytical evaluation of geometric dilution of precision for three-dimensional angle-of-arrival target localization in wireless sensor networks

2020 ◽  
Vol 16 (5) ◽  
pp. 155014772092047
Author(s):  
Jiao Zhang ◽  
Jianfeng Lu
Keyword(s):  
Wireless Sensor Networks ◽  
Sensor Networks ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Target Localization ◽  
Wireless Sensor ◽  
Angle Of Arrival ◽  
Dilution Of Precision ◽  
Geometric Dilution Of Precision ◽  
The One

This article focuses on the evaluation of geometric dilution of precision for three-dimensional angle-of-arrival target localization in wireless sensor networks. We calculate a general analytical expression for the geometric dilution of precision for three-dimensional angle-of-arrival target localization. Unlike the existing works in the literature, in this article, no assumptions are made regarding the observation ranges, noise variances, or the number of sensors in the derivation of the geometric dilution of precision. Necessary and sufficient conditions regarding the existence of geometric dilution of precision are also derived, which can be readily used to evaluate the observability of three-dimensional angle-of-arrival target localization in wireless sensor networks. Moreover, a concise procedure is also presented to calculate the geometric dilution of precision when it exists. Finally, several examples are used to illustrate our results, and it is shown that the performance of the proposed regular deployment configurations of angle-of-arrival sensors is better than the one with random deployment patterns.

scholarly journals Calculation of Weighted Geometric Dilution of Precision

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Chien-Sheng Chen ◽  
Yi-Jen Chiu ◽  
Chin-Tan Lee ◽  
Jium-Ming Lin
Keyword(s):  
Communication Systems ◽  
Approximation Error ◽  
Matrix Inversion ◽  
Location Estimation ◽  
Inversion Method ◽  
Error Statistics ◽  
Positioning Systems ◽  
Dilution Of Precision ◽  
Measurement Units ◽  
Geometric Dilution Of Precision

To achieve high accuracy in wireless positioning systems, both accurate measurements and good geometric relationship between the mobile device and the measurement units are required. Geometric dilution of precision (GDOP) is widely used as a criterion for selecting measurement units, since it represents the geometric effect on the relationship between measurement error and positioning determination error. In the calculation of GDOP value, the maximum volume method does not necessarily guarantee the selection of the optimal four measurement units with minimum GDOP. The conventional matrix inversion method for GDOP calculation demands a large amount of operation and causes high power consumption. To select the subset of the most appropriate location measurement units which give the minimum positioning error, we need to consider not only the GDOP effect but also the error statistics property. In this paper, we employ the weighted GDOP (WGDOP), instead of GDOP, to select measurement units so as to improve the accuracy of location. The handheld global positioning system (GPS) devices and mobile phones with GPS chips can merely provide limited calculation ability and power capacity. Therefore, it is very imperative to obtain WGDOP accurately and efficiently. This paper proposed two formations of WGDOP with less computation when four measurements are available for location purposes. The proposed formulae can reduce the computational complexity required for computing the matrix inversion. The simpler WGDOP formulae for both the 2D and the 3D location estimation, without inverting a matrix, can be applied not only to GPS but also to wireless sensor networks (WSN) and cellular communication systems. Furthermore, the proposed formulae are able to provide precise solution of WGDOP calculation without incurring any approximation error.

scholarly journals A Geometric Layout Method for Synchronous Pseudolite Positioning Systems Based on a New Weighted HDOP

2021 ◽  
Vol 10 (9) ◽  
pp. 601
Author(s):  
Xinyang Zhao ◽  
Qiangqiang Shuai ◽  
Guangchen Li ◽  
Fangzhou Lu ◽  
Bocheng Zhu
Keyword(s):  
Indoor Environment ◽  
Simulated Annealing Algorithm ◽  
Time Synchronization ◽  
Simple Calculation ◽  
Positioning Systems ◽  
Dilution Of Precision ◽  
The Monte Carlo Method ◽  
Connection System ◽  
Geometric Dilution Of Precision ◽  
Geometric Layout

The positioning accuracy of a ground-based system in an indoor environment is closely related to the geometric configuration of pseudolites. This paper presents a simple closed-form equation for computing the weighted horizontal dilution of precision (WHDOP) with four eigenvalues, which can reduce the amount of calculation. By comparing the result of WHDOP with traditional matrix inversion operation, the effectiveness of WHDOP of the proposed simple calculation method is analyzed. The proposed WHDOP has a linear relationship with the actual static positioning result error in an indoor environment proved by the Pearson analysis method. Twenty positioning points are randomly selected, and the positioning variance and WHDOP of each positioning point have been calculated. The correlation coefficient of WHDOP and the positioning variance is calculated to be 0.82. A pseudolite system layout method based on a simulated annealing algorithm is proposed by using WHDOP, instead of Geometric dilution of precision (GDOP). In this paper, the constraints of time synchronization are discussed. In wireless connection system, the distance between master station and slave station should be kept within a certain range. Specifically, for a given indoor scene, many positioning target points are randomly generated in this area by using the Monte Carlo method. The mean WHDOP value of all positioning points corresponding to the synchronous pseudolite layout is used as the objective function. The results of brute force search are compared with the method, which proves the accuracy of the new algorithm.

scholarly journals GEOMETRIC DILUTION OF PRECISION OF THE GNSS FOR MARS (GNSS FATIMA)

Aviation ◽  
2016 ◽  
Vol 20 (4) ◽  
pp. 183-190
Author(s):  
Jozef KOZAR ◽  
Stanislav DURCO ◽  
Frantisek ADAMCIK
Keyword(s):  
Satellite System ◽  
Navigation Satellite ◽  
Positioning Systems ◽  
Dilution Of Precision ◽  
Positioning Errors ◽  
Factors Influencing ◽  
Main Factors ◽  
Geometric Dilution Of Precision ◽  
Global Navigation Satellite ◽  
Critical Aspects

Positioning on Mars is one of the critical aspects of every planetary mission. Current complex planetary exploration systems (orbital and surface) rely on complex navigation and positioning systems, which make these systems complicated, expensive and their missions dangerous. The project of the global navigation satellite system for Mars (proposed system name – FATIMA) can make this and even future manned missions more safe, less expensive and the whole positioning in real time more reliable. The GNSS can be used by more systems or users simultaneously. In this research paper we focus on possible positioning errors when such a system is used. This research is focused on the GDOP – Geometric Dilution of Precision as one of the main factors influencing the GNSS.

scholarly journals Characterization of Multipath Effects in Indoor Positioning Systems by AoA and PoA Based on Optical Signals

Sensors ◽  
2019 ◽  
Vol 19 (4) ◽  
pp. 917 ◽  
Author(s):  
Álvaro De-La-Llana-Calvo ◽  
José-Luis Lázaro-Galilea ◽  
Alfredo Gardel-Vicente ◽  
David Rodríguez-Navarro ◽  
Ignacio Bravo-Muñoz ◽  
...  
Keyword(s):  
Phase Shift ◽  
Indoor Positioning ◽  
Optical Signal ◽  
Angle Of Arrival ◽  
Optical Signals ◽  
Positioning Systems ◽  
Positioning Errors ◽  
Multipath Effects ◽  
Position Sensitive

In this paper, we characterize and measure the effects of the errors introduced by the multipath when obtaining the position of an agent by means of Indoor Positioning Systems (IPS) based on optical signal. These effects are characterized in Local Positioning Systems (LPSs) based on two different techniques: the first one by determining the Angle of Arrival (AoA) of the infrared signal (IR) to the detector; and the second one by working with the measurement of the Phase shift of signal Arrival from the transmitter to a receiver (PoA). We present the obtained results and conclusions, which indicate that using Position Sensitive Devices (PSD) the multipath effects for AoA have little impact on the measurement, while for PoA the positioning errors are very significant, making the system useless in many cases.

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