Next Article in Journal
Evaluation of Food Fineness by the Bionic Tongue Distributed Mechanical Testing Device
Next Article in Special Issue
Design, Implementation and Validation of a GNSS Measurement Exclusion and Weighting Function with a Dual Polarized Antenna
Previous Article in Journal
Suppression Technique of HeLa Cell Proliferation Using Ultrasonic Power Amplifiers Integrated with a Series-Diode Linearizer
Previous Article in Special Issue
Enhancement of Localization Systems in NLOS Urban Scenario with Multipath Ray Tracing Fingerprints and Machine Learning
Article Menu
Issue 12 (December) cover image

Export Article

Open AccessArticle
Sensors 2018, 18(12), 4249;

Accuracy Bounds for Array-Based Positioning in Dense Multipath Channels

Signal Processing and Speech Communication Laboratory, Graz University of Technology, 8010 Graz, Austria
Christian Doppler Laboratory for Location-aware Electronic Systems, Graz University of Technology, 8010 Graz, Austria
NXP Semiconductors, 8101 Gratkorn, Austria
Author to whom correspondence should be addressed.
This paper is an extended version of our paper published in the 8th International Conference on Localization and GNSS (ICL-GNSS) in 2018.
Received: 30 September 2018 / Revised: 23 November 2018 / Accepted: 26 November 2018 / Published: 3 December 2018
Full-Text   |   PDF [1068 KB, uploaded 7 December 2018]   |  


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 . View Full-Text
Keywords: indoor positioning; wireless positioning; CRLB; AoA; ToA; antenna-array signal processing indoor positioning; wireless positioning; CRLB; AoA; ToA; antenna-array signal processing

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Wilding, T.; Grebien, S.; Mühlmann, U.; Witrisal, K. Accuracy Bounds for Array-Based Positioning in Dense Multipath Channels. Sensors 2018, 18, 4249.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Sensors EISSN 1424-8220 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top