Ziv‐Zakai Bound for Direct Position Estimation

As maritime traffic strongly relies on Global Navigation Satellite Systems (GNSS) such as GPS or Galileo, there are efforts to mitigate the risks that come with this reliance. One such effort is the development of VDES R-Mode, which aims to provide a terrestrial contingency system to GNSS that is based on the VHF Data Exchange System (VDES).Terrestrial VDES provides a bandwidth of 100 kHz. To make best use of the available bandwidth, VDES R-Mode can use a signal that is optimized for a high effective bandwidth. This signal however, has a very regular structure that leads to ambiguities that degrade the ranging performance at lower SNRs. We found that this drawback can be mitigated by evaluating the signals of multiple base stations jointly in a direct position estimation approach.To assess the improvement, we applied the Ziv-Zakai Bound and performed simulations. We found that using the direct position estimation approach can significantly lower the SNR at which it is still possible to resolve the ambiguities caused by the regular signal structure.

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“…The Cramér-Rao Bound can also be applied to position estimation [8]. We consider the CRB for a fixed geometry.…”

Section: S(f ) Is the Frequency Domain Representation Of S(t)mentioning

confidence: 99%

“…We consider the bound for the case of the mobile station being in a deterministic position x m . The Ziv-Zakai bound for this case is given as [8]:…”

Section: B Ziv-zakai Boundmentioning

confidence: 99%

Direct Position Estimation for VDES R-Mode

Wirsing

Dammann

Raulefs

2023

2023 IEEE/ION Position, Location and Navigation Symposium (PLANS)

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“…4) Ziv-Zakai Lower Bound Familiy Recently, based on the second order Taylor series approximation, an approximate Ziv-Zakai lower bound (ZZLB) for a deterministic parameter was derived for the TOA estimation problem [71]. An approximate ZZLB for deterministic parameters was also introduced [72]. Unfortunately, this approximation provides a lower bound on the estimation error only for unbiased estimators.…”

Section: ) Barankin Lower Bound Familymentioning

confidence: 99%

Fundamental Limitations and State-of-the-art Solutions for Target Node Localization in WSNs

Najarro¹,

Song²,

Kim³

2021

Preprint

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With the advances in new technological trends and the reduction in prices of sensor nodes, wireless sensor networks (WSNs) and their applications are proliferating in several areas of our society such as healthcare, industry, farming, and housing. Accordingly, in recent years attention on localization has increased significantly since it is one of the main facets in any WSN. In a nutshell, localization is the process in which the position of any sensor node is retrieved by exploiting measurements from and between sensor nodes. Several techniques of localization have been proposed in the literature with different localization accuracy, complexity, and hence different applicability. The localization accuracy is limited by fundamental limitations, theoretical and practical, that restrict the localization accuracy regardless of the technique employed in the localization process. In this paper, we pay special attention to such fundamental limitations from the theoretical and practical points of view and provide a comprehensive review of the state-of-the-art solutions that deal with such limitations. Additionally, discussion on the theoretical and practical limitations together with their recent solutions, remaining challenges, and perspectives are presented.

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“…Such a one‐step approach – referred to as Direct Position Estimation (DPE) for reasons discussed in Section 2 – pivots the GNSS‐based localization problem, providing ways to address the challenges of conventional two‐step receivers at the expense of added computation load. The potential of the DPE approach has begun to be explored with conceptual motivations (Axelrad, Bradley, et al, 2011; Brown, 2012; Closas & Gusi‐Amigó, 2017), analytical advantages (Closas, Fernández‐Prades, & Fernández‐Rubio, 2007a, 2009a; Gusi‐Amigó et al, 2018), and demonstrated benefits of DPE‐based receivers (Chu, 2018; Dampf et al., 2017; Ng & Gao, 2016b) being presented in the literature. This work aims to support the growth of the DPE body‐of‐knowledge through a survey of DPE processing techniques, the release of open‐source parallelized DPE‐based receiver software, and a discussion of considerations for practical DPE‐based receiver design.…”

Section: Introductionmentioning

confidence: 99%

Design of a parallelized direct position estimation‐based GNSS receiver

Peretic

Gao

2020

Navigation

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Theoretical results conclude that Direct Position Estimation (DPE)‐based Global Navigation Satellite System (GNSS) receivers can achieve more robust localization than their conventional two‐step counterparts. However, compared to conventional approaches, there is a much smaller body of work for DPE, and DPE receiver implementations are highly experimental. This work surveys DPE techniques from the literature and presents a software‐defined parallelized DPE‐based receiver prototype built on popular DPE techniques. The parallelized receiver software, along with a companion sequential implementation, is made available to the community as an open source. The GPU usage of the parallelized DPE‐based receiver is profiled and compared to the companion sequential implementation and another sequential implementation presented in the literature. Through the literature survey, discussion of the open‐source receiver software, and the performance evaluation of the receiver, resultant insights for design decisions are presented.

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Ziv‐Zakai Bound for Direct Position Estimation

Cited by 21 publications

References 21 publications

Direct Position Estimation for VDES R-Mode

Direct Position Estimation for VDES R-Mode

Fundamental Limitations and State-of-the-art Solutions for Target Node Localization in WSNs

Design of a parallelized direct position estimation‐based GNSS receiver

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