Approximate iterative Least Squares algorithms for GPS positioning

He, Yuheng; Martin, Rainer; Bilgic, Attila

doi:10.1109/isspit.2010.5711784

Cited by 20 publications

(9 citation statements)

References 11 publications

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“…Therefore, the positioning matrix given by Equation 9easily becomes a near-singular matrix or an ill-conditioned matrix, which is difficult to solve. Thus, the Taylor series expansion method [29,30] or the least-squares method [31,32] is widely used in position estimation. Both of these methods require good initial values; otherwise, it is difficult for the solution to achieve convergence [33].…”

Section: Positioning Methods For a Single Shore Stationmentioning

confidence: 99%

The Single-Shore-Station-Based Position Estimation Method of an Automatic Identification System

Jiang

Zheng

2020

Sensors

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In order to overcome the vulnerability of the Global Navigation Satellite System (GNSS), the International Maritime Organization (IMO) initiated the ranging mode (R-Mode) of the automatic identification system (AIS) to provide resilient position data. As the existing AIS is a communication system, the number of shore stations as reference stations cannot satisfy positioning requirements. Especially in the area near a shore station, it is very common that a vessel can only receive signals from one shore station, where the traditional positioning method cannot be used. A novel position estimation method using multiple antennas on shipborne equipment is proposed here, which provides a vessel’s position even though the vessel can only receive signals from a single shore station. It is beneficial for solving positioning issues in proximity to the coast. Further, as the distances between different antennas to the shore station are not sufficiently independent, the positioning matrix can easily be near singularity or ill-conditioned; thus, an effective position solving method is derived. Furthermore, the proposed method is verified and evaluated in different scenarios by numerical simulation. We assessed the influencing factors of positioning performance, such as the vessel’s heading angle, the relative position, and the distances between the shore station and the vessel. The proposed method widely expands the application scope of the AIS R-Mode positioning system.

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Section: Positioning Methods For a Single Shore Stationmentioning

confidence: 99%

The Single-Shore-Station-Based Position Estimation Method of an Automatic Identification System

Jiang

Zheng

2020

Sensors

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“…The batch least squares solution is given by, δX = (A T × A) -1 × A T ×δρ (5) At the end of first iteration, [5] the estimated satellite state is given by, Est_state_1 = Initial satellite state + δX.The initial satellite state here is as in table III and the δX obtained is a (6×1) matrix. For the second iteration, the estimated satellite state at the end of first iteration is considered as the initial state.…”

Section: Least Squares Solutionmentioning

confidence: 99%

Orbit Estimation of GEO-missions Applicable to NavIC Data

S.*,

Vighnesam

et al. 2020

IJITEE

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Indian Regional Navigation Satellite System (IRNSS) is India’s own navigation system. It is a seven satellite constellation with the operational name NavIC – Navigation with Indian Constellation. Satellite Orbit determination (OD) estimates the position and velocity of orbiting satellite. The two main estimation algorithms widely used in Global Navigation Satellite Systems (GNSS) are Extended Kalman Filter (EKF) and Least Squares. This study on Batch Least Squares (BLS) - Differential Correction (DC) algorithm demonstrates precise orbit estimation of any GEO missions using only range measurements with crude initial state parameters. Currently, the study is based on simulated inputs and the satellite orbits are successfully estimated with position error in sub-centimeters level. Further, the work will be extended to live data of IRNSS satellites.

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“…Moreover, compared to (linearized) multilateration based on pairwise subtraction of the range measurement equations, significantly greater accuracy is achieved without major increase in computational complexity [8]. Indeed, several optimized variants of ILS have also been proposed in literature, which make ILS amenable to practical implementation even on resource-constrained devices, such as low-cost WSN nodes [56,57]. Although the whole localization procedure is suboptimal with respect to the initial ML estimation problem in Equation 8, we will show that the achievable performance of the proposed algorithm can be very close to the ones obtained via a two-dimensional grid search.…”

Section: Resolution Approachesmentioning

confidence: 99%

Hybrid TOA/RSS Range-Based Localization with Self-Calibration in Asynchronous Wireless Networks

Coluccia

Fascista

2019

JSAN

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The paper addresses the problem of localization based on hybrid received signal strength (RSS) and time of arrival (TOA) measurements, in the presence of synchronization errors among all the nodes in a wireless network, and assuming all parameters are unknown. In most existing schemes, in fact, knowledge of the model parameters is postulated to reduce the high dimensionality of the cost functions involved in the position estimation process. However, such parameters depend on the operational wireless context, and change over time due to the presence of dynamic obstacles and other modification of the environment. Therefore, they should be adaptively estimated “on the field”, with a procedure that must be as simple as possible in order to suit multiple real-time re-calibrations, even in low-cost applications, without requiring human intervention. Unfortunately, the joint maximum likelihood (ML) position estimator for this problem does not admit a closed-form solution, and numerical optimization is practically unfeasible due to the large number of nuisance parameters. To circumvent such issues, a novel two-step algorithm with reduced complexity is proposed: A first calibration phase exploits nodes in known positions to estimate the unknown RSS and TOA model parameters; then, in a second localization step, an hybrid TOA/RSS range estimator is combined with an iterative least-squares procedure to finally estimate the unknown target position. The results show that the proposed hybrid TOA/RSS localization approach outperformed state-of-the-art competitors and, remarkably, achieved almost the same accuracy of the joint ML benchmark but with a significantly lower computational cost.

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Approximate iterative Least Squares algorithms for GPS positioning

Cited by 20 publications

References 11 publications

The Single-Shore-Station-Based Position Estimation Method of an Automatic Identification System

The Single-Shore-Station-Based Position Estimation Method of an Automatic Identification System

Orbit Estimation of GEO-missions Applicable to NavIC Data

Hybrid TOA/RSS Range-Based Localization with Self-Calibration in Asynchronous Wireless Networks

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