&lt;title&gt;Iterative version of the QRD for adaptive recursive least squares (RLS) filtering&lt;/title&gt;

Goetze, Juergen

doi:10.1117/12.190856

Cited by 5 publications

(4 citation statements)

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“…The iterative version of the QR decomposition (QRD) presented in [12] is used for the iterative solution of (8), since it is well suited for hardware implementation, suitable for the adaption to measurement errors (pseudoranges), and yields a solution vector which converges linearly to the exact solution.…”

Section: Iterativ E Solution Of Lsmentioning

confidence: 99%

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Approximate iterative Least Squares algorithms for GPS positioning

Martin

Bilgic

2010

The 10th IEEE International Symposium on Signal Processing and Information Technology

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The efficient implementation of positioning algo rithms is investigated for Global Positioning System (GPS) and Differential GPS (DGPS). This is particularly important for smart phones with battery limitations. With the help of the information from base stations, Assisted GPS (AGPS) and DGPS can do the positioning more efficiently and more precisely than GPS. In order to do the positioning, the pseudoranges between the receiver and the satellites are required. The most commonly used algorithm for position computation from pseudoranges is non-linear Least Squares (LS) method. Linearization is done to convert the non-linear system of equations into an iterative procedure, which requires the solution of a linear system of equations in each iteration, i.e. linear LS method is applied iteratively. CORDIC-based approximate rotations are used while computing the QR decomposition for solving the LS problem in each iteration. By choosing accuracy of the approximation, e.g. with a chosen number of optimal CORDIC angles per rotation, the LS computation can be simplified. The accuracy of the positioning results is compared for various numbers of required iterations and various approximation accuracies using real GPS data. The results show that very coarse approximations are sufficient for a reasonable positioning accuracy. Therefore, the presented method reduces the computational complexity significantly and is highly suitable for hardware implementation.

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Section: Iterativ E Solution Of Lsmentioning

confidence: 99%

“…linear LS metllod is applied in each iteration step itr. For solving the linear LS problems in each iteration step an iterative version of tlle QR decomposition (QRD) [12] is applied in this paper. Instead of annihilating tlle lower diagonal elements during tlle QRD, CORDIC-based approximate rotations are used.…”

Section: Introductionmentioning

confidence: 99%

Approximate iterative Least Squares algorithms for GPS positioning

Martin

Bilgic

2010

The 10th IEEE International Symposium on Signal Processing and Information Technology

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“…Since the pseudoranges are subject to measurement errors and the convergence (number of required iterations) of the algorithm depends on the accuracy of these LS solutions, it is worthwhile to investigate the use of an iterative LS solver and the trade-off between the number of iterations of the positioning method and the number of iterations of the iterative LS solver. The iterative version of the QR decomposition (QRD) presented in Götze (1994) is used for the iterative solution of Eq. (8), since it is well suited for hardware implementation, suitable for the adaption to measurement errors (pseudoranges), and yields a solution vector which converges linearly to the exact solution.…”

Section: Iterative Solution Of Lsmentioning

confidence: 99%

“…linear LS method is applied in each iteration step itr. For solving the linear LS problems in each iteration step an iterative version of the QR decomposition (QRD) (Götze, 1994) is applied in this paper. Instead of annihilating the lower diagonal elements during the QRD, CORDIC-based approximate rotations are used.…”

Section: Introductionmentioning

confidence: 99%

Iterative least squares method for global positioning system

Bilgic²

2011

Adv. Radio Sci.

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Abstract. The efficient implementation of positioning algorithms is investigated for Global Positioning System (GPS). In order to do the positioning, the pseudoranges between the receiver and the satellites are required. The most commonly used algorithm for position computation from pseudoranges is non-linear Least Squares (LS) method. Linearization is done to convert the non-linear system of equations into an iterative procedure, which requires the solution of a linear system of equations in each iteration, i.e. linear LS method is applied iteratively. CORDIC-based approximate rotations are used while computing the QR decomposition for solving the LS problem in each iteration. By choosing accuracy of the approximation, e.g. with a chosen number of optimal CORDIC angles per rotation, the LS computation can be simplified. The accuracy of the positioning results is compared for various numbers of required iterations and various approximation accuracies using real GPS data. The results show that very coarse approximations are sufficient for reasonable positioning accuracy. Therefore, the presented method reduces the computational complexity significantly and is highly suited for hardware implementation.

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Scalable low-complexity GPS and DGPS positioning using approximate QR decomposition

Martin

Bilgic³

2014

Signal Processing

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<title>Iterative version of the QRD for adaptive recursive least squares (RLS) filtering</title>

Cited by 5 publications

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Approximate iterative Least Squares algorithms for GPS positioning

Approximate iterative Least Squares algorithms for GPS positioning

Iterative least squares method for global positioning system

Scalable low-complexity GPS and DGPS positioning using approximate QR decomposition

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