Modified Faddeev Algorithm For Matrix Manipulation

Nash, J.G.; Hansen, S.

doi:10.1117/12.944007

Cited by 26 publications

(4 citation statements)

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“…Matrices A, B, C and D are loaded into compound matrix: (9) The Fadeev algorithm then involves reducing C to zero, in the compound matrix of (9), by ordinary row manipulation of the Gaussian elimination type. In practice a modified Fadeev algorithm, where matrix A is changed to triangular form prior to annulment of C, is more suitable for systolic array processing [5], [6]. This is summarized as, (10) where TA is an upper triangular matrix.…”

Section: Parallel Kalman Conceptmentioning

confidence: 99%

An Efficient Transputer Implementation of a Systolic Architecture for Parallel Kalman Filtering

Seddiki¹

2013

IJIEE

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The computations involved in Kalman filter algorithms are highly structured with regular matrix-type operations. Moreover, Kalman filter algorithms can be specified as a set of parallel passes rearranged to be the type of the Fadeev algorithms for generalizing matrix/vector manipulations. Based on that, and in order to further improve the speed of updating the state estimate of Kalman filter equations and taking full advantage of the two parallel pipeline structures, a new combined SIMD/MISD (Single Instructions Multiple Data stream/ Multiple Instructions Single Data stream) Transputer implementation scheme is presented. This configuration has expanded the utilization of the twodimensional systolic architecture and significantly improved the speed of updating the state estimate and resulted in a significant saving in processing time complexity compared to SIMD transputer implementation.

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Section: Parallel Kalman Conceptmentioning

confidence: 99%

An Efficient Transputer Implementation of a Systolic Architecture for Parallel Kalman Filtering

Seddiki¹

2013

IJIEE

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“…Application Area Time Guibas et al [5] tc n 2 6n Nash-Hansen [9] mi 3n 2 /2 5n Robert-Tchuent [13] mi n 2 5n Kung-Lo [6] tc n 2 7n Rote [15] app n 2 7n Robert-Trystam [14] app n 2 5n Kung-Lo-Lewis [7] tc & sp n 2 5n Benaini et al [1] app n 2 /2 5n Benaini-Robert [2] app n 2 /3 5n Scheiman-Cappello [16] app n 2 /3 5n Clauss-Mongenet-Perrin [4] app n 2 /3 5n Takaoka-Umehara [17] sp n 2 4n Rajopadhye [11] app n 2 4n Risset-Robert [12] app n 2 4n Chang-Tsay [3] app n 2 4n Djamegni et al [18] app n 2 /3 4n Linear arrays (systolic and otherwise) Kumar-Tsay [10] app n 2 7n 2 Kumar-Tsay [10] app n 2 7n 2 Myoupo-Fabret [8] app…”

Section: Authorsmentioning

confidence: 99%

The Algebraic Path Problem Revisited

Rajopadhye

Tadonki

Risset

1999

Lecture Notes in Computer Science

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We derive an efficient linear simd architecture for the algebraic path problem (app). For a graph with n nodes, our array has n processors, each with 3n memory cells, and computes the result in 3n 2 − 2n steps. Our array is ideally suited for vlsi, since the controls is simple and the memory can be implemented as fifos. i/o is straightforward, since the array is linear. It can be trivially adapted to run in multiple passes, and moreover, this version improves the work efficiency. For any constant α, the running time on n α processors is no more than (α + 2)n 2 . The work is no more than (1 + 2 α )n 3 and can be made as close to n 3 as desired by increasing α.

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“…The Attitude matrix is then estimated by developing a form of the unsymmetrical TRIAD. All the complex matrix operations are arranged in the form of a Faddeev algorithm [27], which can be implemented on FPGA using one single compact systolic array architecture [28]. The use of the same architecture for all the complex matrix operations leads to an increase in the system and algorithm efficiency.…”

Section: Introductionmentioning

confidence: 99%

A Magnetometer-Only Attitude Determination Strategy for Small Satellites: Design of the Algorithm and Hardware-in-the-Loop Testing

2020

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Attitude determination represents a fundamental task for spacecraft. Achieving this task on small satellites, and nanosatellites in particular, is further challenging, because the limited power and computational resources available on-board, together with the low development budget, set strict constraints on the selection of the sensors and the complexity of the algorithms. Attitude determination is obtained here from the only measurements of a three-axis magnetometer and a model of the Geomagnetic field, stored on the on-board computer. First, the angular rates are estimated and processed using a second-order low-pass Butterworth filter, then they are used as an input, along with Geomagnetic field data, to estimate the attitude matrix using an unsymmetrical TRIAD. The computational efficiency is enhanced by arranging complex matrix operations into a form of the Faddeev algorithm, which is implemented using systolic array architecture on the FPGA core of a CubeSat on-board computer. The performance and the robustness of the algorithm are evaluated by means of numerical analyses in MATLAB Simulink, showing pointing and angular rate accuracy below 10° and 0.2°/s. The algorithm implemented on FPGA is verified by Hardware-in-the-loop simulation, confirming the results from numerical analyses and efficiency.

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Modified Faddeev Algorithm For Matrix Manipulation

Cited by 26 publications

References 0 publications

An Efficient Transputer Implementation of a Systolic Architecture for Parallel Kalman Filtering

An Efficient Transputer Implementation of a Systolic Architecture for Parallel Kalman Filtering

The Algebraic Path Problem Revisited

A Magnetometer-Only Attitude Determination Strategy for Small Satellites: Design of the Algorithm and Hardware-in-the-Loop Testing

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