FPGA-based matrix inversion using an iterative Chebyshev-type method in the context of compressed sensing

Rico-Aniles, Hector Daniel; Ramírez-Cortés, Juan Manuel; Rangel-Magdaleno, José

doi:10.1109/i2mtc.2014.6860890

Cited by 5 publications

(7 citation statements)

References 14 publications

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“…So we use Chebyshev Method to perform matrix inversion in HDL [7]. In order to find the solution to the inverse matrix problem through the Chebyshev-type method, it is important to choose a suitable initial guess, otherwise the method diverges.…”

Section: Algorithm a Chebyshev Inversion Algorithmmentioning

confidence: 99%

“…In order to find the solution to the inverse matrix problem through the Chebyshev-type method, it is important to choose a suitable initial guess, otherwise the method diverges. With the equation given below a suitable initial guess can be computed [7]. N0=A T ÷A l * A ∞ N0= initial guess A =matrix to be inverted A T = transpose of A A l = maximum value of the summation of the elements on each column.…”

Section: Algorithm a Chebyshev Inversion Algorithmmentioning

confidence: 99%

“…Z k is actual observation matrix. Difference of Z k and z k =C x k has taken in equation (7). z k is estimated observation matrix calculated in equation (2).…”

Section: Introductionmentioning

confidence: 99%

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HDL implementation of Kalman Filter for GNSS receiver

Rawal

2015

2015 IEEE International Advance Computing Conference (IACC)

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This paper presents HDL implementation of Kalman Filter. Kalman Filter is a mathematical tool, which uses sequence of noisy measurement taken over time to predict unknown state vector parameter. In this paper implementation in HDL has been done using new method that is chebyshev inversion method. The approach of new method is for reducing hardware and complexity. Kalman Filter has very complex matrix calculation and matrix inversion. To perform matrix inversion in HDL(Hardware Description Language) using less hardware is difficult. Chebyshev method is less complex so hardware can reduced for calculation of Kalman Filter equations Here simulation is done in FPGA(Field Programmable Gate Array) Vertex-6.

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Section: Algorithm a Chebyshev Inversion Algorithmmentioning

confidence: 99%

Section: Algorithm a Chebyshev Inversion Algorithmmentioning

confidence: 99%

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HDL implementation of Kalman Filter for GNSS receiver

Rawal

2015

2015 IEEE International Advance Computing Conference (IACC)

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“…However, developing and implementing these algorithms in FPGA is not easy. Hence, Chebyshev algorithm have been used to find matrix inverse to purpose of decreasing complexity and development time (Rico-Aniles et al, 2014), (Rawal, 2015).…”

Section: Introductionmentioning

confidence: 99%

Kalman Filter Implementation on Field-programmable Gate Array for Navigation Applications of Unmanned Aerial Vehicles

Deniz¹,

Sakarya²

2021

European Journal of Science and Technology

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In recent years, unmanned aerial vehicle (UAV) applications have been widely used in various manufacturing areas for the purpose of material handling or monitoring tasks. This situation increased the importance of proper estimation of UAVs' location. This paper presents hardware based Kalman Filter implementation for UAVs to accurately locate/detect its positions. To maintain high performance and compact form factor, Field-programmable Gate Array (FPGA) has been used as a hardware source. However, Kalman Filter algorithm needs lots of matrix computation and the typical implementation of matrix computations in hardware is complex and requires more effort than traditional software-based approaches. Matrix inversion computation in the Kalman gain formula is one of the most difficult matrix calculations in Kalman Filter algorithm and Chebyshev type inversion is used as a matrix inversion method to simplify hardware implementation. The proposed method simulated on both Matlab and Vivado based on the same scenario and numerical results of Kalman Filter and Chebyshev algorithm compared between these two simulation platforms. According to experimental results, the proposed solution serves compact and high performance standalone solution via FPGA for Kalman Filter implementation for UAVs.

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“…Details of the implementation and some required considerations such as a suitable initial guess to ensure convergence, and stop criteria, can be consulted in Ref. .…”

Section: Introductionmentioning

confidence: 99%

MATLAB and FPGA‐based interactive tool for exploring concepts on compressed sensing

Rico-Aniles

Ramírez-Cortés

Rangel-Magdaleno

et al. 2015

Comp Applic In Engineering

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This paper presents an educational platform developed to explore some concepts related to the relatively new signal acquisition paradigm known as Compressed Sensing (CS). CS aims to acquire a signal with sparse or compressible representation in a suitable domain, using a number of samples under the limit established by the Nyquist–Shannon sampling theorem. The application consists of a graphical user interface in MATLAB, and a low‐cost FPGA Xilinx Spartan 6, which in that way form a powerful and low‐cost design station adequate to perform a number of CS experiments. Reconstruction of signals is carried out using a Greedy algorithm which solves the underdetermined system in real time with a novel Chebyshev‐type matrix inversion. Effects related to the number of samples defined in the measurement matrix, and the use of different spaces, such as Discrete Cosine Transform, or Discrete Wavelet Transform, can be easily studied with the described tool. Results derived from its use in graduate courses are discussed. © 2015 Wiley Periodicals, Inc. Comput Appl Eng Educ 23:921–930, 2015; View this article online at http://wileyonlinelibrary.com/journal/cae; DOI

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FPGA-based matrix inversion using an iterative Chebyshev-type method in the context of compressed sensing

Cited by 5 publications

References 14 publications

HDL implementation of Kalman Filter for GNSS receiver

HDL implementation of Kalman Filter for GNSS receiver

Kalman Filter Implementation on Field-programmable Gate Array for Navigation Applications of Unmanned Aerial Vehicles

MATLAB and FPGA‐based interactive tool for exploring concepts on compressed sensing

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