Real-Time and High-Accuracy Arctangent Computation Using CORDIC and Fast Magnitude Estimation

Abstract

This paper presents an improved VLSI (Very Large Scale of Integration) architecture for real-time and high-accuracy computation of trigonometric functions with fixed-point arithmetic, particularly arctangent using CORDIC (Coordinate Rotation Digital Computer) and fast magnitude estimation. The standard CORDIC implementation suffers of a loss of accuracy when the magnitude of the input vector becomes small. Using a fast magnitude estimator before running the standard algorithm, a pre-processing magnification is implemented, shifting the input coordinates by a proper factor. The entire architecture does not use a multiplier, it uses only shift and add primitives as the original CORDIC, and it does not change the data path precision of the CORDIC core. A bit-true case study is presented showing a reduction of the maximum phase error from 414 LSB (angle error of 0.6355 rad) to 4 LSB (angle error of 0.0061 rad), with small overheads of complexity and speed. Implementation of the new architecture in 0.18 µm CMOS technology allows for real-time and low-power processing of CORDIC and arctangent, which are key functions in many embedded DSP systems. The proposed macrocell has been verified by integration in a system-on-chip, called SENSASIP (Sensor Application Specific Instruction-set Processor), for position sensor signal processing in automotive measurement applications.

A Polar Initial Alignment Algorithm for Unmanned Underwater Vehicles

“…The accuracy of other hardware needed to support calculation is as follows. The gyro constant drifts and random drifts of OCTANS are 0.01 °/h and (0.0005 °/h) 2 , respectively [21,22]. Simulation results demonstrate that polar initial alignment algorithm proposed in this paper is obviously superior to conventional and transversal fine alignment algorithms in alignment accuracy and alignment speed.…”

Real-Time Embedded Systems: Present and Future

“…An FPGA implementation of a multi-band real-time speech enhancement system is shown in Reference [9], which includes specific architectural optimizations for speed and energy consumption. An application-specific integrated circuit (ASIC) implementation of real-time and accuracy optimizations for arctangent calculation based on a coordinate rotation digital computer (CORDIC) is shown in Reference [10] (a trigonometric function that is essential for many embedded DSP calculations), while an automated folding scheme for efficient FPGA implementation of fast Fourier transform (FFT), an algorithm widely used in many embedded application domains, is proposed and experimentally evaluated in Reference [11].…”

A Noniterative Radix-8 CORDIC Algorithm with Low Latency and High Efficiency

“…As one of the most common transcendental functions, the sine or cosine function has been widely used in real-time digital signal processing systems, such as radar, ultrasound, robotics, communication and so on [1][2][3][4][5][6][7]. The accuracy and efficiency of the computation of the functions are two key requirements for evaluating the performance of these systems.…”