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Fixed-point calculation method and calculation device for spherical distance based on fpga

A spherical distance and fixed-point calculation technology, applied in the field of circuit and information processing, can solve the problems of increased hardware storage overhead, error accumulation, large hardware storage overhead, etc., and achieves the effects of high reliability, easy implementation, and reduced storage overhead.

Active Publication Date: 2020-09-04
NAT INNOVATION INST OF DEFENSE TECH PLA ACAD OF MILITARY SCI
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

[0013] To quickly obtain the function value of a nonlinear function such as a trigonometric function based on a lookup table is to reduce the computational complexity by increasing the storage overhead; usually in order to ensure the calculation accuracy, it is hoped that the independent variable has a smaller quantization interval, but a smaller quantization interval will Increase the length of the lookup table, so that the hardware storage overhead increases accordingly
Because in the distance calculation formula, the error of the arcsine function lookup table will be enlarged when it is multiplied by the spherical radius r, in the coordinate conversion formula, the multiplication of trigonometric functions will cause error accumulation, and after multiplying the spherical radius by r, it will be Further enlarge the error; therefore, the calculation of the spherical distance has higher requirements on the accuracy of the trigonometric function lookup table. When using the existing technology to construct the lookup table, if the accuracy of the calculation result of the spherical distance is to be guaranteed, it will lead to a huge hardware storage overhead

Method used

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  • Fixed-point calculation method and calculation device for spherical distance based on fpga
  • Fixed-point calculation method and calculation device for spherical distance based on fpga
  • Fixed-point calculation method and calculation device for spherical distance based on fpga

Examples

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example 1

[0089] Specifically, assuming: N=8192, [0, π / 2] interval is divided into 8192 sub-intervals, and the calculated sine function value is represented by 15 specific points, so that N=B·E·M=128×8 ×8, according to the construction method provided by the embodiment of the present invention, respectively construct the reference lookup table, the first-order increment lookup table and the second-order increment lookup table of the sine function. as attached figure 2 , attached image 3 And attached Figure 4Shown, the length of the benchmark look-up table of sine function is B E=1024, and the data bit width is 15 bits; The length of the first-order incremental look-up table of sine function is B (M-1)=896, and the data bit width is 6 bits; the length of the second-order incremental look-up table of the sine function is B(E-1) (M-1)=6272, and the data bit width is 2 bits; then it can be seen that the reference look-up table of the sine function, the first-order The storage overhead...

example 2

[0110] Specifically, assuming that r is the radius of the earth, when the distance estimation accuracy is required to be on the order of Km, in [0,2r 2 ] with Δ=2 23 For the quantization interval, N'=11150848 arcsine function values ​​can be obtained; take N 1 =512,N 2 =1536,N 3 =9728,N 4 =140800,N 5 =665088,N 6 = 2762240 and N 7 =11150848=N', take at the same time and Then, based on the parameters set above, after the non-uniform quantization process, the arcsine function value can be reduced to N "=32768. Further, let N "=B"·E"·M"=512×8×8, Construct the benchmark lookup table, first-order increment lookup table and second-order increment lookup table of the arcsine function respectively according to the construction method provided by the embodiment of the present invention. As attached Figure 5 , attached Image 6 And attached Figure 7 Shown, the length of the benchmark lookup table of arcsine function is B " E "=4096, and the data bit width is 14 bits; The...

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Abstract

The invention discloses a FPGA-based spherical distance fixed-point calculation method.. The method comprises the following steps: 1) quantizing a function value of a sine function in an independent variable value interval of the sine function; 2) constructing a lookup table of a sine function; 3) determining an independent variable and an independent variable value range of the arcsine function,and performing non-uniform quantization and compression on a function value of the arcsine function; 4) constructing a lookup table of an arcsine function; and 5) respectively determining an independent variable corresponding to the sine function and an independent variable corresponding to the arcsine function, generating an index address, and accessing a lookup table of the sine function and thearcsine function to obtain a spherical distance between the corresponding fixed points. The invention also discloses a spherical distance fixed-point calculation device for realizing the FPGA-based spherical distance fixed-point calculation method. According to the FPGA-based spherical distance fixed-point calculation method and the FPGA-based spherical distance fixed-point calculation device, the storage overhead of the lookup table can be reduced on the premise of ensuring the calculation precision of the FPGA for calculating the spherical distance.

Description

technical field [0001] The invention relates to the technical field of circuits and information processing, in particular to an FPGA-based fixed-point calculation method for spherical distance and a calculation device thereof. Background technique [0002] Solving the spherical distance between two points is one of the commonly used calculations in the fields of astronomy and geography. For example, when satellites in orbit perform tasks such as real-time target search and cone retrieval, they need to use the acquired longitude and latitude or geocentric coordinate data, such as WGS84( World Geodetic System 1984) coordinates, CGCS2000 (China Geodetic Coordinate System2000) coordinates, and perform a large number of spherical distance calculations. At present, because FPGA (Field Programmable Gate Array, Field Programmable Logic Gate Array) has good stability and hardware parallel computing capability, it is widely used in hardware-limited environments such as micro-nano sate...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G06F17/10
CPCG06F17/10
Inventor 王建李献斌陈小前曹璐姚雯范广腾
Owner NAT INNOVATION INST OF DEFENSE TECH PLA ACAD OF MILITARY SCI