Absolute Angle Determination Using Lookup Tables
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Solution Overview
Problem
Existing methods for determining the angle of a magnetic field are prone to measurement errors and require high-bit encoding of magnetic field components, leading to complex implementations and increased power consumption, especially due to the use of the arctan function.
Innovation Solution
The method uses lookup tables to simplify angle determination by reducing the precision of magnetic field components and avoiding division-based calculations, employing arcsin and arccos functions for specific intervals and utilizing a digital signal processor with reduced parallelism and computational needs, thereby minimizing measurement errors and power consumption.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the arctan function is used to calculate the angle from magnetic field components, then the angle can be determined, but measurement errors in Bx and Bz have a strong effect on the resulting angle and the implementation becomes complex
Solution Approach 1:
The method segments the angle determination process into two parts: first determining the quadrant based on the signs of Bx and Bz, then calculating the angle within that quadrant using a simplified formula. This segmentation avoids the complexity of the full arctan function while maintaining accuracy within each segment.
Solution Approach 2:
The invention changes the calculation parameters by using the ratio of the smaller to larger magnetic field component (min(|Bx|,|Bz|)/max(|Bx|,|Bz|))) instead of the traditional arctan(Bx/Bz). This parameter transformation reduces sensitivity to measurement errors and simplifies the computational requirements.
2Measurement precision
If high number of bits are used to encode magnetic field components Bx and Bz, then measurement errors are mitigated, but the ADC requires long conversion time or complex implementation
Solution Approach 1:
The invention changes the encoding precision requirements by using a different calculation approach that is less sensitive to quantization errors. The ratio-based method within quadrants maintains angle determination accuracy with fewer bits, reducing ADC conversion time and complexity.
Solution Approach 2:
Instead of using high-precision encoding for the entire 360-degree range, the method uses lower precision encoding sufficient for the reduced range within each quadrant, achieving the necessary overall precision with fewer bits.
3Ease of operation
If the arctan computation is implemented, then the angle can be calculated, but the implementation becomes complex
Solution Approach 1:
The implementation is segmented into quadrant determination followed by simplified angle calculation within each quadrant. This avoids the need for a complex full-range arctan implementation while maintaining the ease of angle determination.
Solution Approach 2:
The complex arctan computation is extracted and replaced with simpler operations: sign checking for quadrant determination, absolute value calculations, and ratio-based angle computation within quadrants, significantly reducing implementation complexity.
Data Source
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AI summary
The present invention concerns a method of determining an absolute angle of a magnetic field. The method comprises the following steps carried out by a digital signal processor (13): receiving (101) a first digital measurement value of a first magnetic field component, referred to as Bx, indicating the intensity of the magnetic field along a first axis; receiving (101) a second digital measurement value of a second magnetic field component, referred to as Bz, indicating the intensity of the magnetic field along a second axis, orthogonal to the first axis; determining (105) absolute values for the first and second magnetic field components; and determining (115) the angle of the magnetic field with respect to the first or second axis. The angle is determined so that the angle is derivable from the value of arcsin of Bz or of its approximation, when the absolute value of Bz ≤ the absolute value of Bx, and derivable from the value of arccos of Bx or of its approximation, when the absolute value of Bz > the absolute value of Bx.