Geometric Algebra Positioning for Antenna Arrays
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Solution Overview
Problem
Existing positioning methods using antenna diversity struggle to accurately determine the direction of a signal source due to noise interference and require complex coordinate systems, which can be cumbersome and less generic compared to linear algebra approaches.
Innovation Solution
A positioning method utilizing geometric algebra to solve a cost function that relates position vectors of antennas relative to a shared origin and phase information, determining a position vector for the shared origin, which is more generic and robust to noise, using geometric algebraic expressions and iterative processing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional linear algebra methods are used for positioning, then the coordinate system approach is straightforward, but the system becomes sensitive to noise and less generic
Solution Approach 1:
The patent changes the mathematical parameter system from traditional linear algebra coordinates to geometric algebra. This parameter change makes the positioning system more robust to noise while maintaining generality across different coordinate systems, directly resolving the technical contradiction between reliability and adaptability
2Measurement precision
If geometric algebra is used to solve positioning, then noise robustness and generality are improved, but the computational complexity increases
Solution Approach 1:
The patent substitutes the traditional mechanical coordinate system approach with geometric algebra mathematical framework. This substitution achieves higher measurement precision and noise robustness while the computational complexity is managed through the elegant algebraic structure of geometric algebra
Data Source
AI summary
A positioning method comprising: solving a geometric algebraic expression that relates: position vectors for a plurality of antennas relative to a shared origin, a putative position vector for the shared origin and phase information measured at each of the plurality of antennas, to determine a position vector for the shared origin; and positioning an apparatus using the determined position vector for the shared origin.