GPS Coordinate Extrapolation Using Tangential Plane Approximation
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Solution Overview
Problem
GPS receivers face challenges in accurately determining location when GPS signals are unavailable, often resulting in errors of 5-10 meters due to the complexity of earth's surface and computational intensity, which is inadequate for precise applications.
Innovation Solution
A method using a tangential plane approximation to extrapolate GPS coordinates, modeling the earth as a spherical surface with a constant radius, allowing for simplified latitude/longitude determinations and achieving high accuracy with reduced computational power, achieving errors within 1-4 centimeters.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional GPS coordinate extrapolation methods using complex earth models and datasets are used, then measurement precision is improved, but device complexity and computational power requirements increase
Solution Approach 1:
The patent changes the fundamental parameter of earth modeling from complex biaxial ellipsoid models with granular regional datasets to a simple spherical model with constant radius. This parameter simplification maintains sufficient accuracy for most applications while dramatically reducing computational complexity and device requirements
Solution Approach 2:
The patent extracts only the essential elements needed for coordinate extrapolation (spherical earth model, basic trigonometric relationships) while eliminating unnecessary complexities (biaxial ellipsoid calculations, regional terrain datasets, complex projection transformations). This extraction achieves the minimum viable solution for accurate GPS extrapolation
2Measurement precision
If traditional GPS coordinate extrapolation methods are used, then measurement precision is improved, but use of energy increases
Solution Approach 1:
By changing the earth model parameter from complex to simple spherical geometry, the computational workload is dramatically reduced. This leads to lower CPU usage, reduced processing cycles, and consequently lower power consumption in battery-powered GPS devices
Solution Approach 2:
The patent employs computationally inexpensive algorithms that can be executed quickly and efficiently. The simplified spherical model requires minimal processing power and memory resources, making it ideal for portable devices with limited energy supplies
3Device complexity
If simplified spherical earth model is used, then device complexity is reduced, but measurement precision deteriorates
Solution Approach 1:
The patent applies partial action by using only the portion of earth model complexity that is necessary for accurate coordinate extrapolation. The spherical model provides sufficient precision for most practical applications without requiring the full complexity of biaxial ellipsoid calculations, achieving the right balance between simplicity and accuracy
Solution Approach 2:
The patent demonstrates that changing the earth radius parameter to a constant spherical value, rather than using variable ellipsoid parameters, maintains adequate accuracy for GPS extrapolation while significantly simplifying the computational model. The error introduced is acceptable for most navigation and positioning applications
Data Source
AI summary
Systems and methods for extrapolating GPS coordinates beyond line of sight are disclosed. A coordinate extrapolation system (CES) can include a memory, a processor, and a GPS receiver. The CES can receive GPS signals and determine GPS coordinates corresponding to a location. If GPS signals are unavailable, the CES models the surface of the earth and extrapolates the GPS coordinates corresponding to the location at which GPS signals are unavailable. Methods for extrapolating the GPS coordinates and calibrating the CES are also disclosed.