Aircraft Navigation Using Exponential Map Kinematic Model
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Solution Overview
Problem
Current aircraft navigation systems face computational complexities due to geodesic factors like magnetic variation and wander angles, especially near the poles, leading to errors and increased hardware costs.
Innovation Solution
A computer-implemented method using a kinematic model analogous to a robotic arm, where satellite-based positioning signals derive vectors to simultaneously solve for aircraft translation and attitude information, simplifying navigation by avoiding geodesic complexities and integrating inertial and satellite systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional navigation algorithms process GPS signals and attitude sensor data separately using geodesic calculations, then position and velocity can be determined accurately, but computational complexity increases and errors occur near the poles due to tangent function singularities
Solution Approach 1:
The patent combines position and attitude determination into a unified navigation solution using a single algorithm that processes GPS signals and attitude sensor data simultaneously. This merging eliminates the need for separate geodesic calculation algorithms and their associated computational complexities, while maintaining accuracy across all latitudes including polar regions
Solution Approach 2:
The patent transforms the navigation problem from using geodesic parameters (which have singularities at poles) to using Cartesian coordinates and a unified mathematical model. This parameter transformation eliminates the tangent function singularity issue that occurs at 90° latitude, allowing accurate navigation calculations anywhere on Earth without complex conditional logic
2Reliability
If parameterization methods are used to address tangent function singularities at the poles, then navigation errors are reduced, but computational complexity and hardware costs increase
Solution Approach 1:
The patent changes the mathematical parameters from geodesic coordinates requiring tangent functions to Cartesian coordinates with a unified navigation algorithm. This parameter transformation inherently avoids the singularity problem at polar regions without requiring special parameterization methods or conditional logic, thereby maintaining reliability while reducing computational complexity
Solution Approach 2:
The patent extracts and eliminates the problematic tangent function calculations from the navigation algorithm by using an alternative mathematical approach. This removal of the singular mathematical operation simplifies the computational model and eliminates the need for complex error-handling logic near polar regions
3Ease of manufacture
If separate algorithms are used for position determination and attitude determination, then each can be optimized independently, but the overall navigation system becomes more complex and integration becomes difficult
Solution Approach 1:
The patent merges position determination and attitude determination into a single integrated algorithm that processes all navigation data simultaneously. This unified approach eliminates the integration complexities between separate algorithms while maintaining the ability to optimize the overall system performance, as there are no interface or synchronization issues between separate computational blocks
Data Source
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AI summary
Systems and methods 200 for determining navigation information for an aircraft are provided. In one embodiment, a method 200 can include accessing 202 a satellite-based positioning signal received at a receiver on an aircraft. The satellite-based positioning signal can be indicative of a distance between a satellite and the receiver. The method can include identifying 204 from the satellite-based positioning signal a first vector associated with a distance between the satellite and the receiver and identifying 206 a second vector from the satellite-based positioning signal associated with a distance between a reference point and the satellite. The method can include generating 208 a kinematic model for determining a geometric position of the aircraft based at least in part on a robotic arm using the first vector and the second vector and determining 210 navigation information for the aircraft based at least in part on the kinematic model.