Coordinate Transform Between Distorted 2D Maps and 3D Cartesian Systems
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Solution Overview
Problem
Transforming coordinates between distorted two-dimensional map projections and undistorted three-dimensional Cartesian coordinate systems poses significant challenges, particularly in vehicle localization and annotation integration, due to the infeasibility of explicit transformations between these disparate systems.
Innovation Solution
A method involving the determination of reference coordinates associated with a vehicle's sensing horizon, followed by separate transformation into respective coordinate systems using algorithms specific to each, and the application of a least-squares algorithm to generate an optimal rigid body transform within the special Euclidean group SE(3) to approximate the relationship between the two systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If coordinates are transformed directly between distorted 2D map projection and undistorted 3D Cartesian coordinate systems, then transformation simplicity is improved, but transformation accuracy deteriorates significantly
Solution Approach 1:
The patent introduces an intermediary undistorted 2D coordinate system that serves as a bridge between the distorted map projection and the 3D Cartesian system. The transformation process is divided into two stages: first transforming from the distorted 2D map to the undistorted 2D intermediate system, then transforming to the 3D Cartesian system. This intermediary approach maintains transformation accuracy while keeping the process manageable through modular computation.
Solution Approach 2:
The complex coordinate transformation problem is segmented into multiple manageable stages. Instead of attempting a direct transformation between distorted 2D and 3D systems, the method breaks it down into: (1) transformation from distorted 2D map projection to undistorted 2D intermediate coordinates, and (2) transformation from undistorted 2D to 3D Cartesian coordinates. Each stage can be handled with appropriate algorithms, improving overall accuracy.
2Device complexity
If a single determinative transform is used between distorted and undistorted coordinate systems, then device complexity is reduced, but transformation accuracy deteriorates
Solution Approach 1:
The patent employs dynamic transformation matrices that adapt to the specific characteristics of the coordinate systems being transformed. Rather than using a static single transform, the system computes transformation matrices based on the relationship between the distorted map projection and the undistorted 3D Cartesian system, allowing accurate handling of the distortion while maintaining manageable system complexity through matrix algebra.
3Measurement precision
If annotations encoded in undistorted coordinate systems are integrated with vehicle localization in distorted map projections, then information accuracy is improved, but system complexity increases
Solution Approach 1:
The patent uses the undistorted 2D coordinate system as an intermediary to integrate annotations with vehicle localization. Annotations encoded in undistorted coordinate systems are first transformed to the undistorted 2D intermediate system, then to the distorted map projection system used for vehicle localization. This approach maintains annotation accuracy while enabling integration with the vehicle's localization system through the intermediary coordinate framework.
Data Source
AI summary
System, methods, and other embodiments described herein relate to associating coordinates between separate coordinate systems. In one embodiment, a method includes acquiring location coordinates of a vehicle in a surrounding environment according to sensor data from at least one sensor of the vehicle. The method includes transforming reference coordinates associated with the location coordinates into first intermediate coordinates associated with a first coordinate system that is based, at least in part, on a distorted two-dimensional map projection, and second intermediate coordinates associated with a second coordinate system that is a Cartesian coordinate system associated with a Geodetic datum. The method includes generating, using the first intermediate coordinates and the second intermediate coordinates, an estimated transform for converting between the first coordinate system and the second coordinate system. The method includes projecting one or more annotations encoded in the second coordinate system into the first coordinate system using the estimated transform.