3D Attitude Determination via Constrained Least-Squares Optimization
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Solution Overview
Problem
Current methods for GNSS attitude determination face challenges in resolving carrier phase integer ambiguity, leading to inaccuracies and complex computational requirements, especially when instantaneous attitude information is needed.
Innovation Solution
The method involves receiving satellite information to resolve phase ambiguities using single-difference and double-difference measurements, employing algebraic formulas and search-based strategies with specific antenna geometries and frequency measurements to estimate unambiguous phase differences, and then calculating the 3D attitude using improved direction vectors constrained by angle and length constraints.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of time
If search-based methods are used to resolve carrier phase integer ambiguities, then real-time attitude determination is achievable, but computational complexity increases and requires intensive computational configurations
Solution Approach 1:
The patent transforms the complex integer ambiguity resolution problem into a continuous optimization problem by applying a least-squares approach with constraints. This parameter transformation changes the mathematical nature of the problem from discrete search to continuous optimization, reducing computational complexity while maintaining real-time capability
Solution Approach 2:
The patent extracts and separates the attitude determination from the ambiguity resolution process. By formulating the problem to directly estimate attitude parameters while handling ambiguities through constrained optimization, it decouples the computationally intensive ambiguity search from the attitude calculation, reducing overall computational burden
2Device complexity
If motion-based methods are used to resolve carrier phase integer ambiguities, then computational complexity is reduced, but instantaneous attitude information cannot be obtained
Solution Approach 1:
The patent performs preliminary constraint formulation and model setup that enables direct computation of attitude from current observations. By pre-defining the constrained least-squares framework and constraint structures, the system can process instantaneous data without requiring historical motion information, achieving both simplicity and real-time capability
3Measurement precision
If existing ambiguity resolution methods are used, then attitude determination can be achieved, but measurement precision decreases due to inaccuracies
Solution Approach 1:
The patent implements an iterative constrained least-squares optimization that uses feedback from constraint violations to refine the attitude estimate. The algorithm continuously adjusts the solution to satisfy geometric constraints (unit length of direction vectors, angle constraints), providing feedback-driven refinement that improves both accuracy and reliability
Solution Approach 2:
The patent employs a dynamic optimization approach that adapts the solution based on current observational conditions and constraint satisfaction. The iterative nature of the constrained least-squares method allows the system to dynamically adjust estimates to achieve higher precision while maintaining reliability through constraint enforcement
Data Source
AI summary
A method for determining a 3-dimensional (3D) attitude of a platform includes receiving satellite relayed information regarding an ambiguous phase single-difference measurement (φ); resolving a phase ambiguity of the ambiguous phase single-difference measurement (φ) to determine an unambiguous phase single-difference estimate (ϕ); calculating coarse direction vectors xcor and ycor based on the unambiguous phase single-difference estimate (ϕ); estimating improved direction vectors x and y based on the coarse direction vectors xcor and ycor and by imposing constraints on the improved direction vectors x and y and an angle between the improved direction vectors x and y; and calculating the 3D attitude of the platform from the improved direction vectors x and y.