GPS Attitude Estimation via Double Differenced Carrier Phase Optimization
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Solution Overview
Problem
Existing methods for estimating the attitude of a device using double differenced GPS carrier phase measurements face challenges in resolving integer ambiguity, requiring significant time, computing power, or resources, and are inefficient in the integer domain.
Innovation Solution
A computer-implemented method that determines expected double differenced carrier phase values based on an initial candidate attitude, inputs these values into a cost function for comparison with measured values, and minimizes the cost function using a global optimizer to select a final candidate attitude, thereby estimating the device's attitude accurately.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If existing methods resolve integer ambiguity within the integer domain, then attitude estimation can be performed, but it requires large amounts of time, computing power, or other resources
Solution Approach 1:
The patent transforms the integer ambiguity resolution problem from the integer domain to the attitude domain by changing the parameter space. Instead of searching for integer solutions, the method formulates the problem as a continuous optimization problem where the attitude parameters (rotation matrix elements) are the optimization variables. This parameter transformation allows the use of efficient continuous optimization algorithms rather than exhaustive integer search methods.
Solution Approach 2:
The patent replaces the traditional computational approach (integer domain search) with a different mathematical framework (continuous optimization in attitude domain). By substituting the mechanical/computational method of integer search with a continuous optimization formulation using cost functions and gradient-based methods, the system achieves faster convergence and reduced computational burden while maintaining estimation accuracy.
2Measurement precision
If existing methods resolve integer ambiguity within the integer domain, then attitude estimation can be performed, but it requires large amounts of computing power or other resources
Solution Approach 1:
The patent transforms the integer ambiguity resolution problem from the integer domain to the attitude domain by changing the parameter space. Instead of searching for integer solutions, the method formulates the problem as a continuous optimization problem where the attitude parameters (rotation matrix elements) are the optimization variables. This parameter transformation allows the use of efficient continuous optimization algorithms rather than exhaustive integer search methods.
Solution Approach 2:
The patent replaces the traditional computational approach (integer domain search) with a different mathematical framework (continuous optimization in attitude domain). By substituting the mechanical/computational method of integer search with a continuous optimization formulation using cost functions and gradient-based methods, the system achieves faster convergence and reduced computational burden while maintaining estimation accuracy.
3Reliability
If double differenced carrier phase measurements are used, then errors common to both receivers or both satellites are eliminated, but integer ambiguity remains
Solution Approach 1:
The patent extracts and isolates the integer ambiguity component from the double differenced carrier phase measurements. By formulating the optimization problem to explicitly account for and eliminate the integer ambiguity term, the method separates the reliable continuous phase information (which contains position and attitude data) from the discrete integer component (which causes ambiguity). This extraction allows the continuous optimization to proceed using only the reliable measured quantities.
Solution Approach 2:
The patent transforms the integer ambiguity resolution problem from the integer domain to the attitude domain by changing the parameter space. Instead of searching for integer solutions, the method formulates the problem as a continuous optimization problem where the attitude parameters (rotation matrix elements) are the optimization variables. This parameter transformation allows the use of efficient continuous optimization algorithms rather than exhaustive integer search methods.
Data Source
AI summary
Systems and methods for estimating attitude using double differenced GPS carrier phase measurements are provided. An exemplary computer-implemented method includes obtaining, by one or more computing devices, an initial candidate attitude. The method includes determining, by the one or more computing devices, a plurality of expected double differenced carrier phase values based on the initial candidate attitude. The method includes inputting, by the one or more computing devices, the plurality of expected double differenced carrier phase values into a cost function. The cost function respectively compares the plurality of expected double differenced carrier phase values to a plurality of measured double differenced carrier phase values. The method includes minimizing, by the one or more computing devices, the cost function. The method includes selecting, by the one or more computing devices, a final candidate attitude associated with the minimized cost function as the attitude of the device.