Inertial Navigation Chebyshev Polynomial Integration
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Solution Overview
Problem
Current inertial navigation systems face challenges in accurately calculating rigid body motion in three-dimensional space due to approximation defects in algorithms and high computational burdens, particularly in velocity and position solutions.
Innovation Solution
A functional iterative integration-based method using Chebyshev polynomials to fit angular velocity and specific force measurements, iteratively calculating Chebyshev polynomial coefficients for attitude, velocity, and position, with polynomial truncation to enhance calculation efficiency and accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If functional iterative integration with polynomial fitting is used to improve attitude calculation accuracy, then manufacturing precision is improved, but device complexity increases due to iterative polynomial coefficient calculations
Solution Approach 1:
The patent transforms the attitude calculation problem from direct integration of angular velocity to iterative calculation using polynomial coefficients. By representing angular velocity as a polynomial function and iteratively computing Rodrigues vector coefficients, the method achieves higher precision while managing computational complexity through parameter transformation rather than direct complex integration
Solution Approach 2:
The patent performs preliminary polynomial fitting of angular velocity data before integration. By pre-fitting the angular velocity signal to a polynomial function and calculating its coefficients, the system prepares the data in a form that enables accurate iterative integration without requiring complex real-time computation during the navigation solution
2Manufacturing precision
If polynomial order is increased to improve velocity and position solution accuracy, then manufacturing precision is improved, but productivity decreases due to sharp increase in computational burden
Solution Approach 1:
The patent segments the velocity and position calculation into separate iterative processes from the attitude calculation. By independently fitting polynomial functions to specific force measurements and separately iteratively computing velocity and position coefficients, the system achieves high accuracy without requiring excessively high polynomial orders, thus maintaining computational efficiency
Solution Approach 2:
The patent applies partial polynomial truncation during the iterative calculation process. By calculating polynomial coefficients iteratively and truncating at appropriate orders based on required precision rather than using excessively high orders from the start, the system achieves the necessary accuracy while avoiding the computational burden of high-order polynomials throughout all calculation stages
3Device complexity
If approximation methods are used in inertial navigation algorithms to simplify calculations, then device complexity is reduced, but measurement precision deteriorates due to principle defects in the algorithms
Solution Approach 1:
The patent replaces traditional mechanical integration methods with functional iterative integration based on polynomial representations. Instead of using simple Euler or Runge-Kutta integration of raw sensor data, the system substitutes polynomial fitting and coefficient-based iterative calculation, which eliminates approximation errors inherent in traditional numerical integration while maintaining computational feasibility
Solution Approach 2:
The patent introduces polynomial coefficient representations as intermediary variables between sensor measurements and final navigation solutions. By representing angular velocity and specific force as polynomial functions and computing their coefficients iteratively, the system creates an intermediate mathematical representation that preserves measurement information without the approximation losses of direct integration methods
Data Source
AI summary
A functional iterative integration-based method for an inertial navigation solution includes: fitting a Chebyshev polynomial function of an angular velocity and a Chebyshev polynomial function of a specific force according to gyroscope-measured values and accelerometer-measured values on a time interval; iteratively calculating Chebyshev polynomial coefficients of an attitude quaternion by using the obtained Chebyshev polynomial coefficients of the angular velocity and an integral equation of the attitude quaternion, and performing polynomial truncation on a result obtained from each iterative calculation according to a preset order; iteratively calculating Chebyshev polynomial coefficients of a velocity/position by using the obtained Chebyshev polynomial coefficients of the specific force, the Chebyshev polynomial coefficients of the attitude quaternion and an integral equation of the velocity/position, and performing polynomial truncation on a result obtained from each iterative calculation according to a preset order; and obtaining attitude/velocity/position information on the corresponding time interval.