Polynomial Regression for GNSS Pseudorange Error Reduction
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
The increasing number of GNSS satellites and varying update rates pose challenges in efficiently transmitting differential error correction information to GNSS receivers without excessive bandwidth usage and susceptibility to message loss or corruption, particularly in real-time kinematic positioning applications.
Innovation Solution
A processor-based system that uses mathematical modeling to establish past and predicted pseudorange measurements, allowing for data compression by representing pseudorange histories with polynomial regression models, which can be used to correct errors and predict future values, thereby reducing the need for frequent raw data transmission.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If differential correction data is transmitted frequently to maintain positioning accuracy, then measurement precision is improved, but bandwidth consumption increases and susceptibility to message loss increases
Solution Approach 1:
The patent extracts only the essential correction information (difference between reference and rover measurements) and transmits it separately from the full measurement data. By transmitting only the differential correction values rather than complete pseudorange measurements, the system reduces bandwidth consumption while maintaining positioning accuracy.
Solution Approach 2:
The reference station performs measurements and computes differential corrections in advance before the rover needs them for positioning. By preparing correction data ahead of time and making it available for interpolation, the system ensures accuracy is maintained without requiring frequent real-time transmissions.
2Quantity of substance
If differential correction data is transmitted at lower rates to conserve bandwidth, then bandwidth consumption is reduced, but reliability of continuous positioning degrades
Solution Approach 1:
The system uses the transmitted differential correction values as feedback to continuously update the rover's positioning calculations. By providing correction data at lower rates with polynomial coefficients that can be interpolated over time, the feedback mechanism maintains positioning reliability without requiring high transmission rates.
Solution Approach 2:
Polynomial coefficients are computed in advance from multiple measurement points and transmitted before they are needed for positioning. This preliminary computation allows the rover to interpolate correction values continuously without requiring frequent new transmissions, maintaining reliability while reducing bandwidth usage.
3Quantity of substance
If polynomial regression models are used to compress pseudorange measurement data, then data compression is achieved, but measurement precision may be reduced due to modeling errors
Solution Approach 1:
Instead of compressing the entire pseudorange measurement data, the patent extracts only the differential correction component (the difference between reference and rover measurements) and applies polynomial regression only to this correction data. This extraction approach minimizes precision loss because the correction values are typically much smaller and vary more smoothly than the full pseudorange measurements.
Solution Approach 2:
The patent changes the parameter being modeled from raw pseudorange measurements to differential correction values. By transforming the data to represent corrections rather than absolute ranges, the polynomial regression operates on smaller, smoother variations that can be compressed more effectively with less precision loss.
4Quantity of substance
If polynomial coefficients are transmitted instead of raw pseudorange measurements, then data compression is achieved, but device complexity increases at the receiver to evaluate the polynomials
Solution Approach 1:
The reference station performs the computationally intensive polynomial regression analysis and prepares the coefficients in advance. The receiver's role is simplified to receiving the coefficients and evaluating the polynomials at required time points. By making the reference station self-serve the computational burden of model fitting, the receiver complexity is minimized while still achieving data compression.
Data Source
AI summary
Polynomial regression models are used to reduce errors in measurements of pseudorange between a GNSS satellite and a receiving station; for data compression by replacing a large number of measurements with a small number of coefficients of the model polynomial, optionally combined with modeling residuals; for extrapolating usefully accurate estimates of future range between the GNSS satellite and the receiving station; and for providing usefully accurate estimates of future coefficient values of the polynomial regression models themselves.