Lookup Table for Lambda Method Failure Probability Estimation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current methods for estimating double difference carrier phase integer ambiguity in GPS systems, such as the Boot-Strap Method and LAMBDA method, lack a practical analytical solution for the probability of failure and do not effectively reject anomalous data, leading to potential system updates with incorrect integers.
Innovation Solution
A method that employs both the lambda and boot-strap methods to determine double difference carrier phase integer ambiguity using a lookup table created through Monte Carlo simulations, which calculates the probabilities of failure and rejection, allowing for improved data validation and system integrity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the lambda method is used to estimate integer ambiguity, then the capability to reject anomalous data through residual error analysis is improved, but the ability to provide an analytical solution for probability of failure deteriorates
Solution Approach 1:
The patent introduces a lookup table as an intermediary that bridges the lambda method and probability of failure calculation. The lookup table stores pre-computed probability values based on statistical simulations, allowing the system to obtain failure probabilities without deriving complex analytical solutions, thus maintaining both anomaly rejection capability and failure probability assessment
Solution Approach 2:
The patent performs statistical simulations and pre-computes probability of failure values in advance, storing them in a lookup table before actual GPS processing. This preliminary action eliminates the need for real-time analytical calculations during operational use, providing both reliability through the lambda method and accessible failure probability data
2Loss of information
If the boot-strap method is used to estimate integer ambiguity, then the analytical solution for probability of failure is provided, but the capability to reject anomalous data through residual errors deteriorates
Solution Approach 1:
The patent merges the advantages of both the boot-strap method and the lambda method by using the lookup table (derived from boot-strap statistical analysis) to provide failure probabilities while simultaneously employing the lambda method for anomaly detection and rejection through residual error analysis, thus combining the strengths of both approaches
3Measurement precision
If Monte Carlo simulations are performed to create lookup table, then the probability of failure estimation accuracy is improved, but the computational time and complexity increase
Solution Approach 1:
The patent performs computationally intensive Monte Carlo simulations in advance to create a lookup table with high accuracy probability of failure estimates. By completing this time-consuming work beforehand, the system achieves precise probability estimation without incurring computational delays during actual real-time GPS processing operations
Data Source
Figure 1
Figure 2~5
Figure 3
AI summary
A method for estimating a probability of failure of a least-squares ambiguity decorrelation adjustment (LAMBDA) method is provided. The LAMBDA method is used for estimation of double difference carrier phase integer ambiguity. A plurality of condition sets are selected. Each condition set comprises a probability of failure (Pboot-fail) for a boot-strap method of estimation of the double difference carrier phase integer ambiguity, a number of space vehicles (Nsv), and a ratio test tolerance for the LAMBDA method. A plurality of Monte Carlo simulations are run on the plurality of condition sets to obtain a plurality of result sets. Each result set comprises a probability of lambda fail (Pλ-fail) and a probability of lambda reject (Pλ-reject) for one condition set of the plurality of condition sets. A lookup table is created with the plurality of result sets. A value of Pλ-fail for given values of Pλ-reject, Pboot-fail, and Nsv is estimated through employment of the lookup table.