Navigation Protection Limits Extrapolation
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Solution Overview
Problem
Current navigation systems face challenges in providing temporally consistent protection limits for navigation states due to delays in calculation and asynchrony between navigation systems, leading to reduced validity and increased calculation load, especially in multi-navigation contexts.
Innovation Solution
A method and system that extrapolate protection limits by applying a constant and positive transition matrix to the standard deviations of the covariance matrix, compensating for delays and asynchrony, allowing for integrated and real-time calculation of predictive protection limits.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If protection limits are calculated using conventional methods with Kalman filtering and statistical models, then the accuracy and reliability of navigation state estimates are improved, but the calculation time increases and temporal consistency is degraded
Solution Approach 1:
The patent applies preliminary action by pre-calculating and storing transition matrices for various navigation states and time intervals. These pre-computed matrices are then applied to extrapolate protection limits forward in time without performing full recalculations, thus maintaining reliability while reducing real-time computation delay
Solution Approach 2:
The patent implements dynamics by using time-varying transition matrices that adapt to changing navigation conditions. The transition matrices are updated based on current navigation state dynamics and applied to extrapolate protection limits to future time points, allowing the system to maintain temporal consistency while adapting to dynamic operational conditions
2Loss of time
If protection limits are calculated at high frequency to reduce delay, then temporal validity is improved, but the calculation load and processing complexity increase
Solution Approach 1:
The patent applies partial action by performing complete Kalman filtering and protection limit calculations only at reference time points, then using simplified extrapolation with pre-computed transition matrices for intermediate time points. This partial recalculation approach maintains temporal validity without requiring full calculation frequency
Solution Approach 2:
The transition matrices are pre-calculated and stored before real-time operation. During runtime, only the application of these pre-computed matrices to current state vectors is required, dramatically reducing the computational burden compared to performing full statistical model calculations at every time step
3Stability of the object's composition
If extrapolation is applied to compensate for calculation delays, then temporal consistency of protection limits is improved, but the complexity of the extrapolation process increases
Solution Approach 1:
The patent changes parameters by using pre-computed transition matrices that encapsulate the statistical properties of navigation state evolution. Instead of implementing complex real-time extrapolation algorithms, the system transforms the problem into applying simple matrix operations with pre-determined parameters, reducing computational complexity while maintaining temporal consistency
Data Source
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AI summary
The invention relates to a method for determining protection limits at a future moment associated with navigation states of a bearer, including the steps of: estimating the navigation states of the bearer at the present moment, developing a statistic model of the estimation errors of navigation states of the bearer at the present moment in the form of a covariance matrix, extrapolating, for a future moment, the statistical model of the estimation errors, calculating protection limits at the future moment from the extrapolated statistical model, wherein the extrapolation of the statistical model of the estimation errors implements the application of a constant and positive transition matrix to a standard deviation vector constructed from the square root of the elements of the diagonal of the covariance matrix, in order to propagate, up to the future moment, the standard deviations of the navigation states developed at the present moment. The invention also relates to a navigation system configured to implement the method.