ARAIM Kalman Filter Navigation Integrity Monitoring
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Solution Overview
Problem
Current GNSS-based navigation systems lack sufficient integrity monitoring performance for demanding phases of flight, such as precision approaches, due to limitations in horizontal and vertical position component monitoring, especially with increased satellite constellations and frequency bands.
Innovation Solution
The implementation of advanced receiver autonomous integrity monitoring (ARAIM) methods, including analytical derivation of unmodeled biases' effects on Kalman filter state estimates and computationally effective calculation of protection levels using integrity and non-integrity assured pseudorange error descriptions, enhances the integrity monitoring in hybrid navigation systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If current RAIM techniques are used for integrity monitoring, then horizontal protection level can be determined, but vertical protection level and precision approach support are insufficient
Solution Approach 1:
The patent segments the integrity monitoring into multiple independent sub-solutions, each evaluating a different satellite subset. This allows comprehensive coverage of both horizontal and vertical protection levels by combining results from multiple segmented evaluations, enabling precision approach support while maintaining horizontal monitoring capabilities.
Solution Approach 2:
The patent extends integrity monitoring from the traditional horizontal dimension to include the vertical dimension by computing vertical protection levels alongside horizontal ones. This dimensional expansion enables the system to support precision approaches which require vertical guidance integrity, transforming the monitoring capability from 2D horizontal to 3D spatial coverage.
2Measurement precision
If advanced ARAIM methods with Kalman filter are implemented, then accuracy and reliability improve, but computational complexity increases
Solution Approach 1:
The patent pre-computes and stores the transformation matrix that relates pseudorange biases to Kalman filter state estimate errors. By preparing this matrix in advance rather than computing it in real-time during integrity monitoring, the system achieves high measurement precision through accurate bias effect compensation while reducing the computational burden during critical flight phases.
Solution Approach 2:
The patent changes the computational parameters by using pre-derived analytical relations for bias effects instead of performing full real-time Kalman filter recalculations. This parameter transformation allows the system to maintain high accuracy through rigorous mathematical modeling while operating at lower computational complexity by working with pre-computed transformation matrices and simplified bias effect formulas.
3Reliability
If unmodeled biases are not accounted for, then computational complexity remains low, but protection levels become unrealistic and reliability decreases
Solution Approach 1:
The patent introduces a transformation matrix as an intermediary element that connects pseudorange biases to Kalman filter state estimate errors. This intermediary allows the system to account for unmodeled biases in a systematic and computationally efficient manner, transforming the complex bias handling problem into a manageable matrix multiplication operation that improves protection level accuracy without excessive complexity.
Solution Approach 2:
The patent replaces complex iterative numerical methods for bias estimation with closed-form analytical solutions based on pre-derived transformation matrices. This substitution eliminates the need for computationally intensive mechanical iteration processes while achieving more accurate bias compensation, thereby improving reliability through better protection level calculation without proportionally increasing device complexity.
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AI summary
A method of advanced receiver autonomous integrity monitoring of a navigation system is discussed and two modifications facilitating its implementation in a hybrid navigation system are disclosed. In the first approach, relations describing the effect of unmodeled biases in pseudo-measurement on the Kalman filter state estimate are analytically derived and their incorporation into the integrity monitoring algorithm is described. The method comprises receiving a plurality of signals transmitted from space-based satellites, determining a position full-solution and sub-solutions, specifying a pseudorange bias, computing a transformation matrix for the full-solution and all sub-solutions using a Kalman filter, computing a bias effect on an error of filtered state vectors of all sub-solutions, and adding the effect to computed vertical and horizontal protection levels. In the second approach, a modification for computationally effective calculation of the protection levels of hybrid navigation systems based on both integrity and non-integrity assured pseudorange error descriptions is disclosed.