Navigation Track Association Verification Using Linear Inequalities
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Solution Overview
Problem
Current data association algorithms in navigation and DAA systems, particularly non-linear systems, are challenging to verify using formal methods due to their complexity, leading to insufficient assurance of correctness, which is crucial for certification in the avionics domain.
Innovation Solution
A system that includes a processor and non-cooperative sensors, featuring a correlator module to output correlated tracks and a verification module that reframes data association into linear inequalities, allowing for formal methods-based verification to ensure the correctness of the tracks by comparing properties within sets a and b using branching and bounding techniques.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If formal methods-based verification is applied to non-linear data association algorithms, then verification rigor is improved, but the complexity of the system increases due to the non-linear nature of the algorithms
Solution Approach 1:
The patent transforms the verification problem by changing the parameter representation from non-linear algorithm outputs to linear inequality constraints. By formulating verification conditions as linear inequalities rather than attempting to verify the non-linear algorithms directly, the patent maintains verification rigor while reducing the effective complexity of the verification process.
Solution Approach 2:
The patent introduces an intermediary mathematical framework (linear inequalities and measurement statistics) that mediates between the non-linear data association algorithms and the formal verification process. This intermediary layer allows rigorous verification without directly confronting the complexity of the non-linear algorithms.
2Ease of operation
If testing and simulation methods are used to gain confidence in data association implementations, then ease of operation is improved, but the reliability of verification deteriorates due to insufficiency in guaranteeing correctness
Solution Approach 1:
The patent replaces the mechanical testing and simulation approach with a mathematical proof approach. Instead of empirically testing the system to gain confidence, the patent uses formal mathematical methods to provide definitive verification, substituting empirical validation with rigorous logical proof.
Solution Approach 2:
The patent performs preliminary formulation of linear inequalities and measurement statistics before the actual verification process. By pre-processing the data association results into a standardized mathematical form, the patent makes the subsequent verification step straightforward while ensuring reliability.
3Reliability
If abstractions of data association algorithms are defined in formal notations and proven using theorem provers, then verification reliability is improved, but the device complexity increases and scalability deteriorates
Solution Approach 1:
The patent extracts the essential verification requirements from the complex data association algorithms and formulates them as separate linear inequalities. By separating the verification conditions from the algorithm implementation details, the patent achieves both reliability through formal proof and scalability through modular verification units.
Data Source
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Figure 1B
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AI summary
A method for providing assurance of data association comprises formulating a track permutation matrix of measurement statistics based on sensor measurement returns; receiving a first set of correlated tracks from a correlator module (set a), identified as originating from a target; selecting a second set of correlated tracks from the track permutation matrix (set b), based on branching and bounding techniques; reframing verification of a data association framework into a linear inequality, with a first portion of the linear inequality based on set a, and a second portion of the linear inequality based on set b; and performing a formal methods-based verification procedure to determine whether properties of set a are bounded by properties of set b. If properties of the correlated tracks within set a are bounded by, or are less than or equal to, properties of the correlated tracks within set b, then the correlated tracks are verified.