Coordinated Motion Detection via Multidimensional Indexing
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Solution Overview
Problem
Existing methods for detecting coordinated motion between multiple entities in large datasets, such as ships convoying or shadowing, are inefficient due to their reliance on brute-force algorithms with high computational complexity, particularly when dealing with asynchronous and high-volume data.
Innovation Solution
The implementation of a system using multidimensional indexing, specifically space-filling curves like Morton curves, to transform state space values into efficient indexing keys, allowing for the detection of coordinated motion by applying thresholds to reduce complexity and improve search efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If brute-force algorithms are used to detect coordinated motion in large datasets, then detection accuracy is maintained, but computational complexity increases to Order(N2)
Solution Approach 1:
The patent segments the large dataset into smaller spatial cells using a grid-based indexing system. Each cell contains entities with similar spatial coordinates, reducing the search space from O(N2) to O(N) by only comparing entities within the same or adjacent cells. This segmentation maintains detection accuracy while dramatically reducing computational complexity.
Solution Approach 2:
The patent performs preliminary indexing of entity positions and velocities into multidimensional hash tables before the actual coordinated motion detection. This pre-processing step organizes data in advance, allowing the detection algorithm to quickly retrieve candidate entities without performing exhaustive comparisons, thus reducing computational complexity from O(N2) to O(N) while preserving detection accuracy.
2Reliability
If exhaustive comparison of all entity pairs is performed, then coordinated motion detection is thorough, but processing time increases significantly
Solution Approach 1:
The patent applies local quality by focusing computational resources only on local spatial regions where entities are actually present. Instead of comparing all N entities with all other N entities, the system only compares entities within localized grid cells, reducing processing time while maintaining thoroughness through systematic coverage of all regions.
Solution Approach 2:
The patent transforms the problem from a one-dimensional sequential comparison approach to a multidimensional spatial indexing approach. By organizing entities in multidimensional hash tables keyed on position and velocity, the system enables constant-time O(1) retrieval of candidate entities, reducing processing time from O(N2) to O(N) while maintaining detection thoroughness.
3Ease of manufacture
If traditional indexing methods are used, then implementation simplicity is maintained, but search efficiency decreases in high-dimensional space
Solution Approach 1:
The patent implements preliminary multidimensional indexing of entity attributes (position, velocity, time) into hash tables before the coordinated motion detection process. This pre-computed indexing structure enables efficient O(1) retrieval of candidate entities that match specific criteria, dramatically improving search efficiency from O(N) to O(1) for candidate retrieval while maintaining implementation simplicity through standard hashing techniques.
Solution Approach 2:
The patent extends traditional one-dimensional indexing to multidimensional indexing by creating hash keys from multiple entity attributes simultaneously (position coordinates, velocity components, time). This multidimensional approach organizes data in a way that enables efficient retrieval of entities matching multiple criteria, improving search efficiency while keeping the implementation conceptually simple through generalization of hashing.
Data Source
AI summary
A system is provided for determining coordinated motion between objects. The system includes a velocity data receiving component, a position data receiving component, a multidimensional indexing component and a determining component. The velocity data receiving component receives velocity data of the objects. The position data receiving component receives position data of the objects. The multidimensional indexing component generates multidimensional indices of the objects based on the velocity data and position data. The determining component determines whether there is coordinated motion between objects based on the multidimensional indices.