Sonic Source Estimation via Bipartite Graph Matching
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Solution Overview
Problem
Current methods for estimating the number of sonic sources generating discrete sonic events, such as whale calls, are unreliable due to uncertainties in location and motion, leading to inaccurate abundance calculations and requiring complex brute force calculations that are computationally infeasible with large data sets.
Innovation Solution
A computerized method determines temporal and spatial confidence intervals for each sonic event, classifies pairings based on these intervals, and estimates the minimum number of sources using a bipartite graph maximum matching, allowing for efficient estimation of sonic sources without relying on precise locations or continuous sound emission.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If brute force calculation methods are used to estimate the number of sonic sources, then measurement precision may be improved, but computational complexity becomes infeasible with large data sets
Solution Approach 1:
The patent transforms the estimation problem from a brute force combinatorial search into a graph matching problem by changing the mathematical parameters and representation. Sonic events are represented as nodes in a graph, and potential source relationships are represented as edges with weights based on temporal and spatial compatibility. This parameter transformation enables efficient computation while maintaining estimation accuracy.
Solution Approach 2:
The patent replaces the mechanical brute force calculation approach with a graph-theoretic algorithmic system. Instead of systematically trying all possible source combinations (mechanical enumeration), the system uses graph maximum matching algorithms to efficiently determine the minimum number of sources required to explain observed sonic events, dramatically reducing computational complexity.
2Measurement precision
If precise location information is required for each sonic event, then measurement precision improves, but the system becomes infeasible when location data is uncertain or unavailable
Solution Approach 1:
The patent anticipates location uncertainty by incorporating temporal and spatial confidence intervals into the graph edge weight calculations before performing the matching. Rather than requiring precise locations, the system pre-computes compatibility metrics that account for possible location ranges, cushioning against the impact of location uncertainty on the final estimation reliability.
Solution Approach 2:
The patent changes the representation from requiring precise location parameters to using probabilistic confidence intervals. Instead of treating location as a fixed value, the system represents location as a distribution with associated confidence levels, transforming the problem from deterministic to probabilistic and thereby feasible under uncertain conditions.
3Ease of operation
If assumptions about animal behavior are made to simplify estimation, then ease of operation improves, but measurement precision deteriorates
Solution Approach 1:
The patent enables the system to determine source numbers self-services through objective graph matching algorithms without requiring external assumptions about animal behavior. The algorithm automatically identifies the minimum number of sources needed to explain the sonic events based purely on temporal and spatial compatibility, eliminating the need for behavioral assumptions while maintaining precision.
Data Source
AI summary
A computerized machine (a) determines temporal and spatial confidence intervals for each one of plural sonic events, (b) classifies pairings among the sonic events as either comparable or non-comparable, and (c) estimates a minimum number of sonic sources, some of which are in motion, that could have produced or generated the sonic events. Sonic event times and positions are characterized by corresponding temporal and spatial confidence intervals. A pairing of sonic events is classified as comparable only when that pairing meets one or more preselected constraints, some of which depend on the temporal and spatial confidence intervals. The estimated minimum number of sonic sources is equal to the total number of sonic events minus the cardinality of a maximum matching of a bipartite graph derived from the classifications of the pairings and a chronological ordering of the set of sonic events.