Geometric Containment Determination for Mobile Device Location
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Solution Overview
Problem
Current systems for determining whether a mobile device is inside or outside a defined geographic boundary are computationally intensive, leading to high latency and increased processing demands, especially when assessing multiple devices against numerous boundaries in real-time.
Innovation Solution
The method employs simplified geometries and algorithms to estimate the likelihood of a device's location relative to a boundary, using adjusted uncertainty areas and confidence levels, reducing the need for intensive calculations by forming circles and secants to determine containment decisions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional probability calculations are used to determine containment, then measurement precision is improved, but device complexity and processing intensity increase
Solution Approach 1:
The containment determination process is divided into multiple stages (Stage 1, Stage 2, Stage 3) with increasing computational complexity. Stage 1 uses simple distance comparisons for quick decisions, Stage 2 uses geometric probability calculations for moderate complexity cases, and Stage 3 uses full probability integration only when necessary. This segmentation allows the system to achieve high measurement precision while avoiding unnecessary computational complexity for most cases.
Solution Approach 2:
The system performs only the minimum necessary computational action for each containment determination. By using the simplified distance-based Stage 1 approach for obvious cases and reserving complex probability calculations only for borderline cases, the system achieves accurate containment determination without consistently applying full computational intensity, thus reducing average processing requirements while maintaining precision.
2Productivity
If real-time containment assessment is performed for multiple devices, then productivity is improved, but use of energy and processing power increase
Solution Approach 1:
The system segments the containment determination into hierarchical stages, allowing most device-boundary assessments to be resolved quickly in Stage 1 using simple geometric distance comparisons. Only assessments that require higher precision proceed to Stages 2 and 3. This enables high productivity for multiple simultaneous assessments while minimizing energy consumption by avoiding complex calculations for routine cases.
Solution Approach 2:
The system uses computationally inexpensive approximations (cheap calculations) for the majority of containment determinations, reserving expensive probability integration calculations only for necessary cases. This approach enables processing of multiple devices in real-time with controlled energy expenditure, as most assessments are handled by efficient geometric methods rather than intensive numerical integration.
3Device complexity
If simplified geometric methods are used, then device complexity is reduced, but measurement precision deteriorates
Solution Approach 1:
The system segments containment determination into hierarchical stages with increasing precision. Stage 1 uses simple geometric distance comparisons for quick assessments. Stage 2 introduces geometric probability calculations for improved accuracy. Stage 3 uses full probability integration for maximum precision when needed. This segmentation allows the system to use simplified methods for obvious cases while maintaining high measurement precision for borderline cases through progressive refinement.
Solution Approach 2:
The system dynamically selects the appropriate level of computational complexity based on the specific assessment context. For clear-cut cases where the device is obviously inside or outside a boundary, simple geometric methods suffice. For borderline cases where the device location is near the boundary, the system dynamically transitions to more complex probability-based methods to ensure accurate containment determination, thus adapting precision to actual needs.
Data Source
AI summary
Method for calculating whether an actual location of a target device is on one side of a boundary zone includes: receiving an estimated location of the target device; receiving a desired confidence level; forming a first circle with radius D, centered at the estimated location, where D is the shortest distance from the estimated location to the boundary zone; forming a second circle with radius R′, centered at the estimated location, wherein R′ is determined in such a way so that a likelihood that the actual location is inside the second circle equals or exceeds the desired confidence level; forming an angle with an apex at the estimated location and rays passing through two closest points to the estimated location where the second circle intersects the boundary zone; and using a size of an annulus formed by the first circle, the second circle, and the rays to estimate whether the actual location lies on the same side of the boundary zone.