Conical Boundary Estimation for Moving Object Trajectory Prediction
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Solution Overview
Problem
Current position estimation methods do not predict the future position of a moving object and only provide a point estimate with error probability parameters, failing to account for the object's potential trajectory due to obstructions and varying confidence levels.
Innovation Solution
A computer-implemented method that uses previous location estimates represented by elliptical error probabilities to calculate the spatial bounds of a moving object's future location by forming a cone from tangent lines, allowing visualization of probable future paths on a map.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If current position estimation methods are used, then a point estimate with error probability parameters is provided, but the future position boundary and potential trajectory cannot be predicted
Solution Approach 1:
The patent transitions from providing only a point estimate in 2D space to generating a conical boundary surface that adds a temporal dimension. The cone extends from the first EEP through the second EEP, creating a three-dimensional representation of possible future positions that captures both spatial and temporal uncertainty.
Solution Approach 2:
The method performs preliminary calculations by determining tangent lines to the error ellipses before finalizing the future position boundary. By pre-calculating these geometric relationships between the first and second EEPs, the system establishes the conical boundary that encompasses all possible future positions.
2Device complexity
If only point estimate with EEP is provided, then calculation complexity is low, but the spatial bounds and confidence levels for future location cannot be determined
Solution Approach 1:
The patent incorporates confidence levels directly into the geometric construction by using tangent lines to the error ellipses. The tangent lines are determined based on the confidence level parameters of the EEPs, ensuring that the resulting conical boundary reflects the required confidence level for future position estimation.
Solution Approach 2:
The solution adds a geometric dimension by constructing tangent lines and conical surfaces rather than simply extending the error ellipse. This geometric approach allows the system to visualize and communicate confidence levels spatially, making the reliability information intuitive and actionable.
3Measurement precision
If direct observation of moving object trajectory is used, then accurate tracking is achieved, but it becomes impractical when obstructions block the view
Solution Approach 1:
The patent uses error ellipses and conical boundaries as intermediary representations that mediate between the observed position data and the unknown future position. These geometric constructs allow the system to reason about possible trajectories without requiring direct line-of-sight observation of the object's actual movement path.
Solution Approach 2:
The method performs preliminary geometric construction using the observed position data and error characteristics to establish the conical boundary before the object actually moves. This preliminary action creates a predictive framework that remains valid even when obstructions prevent direct observation of the object's trajectory.
Data Source
AI summary
A method for estimating a boundary for a future location of a moving object includes: receiving location information about two previous locations of the moving object represented by a first and a second elliptical error probabilities (EEPs); representing each of the EEPs as a conic section via an implicit quadratic equation; defining four tangent lines from the implicit quadratic equation, each tangent line being tangent to both of the EEPs; determining two transverse tangent lines from the four tangent lines; forming a cone in a direction from the first EEP to the second EEP from the two transverse tangent lines; and estimating the boundary of the future location of the moving object as a first side of the cone formed by a first transverse tangent line and a second side of the cone formed by a second transverse tangent line, of the two transverse tangent lines.