Cubic Hermite Spline Trajectory Estimation for Navigation
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Solution Overview
Problem
Current navigation devices face challenges in accurately estimating vehicle positions between distant probe data points, especially on curvy roads, due to large sampling intervals and the failure of simple linear and spline interpolation methods to consider physical constraints and road design principles.
Innovation Solution
The method employs cubic Hermite splines with control points and vectors to estimate trajectories, along with polynomial interpolation of degree five or higher, and optimization techniques like steepest gradient descent or simulated annealing to ensure continuous derivatives and accurate position estimation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If linear interpolation is used between distant probe points, then computational simplicity is maintained, but position estimation accuracy deteriorates significantly on curvy roads
Solution Approach 1:
The patent changes the interpolation method from simple linear interpolation to cubic Hermite spline interpolation, which incorporates not only positional parameters but also velocity and acceleration parameters. This allows the trajectory estimation to account for vehicle dynamics and road curvature, significantly improving position estimation accuracy while maintaining reasonable computational complexity through the use of standardized mathematical functions.
Solution Approach 2:
The patent applies cubic Hermite spline interpolation which generates curved trajectories instead of straight lines, better representing the actual curved paths of vehicles on roads. The method uses control points and control vectors to define smooth curved segments that follow road geometry, thereby improving accuracy on curvy roads while avoiding the oversimplified angular trajectory estimations of linear interpolation.
2Measurement precision
If basic spline interpolation methods are used, then positional information is incorporated, but physical constraints of vehicles are ignored leading to implausible trajectories
Solution Approach 1:
The patent extends basic spline interpolation by incorporating velocity and acceleration parameters alongside position. The cubic Hermite spline method uses control vectors derived from velocity information to define the shape of interpolated segments, ensuring that estimated trajectories respect vehicle motion constraints and produce physically plausible paths that reflect actual driving behavior.
Solution Approach 2:
The patent incorporates feedback from velocity and acceleration measurements to constrain and guide the interpolation process. By using recorded velocity vectors as control vectors in the cubic Hermite spline formulation, the method ensures that interpolated trajectories are consistent with observed vehicle dynamics, thereby improving trajectory plausibility while maintaining position estimation accuracy.
3Productivity
If larger sampling intervals are used, then data collection frequency is reduced, but the distance between consecutive probe points increases leading to poorer interpolation accuracy
Solution Approach 1:
The patent compensates for larger sampling intervals by enriching the interpolation with additional parameters (velocity and acceleration) beyond simple position data. The cubic Hermite spline method uses these additional parameters to construct more informed trajectory estimates that account for vehicle dynamics, thereby maintaining interpolation accuracy even when probe points are farther apart in space and time.
Solution Approach 2:
The patent performs preliminary calculations to derive control vectors from velocity measurements at probe points before executing the cubic Hermite spline interpolation. This preliminary preparation of derivative information enables the interpolation method to accurately reconstruct trajectories over larger intervals by anticipating the vehicle's path based on its motion state at sampled points.
Data Source
AI summary
A method comprising: collecting a plurality of probe data from a plurality of probe points by a probing device, said probe data comprising at least positional information, a speed vector and a direction of travel of the probing device and a timestamp of recording the probe data at a probe point; and estimating a trajectory of the probing device between two consecutive probe points as a cubic Hermite spline having the positions of said two consecutive probe points as control points and the speed vectors of said two consecutive probe points as control vectors.