Trajectory Accuracy Determination Using Covariance Propagation
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Solution Overview
Problem
Existing methods for determining the accuracy with which a vehicle can follow a prescribed trajectory do not adequately account for dynamic changes and external perturbations, leading to inconsistent and potentially unsafe driving scenarios, especially in complex traffic conditions.
Innovation Solution
A method that uses a state tensor to represent the vehicle's physical state and a covariance tensor to model uncertainty, combined with operators F and W to simulate the vehicle's dynamic behavior and external influences, allowing for the determination of future accuracy through covariance propagation, which can be used to plan trajectories that minimize collision risk.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If existing methods for determining trajectory following accuracy are used, then the determination process is simple, but the accuracy assessment is inconsistent and unsafe in complex traffic conditions
Solution Approach 1:
The patent transforms the static trajectory following accuracy determination into a dynamic assessment by continuously updating the covariance tensor P* through propagation. The system adapts the accuracy assessment in real-time based on changing vehicle states and external perturbations, allowing the determination method to respond dynamically to complex traffic conditions rather than relying on fixed, pre-defined accuracy margins.
Solution Approach 2:
The patent changes the fundamental parameters used for accuracy determination by introducing a probabilistic framework based on covariance tensors. Instead of using fixed geometric margins or deterministic error bounds, the system represents uncertainty through covariance matrices that capture the statistical distribution of possible trajectory deviations, enabling more reliable safety assessments.
2Reliability
If dynamic changes and external perturbations are adequately accounted for in trajectory accuracy determination, then the safety and consistency improve, but the computational complexity increases
Solution Approach 1:
The patent segments the complex problem of trajectory accuracy determination into distinct computational components: the system operator F that models vehicle dynamics, the perturbation operator W that accounts for external influences, and the covariance propagation mechanism that updates uncertainty estimates. This segmentation allows each component to be processed independently and efficiently, managing computational complexity while maintaining comprehensive safety assessment.
Solution Approach 2:
The patent introduces the covariance tensor P* as an intermediary that mediates between the complex dynamic system and the safety determination process. Rather than directly computing trajectory deviations from complex interactions, the system propagates covariance through the system operators to obtain updated uncertainty estimates, which then serve as the basis for safety assessments. This intermediary simplifies the overall computational burden.
3Measurement precision
If a probabilistic accuracy assessment with covariance tensors is used, then the trajectory following precision improves, but the measurement and calculation difficulty increases
Solution Approach 1:
The patent implements feedback by using the propagated covariance tensor P* to continuously refine the trajectory accuracy assessment. The system measures actual trajectory deviations, updates the covariance representation of uncertainty, and uses this updated information to adjust future accuracy determinations. This feedback loop enables progressively more precise measurements while managing calculation complexity through iterative refinement rather than exhaustive computation.
Data Source
AI summary
A method for determining the accuracy with which a vehicle can drive along a prescribed intended trajectory is disclosed. The physical state of the vehicle is represented by a state tensor, the uncertainty of which is known at an initial point in time in the form of a covariance tensor. A continued temporal development of the state tensor is modeled through the application of a first operator, which represents the dynamic behavior of the vehicle, to a combination of the state tensor and the prescribed intended trajectory, and through the subsequent application of a second operator, which represents external perturbations. Through a covariance propagation with the first and second operators, a continued temporal development of the covariance tensor is determined. A future accuracy with which the prescribed intended trajectory can be driven along is determined from the continued temporal development.