Projectile Trajectory Evaluation via Speed-Adaptive Point Relocation
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Solution Overview
Problem
Existing methods for evaluating trajectories, such as the Fréchet distance, are inaccurate when dealing with time series data from projectiles due to assumptions of constant speed and fail to precisely reflect time information, leading to unrealistic mappings and decreased accuracy.
Innovation Solution
A method and apparatus that relocate points on a reference trajectory based on a movable range dependent on the target's speed, determining a similarity by setting a similarity estimation range and using binary search to find the upper limit, allowing for accurate comparison of time series positioning data with a reference trajectory.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the Fréchet distance is applied to discrete time series data by approximating to a polygon curve, then the trajectory similarity can be calculated, but the time information of the time series data is not precisely reflected and the mapping may become unrealistic
Solution Approach 1:
The patent introduces a dynamic speed profile that varies over time, replacing the static constant speed assumption. The speed profile is defined as a function of time that reflects the actual motion characteristics of the projectile, allowing the mapping process to adapt to changing speeds and maintain realism throughout the trajectory evaluation.
Solution Approach 2:
The patent changes the parameter from constant speed to time-varying speed profile. By incorporating speed as a time-dependent parameter v(t), the system can accurately reflect the actual motion dynamics of projectiles during different phases of flight, improving both measurement precision and mapping realism simultaneously.
2Ease of manufacture
If point intervals are adjusted to maintain a reference interval in discrete Fréchet distance measurement, then the calculation can proceed, but the accuracy deteriorates when the speed of the moving object changes
Solution Approach 1:
The patent replaces the static reference interval approach with a dynamic time-based mapping method. Instead of forcing uniform intervals, the system allows interval adjustment based on the speed profile v(t), maintaining calculation feasibility while adapting to speed variations to preserve measurement accuracy.
Solution Approach 2:
The patent changes the interval determination from a fixed reference interval to a time-varying interval based on the speed profile. The mapping interval is dynamically adjusted according to v(t), enabling the system to handle both fast and slow moving segments accurately without sacrificing computational feasibility.
3Device complexity
If the Fréchet distance mapping is performed without considering speed constraints, then the calculation is simpler, but the mapping may exceed the maximum speed of the projectile
Solution Approach 1:
The patent incorporates dynamic speed constraints into the mapping process by using a time-varying speed profile v(t). The mapping algorithm respects the maximum speed at each time point, ensuring physical realism while maintaining a relatively simple implementation through systematic constraint application.
Solution Approach 2:
The patent introduces speed as a constraining parameter in the mapping process. By defining the speed profile v(t) and using it to limit the mapping displacement at each time step, the system ensures compliance with physical speed constraints without requiring overly complex algorithms.
Data Source
AI summary
The present disclosure provides a method and an apparatus for quickly and accurately evaluating a trajectory of a projectile such as a satellite launching rocket or a missile by comparing the trajectory with a reference trajectory. The trajectory evaluation method includes: acquiring time series positioning data for a target and predetermined reference trajectory information; and mapping points representing the time series positioning data on a graph into corresponding points on a reference trajectory representing the predetermined reference trajectory information while relocating each mapped point onto a relocatable section taking into account a movable range dependent on a speed of the target, and determining a maximum value of distances moved by the points while the points are mapped and relocated as a similarity between the time series positioning data and the reference trajectory.