Trajectory Estimation Using Separable Motion Models
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Solution Overview
Problem
Existing trajectory estimation methods for airborne and aquatic objects, such as Kalman filters, provide noisy estimates due to their inability to adjust prior estimations with new measurements and often fit a linear motion model that does not accurately represent complex behaviors like maneuvers or oscillations.
Innovation Solution
A computer-implemented method using separable, nonlinear motion models parameterized for aircraft and other objects, employing curve-fitting algorithms like VarPro to estimate trajectories as a series of linearly separable sections, with models like multi-manoeuvre and weaving/spiralling motion models.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If Kalman filters or similar algorithms are used for trajectory estimation, then the estimation can be computed at each time step, but the output is a noisy estimate that does not adjust prior estimation points with new measurements
Solution Approach 1:
The trajectory is segmented into multiple sections with distinct motion models (e.g., constant velocity, constant acceleration, maneuvering phases). Each segment is fitted independently using measurement data, allowing the algorithm to capture different motion behaviors while maintaining computational efficiency through localized processing rather than global optimization.
Solution Approach 2:
The system dynamically transitions between different motion models based on the observed behavior of the tracked object. When maneuvers or oscillations are detected, the algorithm switches from simple linear models to more complex nonlinear models, allowing adaptive adjustment of estimation accuracy according to the actual motion characteristics at each time segment.
2Device complexity
If a linear motion model is used for trajectory estimation, then the computation is simple and fast, but the model does not fit complex behaviors such as multiple maneuvers or oscillating behavior
Solution Approach 1:
The trajectory estimation is divided into multiple segments, each representing a distinct phase of motion (e.g., straight flight, turning, oscillation). By segmenting the overall trajectory, the system can apply simple linear models to straight sections while applying more complex nonlinear models only to maneuvering sections, thus balancing computational simplicity with modeling accuracy.
Solution Approach 2:
Different motion models are applied to different local segments of the trajectory based on the specific characteristics of each segment. Simple linear models are used where appropriate (reducing complexity), while complex nonlinear models are applied only where needed (improving accuracy locally), rather than using a single complex model for the entire trajectory.
3Measurement precision
If a nonlinear motion model is used to represent complex trajectories, then the model can capture maneuvers and oscillations, but the optimization computation becomes intractable and numerically unstable
Solution Approach 1:
The complex nonlinear optimization problem is broken down into multiple smaller sub-problems, each corresponding to a trajectory segment. Each sub-problem involves optimizing only the parameters relevant to that segment, dramatically reducing the dimensionality and computational burden of each optimization task while collectively capturing the full complex behavior of the trajectory.
Solution Approach 2:
The system dynamically selects the appropriate level of model complexity for each trajectory segment based on the observed motion characteristics. For simple linear segments, simple models are used; for complex maneuvering segments, more sophisticated nonlinear models are employed. This dynamic adaptation ensures high accuracy where needed while maintaining computational tractability overall.
Data Source
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AI summary
Embodiments estimate the trajectory of an airborne or aquatic object. Embodiments comprise obtaining (204) track data of an airborne or aquatic object; fitting (210) at least one motion model to the track data using a curve-fitting algorithm to determine parameter values of the at least one motion model, and estimating (210) a trajectory of the object using the parameter values. The at least one motion model estimates the trajectory of the object as a plurality of linearly separable sections.