Hypersonic Object Tracking via Unscented Kalman Filter
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Solution Overview
Problem
Existing tracking systems face challenges in accurately predicting the trajectory of hypersonic missiles due to their non-linear motion, which traditional Kalman filters struggle to handle effectively.
Innovation Solution
The system employs an unscented Kalman filter (UKF) with geometrically diverse sensors to track hypersonic objects across their full flightpath, using different dynamics models for each phase of flight (boost, ballistic, glide, and terminal) to account for varying forces and maneuvers.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional Kalman filter is used for tracking hypersonic objects, then the system is simple to implement, but the tracking accuracy deteriorates due to non-linear trajectory
Solution Approach 1:
The patent transforms the non-linear state estimation problem into a linear one by changing the parameter representation space. Specifically, it uses a linearized dynamics model with state variables that are linear combinations of position, velocity, and acceleration components, allowing the standard Kalman filter to effectively track hypersonic objects despite their non-linear trajectories.
2Measurement precision
If Extended Kalman Filter is used to handle non-linear dynamics, then the tracking accuracy improves, but computational complexity and error propagation increase
Solution Approach 1:
The patent extracts and handles the non-linear effects separately from the main linear filtering process. By using a linearized dynamics model that captures the essential non-linear behavior through appropriate state variable definitions and process noise modeling, it avoids the computational burden and error propagation issues of the Extended Kalman Filter while maintaining tracking accuracy.
3Adaptability or versatility
If Jacobian matrices are calculated for transformation from filter state to measurement, then non-linear transformation is handled, but computational power and potential for human error increase
Solution Approach 1:
The patent substitutes the mechanical computation of Jacobian matrices with a simplified linearized dynamics approach. By defining state variables and transition models that are inherently linear or can be easily linearized, it eliminates the need for complex Jacobian calculations while still achieving accurate non-linear trajectory tracking through the linear Kalman filter framework.
Data Source
AI summary
A system and method of tracking a hypersonic object over a flightpath includes at least one observer having at least one sensor. The sensor is configured to provide measurements of the hypersonic object that are geometrically diverse such that each observer may independently measure any combination of range, angles, Doppler, and angle rates. The observers transmit measurements to a processing unit as the hypersonic object undergoes three phases including a boost phase, a ballistic phase, and a hypersonic glide phase. The hypersonic object is tracked over many time steps by first selecting a dynamics model representative of expected object kinematics during said phase. Then, an unscented Kalman filter is used to predict a future state and a covariance using the dynamics model that was selected. Finally, the unscented Kalman filter updates the future state and covariance that were predicted based on the geometrically diverse measurements of the sensors.