Mobile Radar Target State Estimation Using Invariant Kalman Filtering
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing radar systems struggle to accurately estimate the state of maneuvering targets due to the limitations of the Extended Kalman Filter, particularly in mobile radar scenarios, which require significant computational power and do not guarantee convergence, especially when targets exhibit nonlinear evolution.
Innovation Solution
Implementing an invariant Extended Kalman Filter (IEKF) in a mobile radar that applies a transformation operation to the frame associated with the radar's position, updating state data in the transformed frame, and using both active and passive estimation signals to estimate target state parameters such as orientation, curvature, and velocity, while considering noise covariance matrices differently for each signal type.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the Extended Kalman Filter (EKF) is used to estimate the state of maneuvering targets, then the estimation accuracy for nonlinear evolution is improved, but the computational complexity increases significantly and convergence is not guaranteed
Solution Approach 1:
The patent introduces an invariant extended Kalman filter (IEKF) as an intermediary solution that bridges the gap between simple linear filters and complex nonlinear EKF. The IEKF uses invariant manifolds and coordinate transformations to handle nonlinear evolution without requiring full EKF computational complexity, thus reducing the burden on mobile radar systems while maintaining estimation accuracy for maneuvering targets.
Solution Approach 2:
The patent transforms the state estimation problem by changing the parameterization approach. Instead of directly estimating target state parameters in the original coordinate system, the IEKF transforms parameters into an invariant coordinate system where the nonlinear evolution becomes linear or simpler, reducing computational complexity while preserving estimation accuracy.
2Adaptability or versatility
If the mobile radar operates in resource-constrained environments (e.g., airborne), then the mobility and versatility are improved, but the available computational power is reduced
Solution Approach 1:
The patent extracts the computationally intensive nonlinear filtering operations from the mobile radar system by using invariant coordinate transformations. The IEKF separates the nonlinear transformation steps from the linear filtering steps, allowing the mobile radar to perform only the simpler linear filtering operations in resource-constrained environments while maintaining the ability to handle nonlinear target evolution.
3Reliability
If the radar tracks maneuvering targets with nonlinear evolution, then the tracking capability is improved, but the convergence of the filtering algorithm is not guaranteed
Solution Approach 1:
The patent applies beforehand cushioning by using invariant coordinate transformations to pre-process the nonlinear evolution model before applying the filtering algorithm. This transformation ensures that the filtering algorithm operates in a coordinate system where convergence is guaranteed, preventing divergence issues that would otherwise occur when tracking maneuvering targets with nonlinear evolution.
Data Source
Figure 1~2
Figure 3~4
AI summary
A method for estimating the status of a target that is implemented in a mobile radar moving within a given space, the radar receiving a plurality of estimation signals related to the target. The method comprises one or more iterations, each associated with a given moment and comprising a step of applying an invariant extended Kalman filter, each iteration providing an estimation of the status of the target represented by status data comprising a set of status parameters and an associated covariance matrix. The status data is defined in relation to a reference point associated with the position of the mobile radar at the moment in question. Each current iteration comprises: - an application of a transformation operation to the reference point (401), which provides a transformed reference point, the transformed reference point being associated with the position of the mobile radar at the moment associated with the current iteration; - an updating (402) in the transformed reference point of the status data determined in the previous iteration; - an application of the invariant extended Kalman filter. The step of applying the invariant extended Kalman filter comprises the steps consisting in: - Determining an a priori estimated status of the target (403) defined in the transformed reference point using data comprising the status data determined in the previous iteration that was updated in the transformed reference point, - Determining an a posteriori status of the target (404) defined in the transformed reference point using data comprising the data from the a priori estimated status of the target and the data from at least one of the estimation signals.