Weighted State Estimation for Nonlinear Filter Consistency
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Solution Overview
Problem
Existing state estimators, such as the extended Kalman filter, face issues with linearization errors and overconfidence, particularly when dealing with non-linear systems and nuisance states that vary rapidly, limiting their effectiveness in providing accurate state estimates.
Innovation Solution
The introduction of a partial-update Schmidt-Kalman filter (PSKF) that uses state update weights to selectively update state estimates, allowing for flexible tuning and accommodating higher degrees of uncertainty and non-linearity, thereby improving the accuracy and robustness of state estimation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If an extended Kalman filter is used to estimate states in non-linear systems, then the estimator can handle non-linear dynamics, but linearization errors cause filter overconfidence and potential divergence
Solution Approach 1:
The patent applies local quality by making the update gain state-dependent through the use of state update weights that are selectively applied to different states based on their uncertainty characteristics. This allows the filter to adapt locally to the specific properties of each state rather than applying a uniform update strategy, thereby reducing linearization errors while maintaining non-linear system handling capability
Solution Approach 2:
The patent implements dynamics by introducing time-varying state update weights that adapt the filter's behavior based on current system conditions. The weights are dynamically adjusted to reflect the actual uncertainty in nuisance states, allowing the filter to transition between more and less aggressive updating strategies as system conditions change, thus improving reliability without sacrificing adaptability
2Reliability
If the Schmidt-Kalman filter fixes nuisance states to address linearization errors, then filter consistency improves, but the estimator cannot provide better estimates of rapidly varying states
Solution Approach 1:
The patent resolves this contradiction by making the state update weights dynamic and adaptive rather than fixed. The weights are adjusted based on the actual uncertainty characteristics of each state, allowing the filter to automatically transition between fixing states (when uncertainty is low) and updating states (when uncertainty is high), thus maintaining both consistency and adaptability
Solution Approach 2:
The patent applies parameter changes by modifying the update gain parameters (state update weights) based on the uncertainty properties of each state. This allows the filter to adapt its updating behavior to match the actual system conditions, enabling it to handle both slowly varying and rapidly varying states effectively without compromising filter consistency
3Measurement precision
If full state updates are applied in traditional Kalman filters, then all states are continuously estimated, but linearization errors in nuisance states cause overconfidence and divergence
Solution Approach 1:
The patent applies partial action by selectively updating only certain states based on their uncertainty characteristics rather than applying full updates to all states. The state update weights control the degree of updating for each state, allowing the filter to apply partial updates to nuisance states with high uncertainty while maintaining accurate estimation for other states, thus improving both precision and reliability
Data Source
AI summary
Properties of a physical system are measured and used to update estimated states of the system in an iterative manner. At each iteration, a state update weight is assigned for each state and the states are predicted from previous estimated states. System states are predicted from prior estimates and then updated dependent upon the measurements and the state update weights to provide updated estimated states. In addition, a prior covariance matrix of state errors is updated dependent upon the state update weights to provide an estimation error covariance matrix that is consistent with the updated estimated states. The updated state may be equivalent to a weighted sum of a prior estimated state and an initial updated estimated state. The approach provides improvements to a variety of estimators, including least squares estimators and estimators such as the Extended, Schmidt and Unscented Kalman Filters and the Rao-Blackwellized Particle Filter.