Gradient-Based Filter for Noisy State Estimation
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Solution Overview
Problem
Existing filtering methods, such as Kalman filters, are sensitive to outlier observations and non-Gaussian noise, leading to misclassification of observations as outliers and divergence from the ground truth state, especially during rapid state changes.
Innovation Solution
A gradient-based method is introduced to learn weighted updates for filter states, where outlying observations are weighted less heavily than inlying observations, using a loss function that penalizes large contributions from outlier observations, allowing for improved outlier rejection and robust state estimation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional Kalman filtering is applied to combine observations, then the ability to estimate system state with lower error than individual observations is improved, but sensitivity to outlier observations and non-Gaussian noise causes misclassification and divergence from ground truth state
Solution Approach 1:
The patent applies preliminary action by performing backward filtering (smoothing) using future observations before final state estimation. The method computes predicted states forward in time, then uses backward recursion to refine these predictions by incorporating future observations, thereby identifying and correcting outlier observations before they cause divergence from ground truth state.
Solution Approach 2:
The patent implements feedback by using the computed predicted states and their covariances to evaluate the consistency of current observations with future observations. The backward filtering process provides feedback about whether current observations are consistent with the system's predicted evolution, allowing the method to identify and downweight outlier observations that would otherwise cause divergence.
2Reliability
If gating mechanism is applied to reject outliers based on distance measure, then outlier rejection capability is improved, but during rapid state changes the filter's projected state becomes poor estimate causing misclassification of valid observations as outliers
Solution Approach 1:
The patent applies preliminary action by computing predicted states forward in time using the motion model before performing the actual state estimation. These predicted states serve as a reference framework that accounts for expected system evolution, allowing the backward filtering process to distinguish between rapid legitimate state changes and actual outlier observations.
Solution Approach 2:
The patent introduces another dimension by incorporating future observations (temporal dimension) into the current state estimation process. By using backward filtering that looks ahead in time, the method gains additional temporal context that helps distinguish between rapid state changes (which will be confirmed by future observations) and outliers (which will not be consistent with future observations).
Data Source
AI summary
A computer-implemented method of filtering noisy observations of a system to estimate a state of the system, the method comprising: applying a filter to a sequence of observations based on one or more filter parameters, to compute a set of system states, the filter parameters configurable to change respective contributions of the observations to the set of system states; wherein the filter is applied in multiple iterations with different values of the configurable parameter(s), to update the set of system states, wherein the different values of the configurable filter parameter are determined via a gradient-based optimization of a loss function that penalizes values of the configurable parameters that result in relatively large contributions from outlier observations that deviate from the set of system states by a relatively large amount.