State Uncertainty Control Using Student-t Noise Estimation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing control systems face challenges in handling uncertainty in system dynamics, particularly when noise parameters are unknown or varying, leading to suboptimal performance and instability, as conventional methods like the Kalman filter are not applicable in such scenarios.
Innovation Solution
The approach involves estimating probabilistic parameters of process and measurement noise distributions using transformations between Gaussian and Student-t distributions, allowing for uncertainty capture in control methods designed for Gaussian assumptions, while avoiding convergence to a Gaussian distribution that fails to account for uncertainties.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the Kalman filter is used for state estimation in linear state-space models, then optimal estimation performance is achieved under Gaussian noise assumptions, but the filter becomes inapplicable or suboptimal when noise parameters are unknown or varying
Solution Approach 1:
The patent transforms the problem by changing the distributional assumption from Gaussian to Student-t distribution, which has additional parameters (degrees of freedom) that can adapt to unknown noise conditions. This parameter change allows the filter to handle varying noise characteristics while maintaining estimation accuracy.
Solution Approach 2:
The patent introduces dynamic adaptation by allowing the noise parameters (particularly the degrees of freedom parameter of the Student-t distribution) to be estimated and updated recursively over time. This dynamic approach enables the filter to adapt to changing noise conditions rather than requiring fixed Gaussian assumptions.
2Measurement precision
If noise parameters are manually tuned in practice, then filter performance can be optimized for specific conditions, but the process becomes challenging, time consuming, and tedious
Solution Approach 1:
The patent implements self-service by enabling the filter to automatically estimate and adjust its own noise parameters (mean and covariance of process noise, measurement noise, and degrees of freedom) from the data itself. This eliminates the need for manual tuning while maintaining optimal performance under varying conditions.
Solution Approach 2:
The patent incorporates feedback mechanisms where the estimated state and noise parameters are continuously updated based on new measurements and predictions. This recursive feedback loop allows the system to automatically adapt to changing conditions without external intervention.
3Adaptability or versatility
If the state vector is augmented to include noise parameters for estimation, then unknown parameters can be estimated, but the estimation problem becomes unnecessarily complex with a larger state vector
Solution Approach 1:
The patent segments the estimation problem by separating the state estimation from the noise parameter estimation. Instead of jointly estimating everything in a single augmented state vector, the method uses the Student-t distribution framework to handle noise parameters separately, reducing overall complexity.
Solution Approach 2:
The patent introduces the Student-t distribution as an intermediary mathematical framework that bridges the gap between Gaussian assumptions and unknown noise parameters. This intermediary distribution allows noise parameters to be estimated without requiring direct augmentation of the state vector, simplifying the overall estimation problem.
Data Source
Figure 1A
Figure 1B
Figure 1C
AI summary
An apparatus for controlling a system includes a memory to store a model of the system including a motion model of the system subject to process noise and a measurement model of the system subject to measurement noise, such that one or combination of the process noise and the measurement noise forms an uncertainty of the model of the system with unknown probabilistic parameters, wherein the uncertainty of the model of the system causes a state uncertainty of the system with unknown probabilistic parameters. The apparatus also includes a sensor to measure a signal to produce a sequence of measurements indicative of a state of the system, a processor to estimate a Gaussian distribution representing the state uncertainty, and a controller to determine a control input to the system using the model of the system with state uncertainty represented by the Gaussian distribution and control the system according to the control input. The processor is configured to estimate, using at least one or combination of the motion model, the measurement model, and the measurements of the state of the system, a first Student-t distribution representing the uncertainties of the model and a second Student-t distribution representing the state uncertainty of the system, the estimation is performed iteratively until a termination condition is met, and fit a Gaussian distribution representing the state uncertainty into the second Student-t distribution.