Uncertainty-Aware Model-Based Control With Student-t State Estimation
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Solution Overview
Problem
Existing control systems face challenges in handling uncertainty in system dynamics, particularly when noise parameters are unknown or uncertain, leading to suboptimal performance or instability, as conventional methods like the Kalman filter are not applicable in such cases.
Innovation Solution
The system employs a model that includes both a motion model and a measurement model, using a Student-t distribution to represent uncertainties and iteratively estimates parameters to fit a Gaussian distribution, allowing for control input determination and system control despite unknown probabilistic parameters.
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 method becomes inapplicable when noise parameters are unknown or uncertain
Solution Approach 1:
The patent transforms the fixed Gaussian noise assumption into adaptive parameter estimation by introducing time-varying noise parameter estimates. The Kalman filter is modified to continuously update noise parameters (Q and R matrices) based on measurement residuals and innovation sequences, allowing the estimator to adapt to changing noise characteristics while maintaining optimal performance.
Solution Approach 2:
The estimation algorithm performs self-calibration by using the measurement data itself to estimate noise parameters. The method computes noise statistics from the innovation sequence and measurement residuals without requiring external calibration data or manual tuning, enabling the system to automatically adapt to unknown noise conditions.
2Measurement precision
If noise parameters are manually tuned in practice, then some level of performance can be achieved, but the process becomes challenging, time consuming, and tedious
Solution Approach 1:
The algorithm automatically estimates noise parameters from the measurement data using the innovation sequence and residuals. The method computes Q and R matrices directly from the data without requiring manual intervention, eliminating the time-consuming tuning process while maintaining optimal filter performance.
Solution Approach 2:
The noise parameter estimation uses feedback from the measurement residuals and innovation sequences to continuously update the Q and R matrices. This closed-loop adaptation allows the system to automatically adjust to changing noise conditions without manual re-tuning, saving time and maintaining performance.
3Adaptability or versatility
If the state vector is augmented to include noise parameters for estimation, then noise parameter estimation becomes possible, but the estimation problem becomes unnecessarily complex with a larger state vector
Solution Approach 1:
The patent separates noise parameter estimation from state estimation by using distinct computational paths. The state vector is estimated using the standard Kalman filter, while noise parameters are estimated separately from the innovation sequence and residuals. This segmentation avoids the complexity of joint estimation while achieving both objectives.
Solution Approach 2:
The method extracts noise parameter information from the innovation sequence and measurement residuals, separating it from the main state estimation process. By taking out the noise parameter estimation as a distinct task using the available statistical information, the approach avoids augmenting the state vector while still achieving noise parameter estimation.
Data Source
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.