Estimation of Noise Statistics from Data and Performance Monitoring for Model Predictive Control

Travis Arnold

Our group has been actively developing methods for estimating noise statistics from data. The majority of work has focused on developing the Autocovariance Least-Squares (ALS) method (Odelson, Rajamani, and Rawlings, 2006; Rajamani and Rawlings, 2009). Results have also been obtained using maximum likelihood estimation (MLE) methods (Zagrobelny and Rawlings, 2015).

Identification of noise statistics is useful for model predictive control (MPC) because the process and measurement noise covariances must be known in order to calculate the optimal state estimator gain. Knowing these covariances is also necessary for MPC performance monitoring methods, which are used to track how well MPC systems are performing (Zagrobelny, Ji, and Rawlings, 2013).

In my current research I am collaborating with Praxair to apply the ALS method to inustrial data in order to calculate performance monitoring benchmarks for the process. My goal is to compare these results to simulations to demonstrate that the methods described above can achieve better control than is obtainable by many current industrial MPC implementations.


Brian J. Odelson, Murali R. Rajamani, and James B. Rawlings.
A new autocovariance least-squares method for estimating noise covariances.
Automatica, 42(2):303-308, February 2006.

Murali R. Rajamani and James B. Rawlings.
Estimation of the disturbance structure from data using semidefinite programming and optimal weighting.
Automatica, 45:142-148, 2009.

Megan A. Zagrobelny and James B. Rawlings.
Identifying the uncertainty structure using maximum likelihood estimation.
In American Control Conference, Chicago, IL, July 1-3, 2015.

Megan A. Zagrobelny, Luo Ji, and James B. Rawlings.
Quis custodiet ipsos custodes?
Annual Rev. Control, 37:260-270, 2013.