Autocovariance Least Squares with Constrained Noise Covariance Model Identification

In this paper a noise covariance model structure is proposed to constrain the solutions to an Autocovariance Least Squares (ALS) problem. These constraints enable the identification of process and measurement noise covariances simultaneously across multiple operating conditions. This approach benefits real world systems where data at a specific operating condition are limited, by utilizing data across a larger set of conditions. One such system is aircraft flight throughout a range of dynamic pressures. The structured noise covariance constraints result in identified noise covariance models as a function of the operating condition. The identified model can be used to approximate the noise covariances in between the design conditions where datasets are available. The approach is demonstrated first in simulation with a mass-spring-damper and then experimentally with the University of Washington's gust load alleviation wind tunnel test-bed. The wind tunnel ALS problem is solved simultaneously at multiple dynamic pressures with an affine noise covariance model structure. A linear Kalman filter, designed with the constrained ALS identified noise covariances, is demonstrated at a design condition and at a condition where no design data were available.