Confidence Bounds on Identification of Linear Systems with Multiplicative Noise

Linear System Identification Under Multiplicative Noise from Multiple Trajectory Data

“…It is assumed that the multiplicative noise is observed directly so that a concentration inequality can be obtained for the estimation of the noise covariance. The authors in [29] develop, concurrently and independently of the present work, finite-sample error bounds associated with simultaneously estimating the nomial system parameters and noise covariance matrix, by using single trajectory data, which is the most relevant work to ours. A self-normalizing (ellipsoidal) bound and a Euclidean (box) bound are provided for the least-squares estimation, but it is not sure whether the bounds converge to zero under the dynamic system setting.…”

“…Remark 6 This theorem indicates that a relatively small rollout length suffices, while consistency is guaranteed by an increasing number of rollouts. In [29], the estimation of the first and second moments of multiplicative noise is decoupled, while here the estimate of [ Σ′…”

“…t , F t } is also a martingale difference sequence. To estimate the covariance matrix of the multiplicative noise, [29] applies OLS, equivalent to RLS, to the above dynamic. It should be noted that when utilizing OLS/RLS, one estimates the second moments of A + Āt and B + Bt , rather than their covariance matrices, Σ A and Σ B in our context.…”