In this letter, we study the problem of estimating the long-run mean of the Ornstein-Uhlenbeck (OU) stochastic process and its effect on the long-term prediction of future vessel states, which is a crucial problem for Maritime Situational Awareness (MSA). We employ a sample mean estimator (SME) to estimate the key OU parameter from the observations, computing the closed-form SME covariance error in both the random and constant sampling time regimes, providing a fundamental building block of the overall long-term state prediction covariance. We show also that the SME is: root n-consistent when the sampling time is random; asymptotically efficient when the sampling time is constant; and very close to the Cramer-Raolower bound in the cases of practical interest for MSA.
Consistent Estimation of Randomly Sampled OrnsteinUhlenbeck Process Long-Run Mean for Long-Term Target State Prediction
Millefiori, LM;Braca, P;
2016-01-01
Abstract
In this letter, we study the problem of estimating the long-run mean of the Ornstein-Uhlenbeck (OU) stochastic process and its effect on the long-term prediction of future vessel states, which is a crucial problem for Maritime Situational Awareness (MSA). We employ a sample mean estimator (SME) to estimate the key OU parameter from the observations, computing the closed-form SME covariance error in both the random and constant sampling time regimes, providing a fundamental building block of the overall long-term state prediction covariance. We show also that the SME is: root n-consistent when the sampling time is random; asymptotically efficient when the sampling time is constant; and very close to the Cramer-Raolower bound in the cases of practical interest for MSA.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.