Nonparametric Estimation of Trends in Linear Stochastic Systems
Abstract
Techniques for the estimation of unknown additive trends present in the state and measurement processes of a Kalman-Bucy linear system are introduced. We obtain asymptotic results describing the performance of the estimators under i.i.d. and periodic observation schemes. The observed process is given by dY(t) = g(t) dt + dZ(t), where Z is the measurement process and g is an unknown trend function, and there is an additive trend f present in the state process X. These two cases need to be treated separately in order to ensure identifiability. The problem is to estimate f and g, and remove them from the measurement process. Trend removal involves replacing f and g in the Kalman filter X(t) = E(X(t) FYt)-based on observation of Y-by appropriate estimates. We show that this can be done under the following observation schemes: (I) n i.i.d. replicates of Y over a fixed interval 0,T, (II) observation of a single trajectory of Y over a long interval 0,NT, where f, g and the functions defining the linear system are periodic with period T. Keywords: Volterra integral equations; Nonparametic estimates.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1989
- Accession Number
- ADA213741
Entities
People
- Ian W. Mckeague
- Tiziano Tofoni
Organizations
- Florida State University