ABSTRACT
Techniques for the estimation of unknown additive trends present in the state and measurement processes of a Kalman–Bucy linear system are introduced. In real applications of the Kaiman filter to signal processing it is often found that unknown additive trends are present in the state and measurement processes. There is a vast literature on the estimation of finite dimensional parameters in discrete time linear stochastic systems. This chapter is concerned with the basic innovations representation of the observation process, identifiability, bias under misspecified trends, and schemes (I) and (II). Observation schemes may similarly be classified into two broad types: partial and full. In the survival analysis setting partial observation may arise from censoring, truncation, or grouping of the data.
