The Relationship between Discrete Time and Continuous Time Linear Estimation

We examine the problem of discrete time system estimation while not ignoring the underlying continuous time system. This leads to the use of a new discrete time operator, the ffi operator, which approximates the continuous time derivative operator d dt . We use this to formulate system estimation algorithms, and discuss their significantly superior numerical properties when compared to the equivalent shift operator formulated algorithms. We provide an overview of this new ffi operator and also discuss some practical considerations in recursive least squares parameter estimation. 1 Introduction Discrete time system analysis is usually done using the q forward shift operator and associated discrete frequency variable z. Unfortunately, the discrete domains resulting are unconnected with the continuous domains which spawn them. This is because the underlying continuous domain descriptions cannot be obtained by setting the sampling period to zero in the discrete domain approximations to t..