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 S operator, which approximates the continuous time derivative operator \( \frac{d}{{dt}} \). 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 δ operator and also discuss some practical considerations in recursive least squares parameter estimation.