Observers are usually formulated as explicit systems of differential e
quations and implemented using standard ODE solvers, In this paper, we
show that there can be advantages in formulating the observer as a di
fferential-algebraic equation (DAE), We propose a canonical DAE observ
er and show that it can be implemented using standard DAE solvers, The
DAE implementation of the observer can be considered regardless of th
e design philosophy used. We present a simple design strategy for this
canonical DAE observer based on the extended linearization method.