  We study the convergence properties of state estimates of an oscillating
qubit being monitored by a sequence of \textit{discrete}, unsharp measurements.
Our method derives a differential equation determining the evolution of the
estimation fidelity from a single incremental step. When the oscillation
frequency $\Omega$ is precisely known, the estimation fidelity converges
exponentially fast to unity. For imprecise knowledge of $\Omega$ we derive the
asypmtotic estimation fidelity.
