We present a protocol for simultaneous estimation of both quadratures of a displacement channel on a quantum harmonic oscillator using a single ancilla qubit, without complex state preparation or adaptive control. The qubit is coupled to the quantum harmonic oscillator via controlled displacements of strength $A$ and undergoes $N$ rounds of measurement and reset, while the oscillator coherently accumulates the displacement signal. Energy is injected and the non-commuting displacements imprint an order-dependent geometric phase at each round, giving a quantum Fisher information that scales as $𝒪(A^2{N}^3)$. Although the measurement record space grows as $2^N$, we show that exact likelihoods for any individual measurement record can be computed in $𝒪(N^2)$ time. We show that measurement in the computational basis approximately saturates the quantum bound and maintains the $𝒪(A^2{N}^3)$ scaling. Furthermore, the periodic information extraction makes the protocol robust to decoherence. Our results provide a framework for the design and analysis of sequential measurement in ancilla-assisted protocols.