a problem of *quantum filtering*, [@BB91], [@VPB92], [@VPB92a], [@HC93], [@WM93], [@AB03], [@BHJ07], [@WM10]. The current state of the art for quantum filtering considers incoming light in a vacuum or other Gaussian state, with quadrature or counting measurements. Both single photon states of light, and superpositions of coherent states of light, are highly non-classical, and are fundamentally different from Gaussian states. In view of the increasing importance of these non-Gaussian states of light, the purpose of this paper is to solve a quantum filtering problem for systems driven by fields in single photon states and superpositions of coherent states.

In the case of single photon fields, the master equation describing unconditional dynamics was shown to be a system of coupled equations in [@GEPZ98], a feature of non-Markovian character. Markovian embeddings were used in [@HPB04] to derive quantum trajectory equations (quantum filtering equations) for a class of non-Markovian master equations. In recent work, the authors have shown how to construct ancilla systems to combine with the system of interest to form a Markovian extended system driven by vacuum from which quantum filtering results may be obtained for single photon states and superpositions of coherent states from the standard filter for the extended 