Abstract
The Bayesian formalism for a continuous measurement of solid-state qubits is derived for a model which takes into account several factors of the detector nonideality. In particular, we consider additional classical output and backaction noises (with finite correlation), together with quantum-limited output and backaction noises, and take into account possible asymmetry of the detector coupling. The formalism is first derived for a single qubit and then generalized to the measurement of entangled qubits.