We develop a systematic framework for the joint modeling of returns and multiple daily realized measures. We assume a linear state space representation for the log realized measures, which are noisy and biased estimates of the log daily integrated variance, at least due to Jensen's inequality. We incorporate filtering methods for the estimation of the latent log-volatility process. The dependence between daily returns and realized measurement errors leads us to develop a two-step estimation method for all parameters in our model specification. The estimation method is computationally straightforward even when the stochastic volatility model has non-Gaussian return innovations and leverage effects. Our extensive empirical study for nine Dow Jones stock return series reveals that measurement errors become significantly smaller after filtering and that the forecasts from our model outperforms those from a set of recently developed alternatives.