In estimation of fixed parameters of vector autoregressive moving-average (VARMA) models, the Kalman filter (KF) has been used to estimate time-varying model states, in particular, when data are partly missing periodically or non-periodically, e.g., when not all variables are observed at the same frequency. A "flipped" KF has also been used to estimate time-varying parameters. But, then, the KF cannot also handle missing data. The paper shows how two such "dual" KFs can be operated simultaneously to estimate VARMA models with time-varying parameters using partly missing data. The key numerical step in a KF computation is evaluating a matrix Riccati equation. The paper shows that the Riccati equations of two such dual KFs converge to each other and are evaluated in their converged form, which is illustrated numerically. The included proof of this result hinges on proving that the dual-coupled Riccati iterations converge.