To complement the conventional fusion methodologies of state fusion and measurement fusion, a time-propagated measurement fusion methodology is proposed. Various aspects of common process noise are investigated regarding information preservation. Based on time-propagated measurement fusion methodology, four compression filters are derived. The derived compression filters are efficient in asynchronous sensor fusion and fault detection since they maintain correct statistical information. A new batch Kalman recursion is proposed to show the optimality under the time-propagated measurement fusion methodology. A simple simulation result evaluates estimation efficiency and characteristic.