Optimal linear data fusion for systems with missing measurements

In this paper, we provide the optimal data fusion filter for linear systems suffering from possible missing measurements. The noise covariance in the observation process is allowed to be singular which requires the use of generalized inverse. The data fusion process is made on the raw data provided by two sensors  observing the same entity. Each of the sensors is losing the measurements in its own data loss rate. The data fusion filter is provided in a recursive form for ease of implementation in real-world applications.