The covariance matrix of unknown parameters has important roles to perform back analysis. In this study, we discuss two topics related to the covariance matrix. When we perform the back analysis with several construction or observation steps, the unknown parameters can be estimated totally from observation data of all steps if the result of back analysis of every step is succeeded to the next step as the prior information. The first topic is the methodology of the back analysis with time update. We discuss the effect of process noise, which is added to the covariance matrix in the update procedure. The second topics is the performance index for senser locations, based on the covariance matrix of unknown parameters or conditional responses. The usefulness of the index is demonstrated for a sensor locations of an embankment model.