The problem of state estimation in continuous-time linear stochastic systems is considered with several constraints on the available information. It is stipulated that the model of the system contains several unknown parameters and the observation process is randomly time-sampled. The classical solution due to Kalman-Bucy cannot be implemented in that case, and we revisit the idea of partitioning the set of unknown parameters, and consider multiple filters corresponding to each possible value of the unknown parameter. The posterior distribution of the unknown parameters conditioned upon available observations is computed from Bayes' rule. The resulting state estimate is a weighted sum of the state estimates generated by multiple Kalman filters, where the weights are determined by the posterior distribution of the unknown parameters. We analyze the performance of the algorithm by looking at its asymptotic behavior and establishing boundedness of the error covariance matrix.