To reduce the computational complexity of the Kalman filter an inverse free Kalman filter (IFKF) was proposed recently in [1]. The IFKF is a trade-off between complexity and accuracy. Motivated by the observation that the innovation covariance matrix structure largely depends on the structure of the observation matrix, in this manuscript, we propose a generalized inverse-free Kalman filter (GIFKF). The proposed GIFKF is a generalization of the IFKF to cases where there are redundant measurements or measurements with strong correlations. Though not encountered often, the case of redundant measurements still has a considerable number of applications. In such cases, we note that the assumption of diagonal dominance on the innovation covariance matrix may no longer be reasonable and could result in poor performance of IFKF. The GIFKF proposed in this paper alleviates this problem by replacing the diagonal dominance assumption with block diagonal dominance, which improves the accuracy and applicability compared to the IFKF. The accuracy of the proposed method and the conformity of the assumption of block diagonal dominance in the case of redundant measurements is established through simulation results. © 2019 IEEE.