We consider the problem of estimating the state of a time-invariant linear Gaussian system in the presence of integrity attacks. The attacker can compromise p out of m sensors, the set of which is fixed over time and unknown to the system operator, and manipulate the measurements arbitrarily. Under the assumption that the system is regular and system matrix A is non-singular, we propose a secure estimation scheme that is resilient to p-sparse attack as long as the system is 2p-sparse detectable, which achieves the fundamental limit of secure dynamic estimation. In the absence of attack, the proposed estimation coincides with Kalman estimation with a certain probability that can be adjusted to trade-off between performance with and without attack. Furthermore, the detectability condition checking in the designing phase and the estimation computing in the online operating phase are both computationally efficient. Two numerical examples including the IEEE 68 bus test system are provided to corroborate the results and illustrate the performance of the proposed estimator.