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Due to unreliable communication between local sensors and the processing center, packet dropouts may happen during transmission. Two existing methods for linear minimum mean-squared error (LMMSE) estimation with multiple packet dropouts were obtained completely or partially based on a stochastic parameter system constructed by augmenting the original state and measurement. They have a high computational load, unclear measurement residual characterization and tough requirements on initialization. To overcome these, an alternative form of LMMSE estimation with multiple packet dropouts is derived. Under a Gaussian assumption, the minimum mean-squared error (MMSE) estimation with multiple packet dropouts is also derived. Numerical examples are provided to compare performance of the proposed estimators.