Sequential measurement processing is of benefit to both estimation accuracy and computational efficiency. When the noises are correlated across the measurement components,decorrelation based on covariance matrix factorization is required in the previous methods in order to perform sequential updates properly. A new sequential processing method, which carries out the sequential updates directly using the correlated measurement components, is proposed. And a typical sequential processing example is investigated, where the converted position measurements are used to estimate target states by standard Kalman filtering equations and the converted Doppler measurements are then incorporated into a minimum mean squared error(MMSE)estimator with the updated cross-covariance involved to account for the correlated errors. Numerical simulations demonstrate the superiority of the proposed new sequential processing in terms of better accuracy and consistency than the conventional sequential filter based on measurement decorrelation. Sequential measurement processing is of benefit to both estimation accuracy and computational efficiency. When the noises are correlated across the measurement components, decorrelation based on covariance matrix factorization is required in the previous methods in order to perform sequential updates properly. A new sequential processing method, which carries out the sequential updates directly using the correlated measurement components, is proposed. And the typical sequential processing example is investigated, where the converted position measurements are used to estimate the target states by standard Kalman filtering equations and the converted Doppler measurements are then incorporated into a minimum mean squared error (MMSE) estimator with the updated cross-covariance involved to account for the correlated errors filter. Numerical simulations demonstrate the superiority of the proposed new sequential processing in terms of better accuracy and consistency than the conventional sequential filter b ased on measurement decorrelation.