This technical note focuses on designing a novel optimal estimation approach for linear discrete-time systems with time-delay and multi-error measurements, inspired by the measurement demands of the Five-hundred-meter Aperture Spherical radio Telescope. Measurement errors from different measurement channels, which are considered equal in many previous estimation methods, are usually negatively correlated with time-delays. Measurements with higher time-delays usually have less errors than the ones with lower delays. Our approach improves the estimation accuracy by decreasing the usage rate of measurements with larger errors. To prove the optimality of the approach in the minimum mean square error sense, a derivation procedure is presented. A numerical example and comparison are also given to demonstrate the feasibility and advantage of the proposed approach.