Standard Kalman filtering does not handle time-delayed measurements, and if the delay is significant, large estimation errors may accumulate over time. Furthermore, the delay value is typically unknown and variable in many real applications. To fuse measurements with unknown time delays, this study incorporates a parameter estimation technique into state estimation. In the combined parameter-state estimator, we directly estimate the delay value as an additional state and simultaneously obtain refined state estimates in the modified Kalman filter that compensates for delayed measurements. Since estimated delay value has some constraints, the estimator requires both interpolation and the truncation of the probability density function. Monte Carlo simulation results of this study show that this approach is more reliable than existing approaches for state estimation using measurements with unknown time delays.