In the practice of tidal analysis and prediction, the number and kind of astronomical tidal components that are to be included in a tidal model depend on the length of available tidal record and the desired accuracy of prediction. Since tidal frequencies, including shallow water constituents, are distributed unequally in a few narrow frequency bands, an inappropriate selection of tidal constituents to be included in the analysis and prediction may cause the normal equations to become ill-conditioned, or even singular, and the prediction to become poor. This investigation shows how to construct lumped tidal frequencies which better characterize ocean tides with diminishing length of observational series. Further, a sequential tidal analysis model is proposed and an algorithm for its implementation is presented, which can rigorously update a tidal solution when the number of observations increases. The algorithm also brings in automatically additional tidal constituents without a large amount of computation work; the CPU time for this analysis is only about 4 percent of that for the conventional harmonic technique. The sequential algorithm for ocean tidal analysis and prediction has a potential to be used in tide gauge stations for providing continuous up-to-date tidal prediction.