Speech signal formant spectrogram. How can we determine F1?
You should be able to see formants very clearly as peaks on the spectrogram slices. The 1st, 2nd ... are the several peaks. In the picture above (in the blue area) the first two peaks seem to have very similar power and so this can introduce errors in the estimation algorithm.

You can use Praat and "Show formants" option to track formants and observe their behaviour over time. You can try to make continuous transitions from vowel to vowel and then try the same vowels with a silence in the middle and observe the differences.

If you are developing an algorithm you can use a Kalman filter for tracking formants. (maybe this helps: http://link.springer.com/content/pdf/10.1007/978-3-540-85980-2.pdf#page=257)