Dispersion curves in ocean environments are accurately estimated from received signals through the extraction of instantaneous modal frequencies and corresponding arrival times for long-range propagation. The ultimate goal is to estimate sediment sound speed using the extracted dispersion pattern. The approach extends work previously conducted in dispersion tracking with sequential filtering, improving on the latter technique. The sequential state-space method that is developed for the extraction of time-frequency information from specific time instances relies on a representation of those as a sum of elemental pulses, resulting from analysis of the received field. The method is tested on synthetic noisy data with different noise levels. After dispersion probability density functions are estimated via a particle filter, they are subsequently employed for sound speed inversion. Correct mode identification is a challenge impacting inversion; this is demonstrated through two examples and a way to remedy the problem is discussed.