This paper proposes a belief propagation (BP)-based algorithm for sequential detection and estimation of multipath component (MPC) parameters based on radio signals. Under dynamic channel conditions with moving transmitter/receiver, the number of MPCs, the MPC dispersion parameters, and the number of false alarm contributions are unknown and time-varying. We develop a Bayesian model for sequential detection and estimation of MPC dispersion parameters, and represent it by a factor graph enabling the use of BP for efficient computation of the marginal posterior distributions. At each time step, a snapshot-based parametric channel estimator provides parameter estimates of a set of MPCs which are used as noisy measurements by the proposed BP-based algorithm. It performs joint probabilistic data association, and estimation of the time-varying MPC parameters and the mean number of false alarm measurements, by means of the sum-product algorithm rules. The algorithm also exploits amplitude information enabling the reliable detection of "weak" MPCs with very low component signal-to-noise ratios (SNRs). The performance of the proposed algorithm compares well to state-of-the-art algorithms for high SNR MPCs, but it significantly outperforms them for medium or low SNR MPCs. Results using real radio measurements demonstrate the excellent performance of the proposed algorithm in realistic and challenging scenarios.