Propagating the transition probabilities ω j → i,t (S j,t − 1,S i,t ) across the whole sequence from left to right and from right to left, respectively, and marginalizing according to (5), will produce the posterior probabilities of each estimated d k.
The cardinalized PHD (CPHD) filter [20] is a variation of the PHD that is able to propagate the entire probability distribution on the number of objects.
Like the MLSE algorithm, the MAP algorithm uses the model in (4) on a trellis, but unlike the MLSE algorithm, the MAP algorithm propagates the transition probabilities forward from past states to future states, as well as backwards from future states to past states, after which the marginalized probability for each estimated symbol/codeword d t is produced, given past and future information.
It is not difficult to imagine that such biases will propagate in the probability forecasting of seismicity at a timescale of weeks or months and cause big errors.
The analysis is conducted by treating the model parameters as random variables, assigning each a suitable probability density function, and propagating the parametric uncertainties through to the predicted species concentrations.
Based on point mass representations of probability densities, particle filters operate by propagating the particle estimation and can be applied to any state-space model [26 29].
Depending on how the destination-probability cost γ p is computed for expanding the seeds and for propagating the 'skinness', we consider two variants of our method.
We first establish a Bayesian recursion, which propagates the target state probability density function.
Unlike the computationally intensive particle filtering solution retained in [12], we use a Gaussian mixture approximation [15] with a single Gaussian per delay/Doppler bin to propagate the target state probability density function (pdf) over time.
The proposed filter jointly propagates the marginal distributions and existence probabilities of each target in the filter recursion.
