Number-of-Track Estimation

Exact implementation of either the joint $K, \mbox{\boldmath$\tau$ }_n^{i(K)}$estimator or the marginalized K estimator requires calculation of costs for all hypothesized track sets $\mbox{\boldmath$\tau$ }_n^{i(K)}$ for all possible K. This in not practical. Alternatively we use the MHT Viterbi algorithm to prune and merge. Assume that K_max is the largest possible value of K. For the trellis and algorithm described in Subsections 4.1 and 4.2 above, consider a trellis for a fixed value of K_max. Embedded in the branch and path costs of this trellis are all of the costs required to evaluate all K-track set hypotheses for all $K=0,1, \cdots , K_{max}$. So, we can use this single trellis structure to solve the K estimation problem. The number-of-tracks estimator we have implemented:

1)

Constructs the trellis for K=K_max.

2)

Employs the Viterbi MHT algorithm to prune hypothesized track sets.

3)

Uses track costs stored in the trellis to generate track set costs for $K=0,1, \cdots , K_{max}$.

4)

Estimates K using (a merged/pruned version of) either (14) or (15).