Marginalization for Number of Track Estimation

If estimation of K is of primary interest, it can be accomplished without explicit estimation of $\mbox{\boldmath$\tau$ }_n^{i(K)}$ by marginalizing $p\left( K, \mbox{\boldmath$\tau$ }_n^{i(K)} \vert {\cal Z}^n \right)$ over the $\mbox{\boldmath$\tau$ }_n^{i(K)}$. Compared to (8), the resulting estimator,

$${\hat K} = \arg \; \; \max_{K} \; \; \left\{ p\left( K \vert... ...ath$\tau$ }_n^{i(K)} \vert {\cal Z}^n \right) \right\} \; \; ,$$ (15)

can have better performance characteristics, particularly for small number-of-measurement cases.