Marginalization for Number of Track Estimation

If estimation of K is of primary interest, it can be estimated without explicit estimation of $\mbox{\boldmath$\tau$ }_n^i$ by marginalizing $p\left( K, \mbox{\boldmath$\tau$ }_n^i \vert {\cal Z}^n \right)$ over $\mbox{\boldmath$\tau$ }_n^i$. Compared to ( 20 ), the resulting estimator,

$${\hat K} = \arg \; \; \max_{K} \; \; \left\{ p\left( K \ver... ...oldmath$\tau$ }_n^i \vert {\cal Z}^n \right) \right\} \; \; ,$$ (20)

can have better performance characteristics, which can be better for small number-of-measurement cases. has different performance characteristics, which can be better for small number-of-measurement cases [10].