Assignment 6

Resources:

• page=141 Ch. 8

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Task 1: Number of association events in JPDA

a)

In the example in figure 8.1 we have three objects, $N=3$, and four measurements, $M=4$. We therefore get

$$\begin{array}{rl}& \sum _{m=0}^{\min (N,M)}\frac{N!M!}{m!(N-m)!(M-m)}\\ & =\sum _{m=0}^{\min (3,4)}\frac{3!4!}{m!(3-m)!(4-m)}\\ & =\sum _{m=0}^3\frac{3!4!}{m!(3-m)!(4-m)}\\ & =1+12+36+24\\ & =73\end{array}$$

b)

By including the validation gates we filter out unlikely association events. This is tiresome to find out, but it will likely be way smaller than 73, thus improving data association.