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Extra info for Adaptive High-Resolution Sensor Waveform Design for Tracking (Synthesis Lectures on Algorith and Software in Engineering)

Sample text

This is true even if, in practice, it is weighted against the whole posterior density. This is important as partitions can be proposed performing no data association. 4. TRACKING MULTIPLETARGETS:THE INDEPENDENT PARTITION PARTICLE FILTER Next, the assumptions that are used to implement the IP algorithm are presented more explicitly. The first assumption is that the dynamics of the particles are independent. Thus, the state transition density of the combination of the partitions, each representing the state of a targets, can be factorized as the following: L n )= p(Xkn |Xk−1 n n p(xl,k |xl,k−1 ).

Therefore, many of the particles that are built receive low weights at the particle weighing step. For example, some of the partitions of the particle might be very good estimates of the state vector of certain targets, while other partitions in the same particle can be bad estimates of other target’s state vectors. Thus, many particles can be composed of both good and bad estimates. This results in particles receiving an overall low weight, due to the bad partitions. The IP algorithm [42], offers a method of constructing better particles.

Iτn For iν = 0, . . 20) λ,k n }N Sample jn ∼ {b˜λ,k n =1 j n = x˜ n xλ,k λ,k j bn = b˜ n λ,k λ,k Particle Weighting: n . . 21) For each particle n = 1, . . 3. SCHEME FOR ADAPTIVE WAVEFORM SELECTION USING IPLPF 55 randomness. Specifically, the predicted error will also depend on the estimate of the multitarget state n n n N Xˆ k = N n=1 k Xk . This estimate depends on the set of particles {Xk }n=1 that will be sampled by the particle filter. A different set of particles, however, may be generated if we were to rerun time step k of the algorithm while keeping the true target state Xk , target strengths Ak , and noise terms vk fixed.