 By Ioannis Kyriakides, Darryl Morrell, Antonia Papandreou-Suppappola, Andreas Spanias

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

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3). Using similar arguments as in the single partition case, we approximate the likelihood for each particle to U N p1n n (yu,k |Xkn n p0n (yu,k |Xkn ) , ) u=1 n=1,n=n n |X n ) p1n (yu,k k where is the likelihood given that the target state equals Xkn and p0n (ykn |Xkn ) is the likelihood when no targets exist having state Xkn . The weight of particle n  using the assumptions above is given by wkn = n k−1 Dividing by the constant U n u=1 p1 U u=1 wkn = N n=1,n=n n λ=1 bλ,k n |X n ) (yu,k k N n n n n=1 p0 (yu,k |Xk ), we n k−1 n |X n ) p0n (yu,k k n p(Xkn |Xk−1 ).

In this section, we explain how the return signal is processed by a radar system and how information on range and range rate is obtained. A radar system collects information regarding the range and range rate of a target relative to the radar sensors by transmitting signal pulses and processing the return reflected by a target of interest. The return signal bears information on the range of a target rl,k relative to a sensor u = 1, . . , U of the radar system in the form of a time delay τu,k relative to the transmitted signal cτ as ru,k = 2u,k , where c is the velocity of propagation of the signals.

A local approximation of the optimal importance density can be obtained with the use of local linearization techniques . A very simple to use importance density is the kinematic prior, p(xk |xk−1 ), which is easy to sample from and its use reduces the weight equation on being dependent on the measurement likelihood. This, however, often causes many particles to be generated that do not represent the posterior adequately, especially when the measurement likelihood is significantly more peaked than the kinematic prior.