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In this paper, we describe a cognitive radar (CR) that mimics the visual brain. Although the visual brain and radar are different in that the visual brain does not transmit a probing signal to the environment while the active radar greatly relies on the probing signal it transmits to the environment, both of them are observers of the surrounding environment. As such, there is much that we can learn from the visual brain in building a new generation of CRs that outperform traditional radars. In this paper, we confine the discussion, in both analytic and experimental terms, to CR aimed at target tracking. From a theoretical perspective, using the posterior Cramér-Rao lower bound (PCRLB), it is shown that a cognitive tracking radar has the potential to improve tracking performance significantly. In particular, computer experiments are presented, which demonstrate that CR can indeed go beyond the theoretical limits of traditional active radars (TARs) as well as fore-active radars (FARs); the latter are radars equipped with feedback from the receiver to the transmitter. Moreover, computer experiments are presented to demonstrate another practical benefit resulting from the combined use of memory and executive attention in CR for a target-tracking application. Specifically, it is shown that with the provision of these two cognitive processes, the transition in switching from one transmit waveform to another goes forward in a smooth manner. Such a capability is beyond that of TAR or FAR.