This paper proposes a burst model of chaotic noise signals with randomly stepped carrier frequencies for velocity estimation and high-resolution range imaging of high-speed moving targets. The random stepping of carrier frequencies is controlled by a combination chaotic map (CCM), which is generated by embedding a Logistic map into a Bernoulli map. The baseband noise signal adopts the CCM based frequency-modulation (CCM-FM) signal, which has good randomness and a thumbtack ambiguity function as well. The velocity estimation includes a coarse search where the coarse search is conducted with a fixed step to makes the velocity deviation less than the velocity resolution, while the precise search adopts the Golden Section Search (GSS) algorithm to get an accurate estimation of velocity. What should be emphasized is that the velocity estimation process can be completed with just a burst of subpulses. Then the spectra are coherently synthesized to obtain ultra-wide bandwidth and high-resolution range imaging. Finally, numerical simulations demonstrate a good performance of the proposed signal model and the processing algorithm.
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