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In this paper, we propose a novel method for the detection of objects moving with changing velocity vector with time in the transform/spatio-temporal mixed-domain (MixeD). The moving objects are considered as arbitrary trajectory signals (ATS). A trajectory signal in the MixeD is a bunch of 1-dimensional(1-D) complex signals. And an ATS is a bunch of quasi-periodic signals with pitch fluctuations in the MixeD. The proposed method is achieved by using a parallel bank of extended complex Kalman filters for the estimation of quasi-periodic signals. Experimental results show the effectivity of our approach.