For Inverse Synthetic Aperture Radar (ISAR) imaging of maneuvering targets, the Doppler frequency induced by an arbitrary scatterer on the target is time-varying, and hence the traditional Range-Doppler (RD) algorithm is not appropriate for obtaining focusing ISAR images. In such a scenario, a novel ISAR technique, called range instantaneous Doppler derivatives (RIDD) algorithm has been recently proposed and two different kinds of well-focused ISAR images, named range Doppler centroid frequency (RDC) image and range Doppler frequency rate (RDR) image can be obtained. In order to improve the accuracy of the target classification and recognition, scaling approach for RIDD algorithm must be taken into consideration. In this paper, the point spread factor (PSF) representations and cross-range scaling factors of RDC image and RDR image obtained by RIDD algorithm are demonstrated analytically. On the basis of the PSFs and cross-range scaling factors, a novel imaging and scaling approach for RIDD algorithm in the presence of a low SNR environment based on Smoothed Integrated High-Resolution Time-Frequency-rate Representation (SIHR) combined with Coherent Integrated Smoothed Generalized Cubic Phase Function (CISCF) is proposed. As the proposed algorithm has high estimation accuracy and good antinoise capability, precise parameter estimation of the received signal can be achieved. Hence, high-quality scaled RDC and RDR images of the target can be reconstructed by the proposed approach. Experimental results of simulated data and real measured data verify the correctness of the PSF representations and demonstrate the effectiveness of the imaging and scaling approach proposed in this paper.