In the modern domain of edge sensing and physically compact smart devices, mmWave radar has emerged as a prominent modality, simultaneously offering high-resolution perception capacity and accommodatingly small form factor. The inevitable presence of device motion, however, corrupts the received radar data, reducing target sensing capability and requiring active correction to address the resultant spectral "blurring". Existing motion compensation techniques utilize computationally intensive post-processing algorithms and/or auxiliary hardware, aspects ill-suited for resource-limited edge devices requiring minimal system latency and complexity. Early works also often consider motion dynamics such as pure single-mode vibration, neglecting additional modes as well as non-harmonic motion content. We resolve both of these limitations by presenting a real-time-compatible, generalized complex motion compensation algorithm capable of correcting multicomponent platform trajectories involving both non-harmonic transients and multimode harmonic vibration. The proposed anchor-based approach achieves average SNR gains of 24.9 dB and 19.7 dB across transient duration and target velocity, respectively, and average multimode harmonic suppressions of 38.9 dB and 29.4 dB across vibration parameters and target velocity, respectively. These results, combined with minimal latency (≤ 240 ms), low algorithmic complexity, and the elimination of any additional auxiliary sensors, render the proposed method suitable for deployment in typical edge sensing applications.INDEX TERMS Real-time sensing, mmWave radar, high-resolution radar, imaging radar, complex motion, deconvolution, radar signal processing, anchor point.