Flying targets are becoming increasingly maneuverable, contributing to the growing problem of their detection with active and passive radars. Rapid acceleration causes blurring of the target echo on the range-Doppler (RD) map, which reduces the signal-to-noise ratio (SNR) in a given range and velocity cell. This paper proposes a novel, non-parametric approach to quickly and efficiently estimating target acceleration on the RD map. In the paper, a universal signal model for an active frequency-modulated continuous wave radar and a passive radar is introduced. Based on this model, an estimation algorithm has been developed that can be applied to both active and passive radars. Compared to the method known from the literature, the proposed solution is much faster (even more than 100 times) while maintaining numerical stability and allowing for the estimation of acceleration of many targets to be performed simultaneously. The proposed method was supported by simulation tests and signals from real-life active and passive radars observing a jet fighter and a drone. The obtained outcomes show that the proposed technique can be successfully used for autonomous real-time systems that detect and estimate the parameters of maneuvering vehicles.