Time derivative estimation of signals plays a very important role in several fields, such as signal processing and control engineering, just to name a few of them. For that purpose, a non-asymptotic algebraic procedure for the approximate estimation of the system states is used in this work. The method is based on results from differential algebra and furnishes some general formulae for the time derivatives of a measurable signal in which two algebraic derivative estimators run simultaneously, but in an overlapping fashion. The algebraic derivative algorithm presented in this paper is computed online and in real-time, offering high robustness properties with regard to corrupting noises, versatility and ease of implementation. Besides, in this work, we introduce a novel architecture to accelerate this algebraic derivative estimator using reconfigurable logic. The core of the algorithm is implemented in an FPGA, improving the speed of the system and achieving real-time performance. Finally, this work proposes a low-cost platform for the integration of hardware in the loop in MATLAB.