(eng): The thesis is devoted to fast Bayesian algorithms, more precisely to the QRD RLS Lattice algorithm combined with hypothesis testing and applied to hand detection problem solution based on ultrasound technology. Due to the proposed structure of regression models and the offered approach to hypothesis testing in the work, the algorithm under consideration is able to solve the problem of noise cancellation and additionally to compute the distance between the hand and the device; thus, potentially enabling to identify simple gestures. Further, the algorithm was implemented in parallel on the HW platform of Xilinx Zynq Ultrascale+ device with a quad-core ARM Cortex A53 processor and FPGA programmable logic and proved to function reliably and accurately in real time using real data from an ultrasound microphone.\nThe work contains an investigation of the state of the art in the corresponding field and gives the theoretical background necessary for the development and modification of the algorithm to fulfill the goals of the thesis.\nThe thesis also includes thorough description of experiments and an analysis of the results including those from simulation and from computation using real ultrasound data both in the MATLAB R2019b environment and on the HW platform of Xilinx Zynq Ultrascale+.