Bayesian filters are most often used to predict the behaviour of dynamic objects in the presence of noise with a non-Gaussian distribution. Another application can be the filtration of measurement data obtained from measurement systems. Noise is present in almost all experimental data, and its distribution is often non-Gaussian. The article presents the application of Bayesian filtering methods to noisy data. For testing, real experimental data and artificially generated and noisy data with a known distribution were used. The following were used for testing: Generic Particle Filter, SIR Particle Filter, Auxiliary Particle Filter, and Regularized Particle Filter. The effect of the number of inserted particles on the estimated result data was examined. The Peak Signal-to-Noise Ratio (PSNR) measure was used to assess the quality of the estimation. The results showed a significant advantage of the Auxiliary Particle Filter over the other Bayesian filters. The same data sets were then subjected to Kalman filters. A basic and an extended Kalman filter were used. It turned out that all the Bayesian filters used, even for a small number of particles, give higher PSNR values than the commonly used Extended Kalman Filter.