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This paper proposes two novel approaches to estimate accurately mobile robot attitudes based on the fusion of low-cost accelerometers and gyroscopes. The first part of the paper demonstrates the use of a special test bench that both enables simulations of various dynamic behaviors of wheeled robots and measures their real attitude angles along with the raw sensor data. These measurements are applied in a simulation environment and we outline an offline optimization of Kalman filter parameters. The second part of the paper introduces a novel adaptive Kalman filter structure that modifies the noise covariance values according to the system dynamics. The instantaneous dynamics are characterized regarding the magnitudes of both the instantaneous vibration and the external acceleration. The proposed adaptive solution measures these magnitudes and utilizes fuzzy-logic to modify the filter parameters in real time. The results show that the adaptive filter improves the overall filter convergence by a remarkable 10.9 % over using the optimized Kalman filter, thereby demonstrating its efficacy as an accurate and robust attitude filter. The proposed filter performances are also benchmarked against other common methods indicating that the flexibility of the developed adaptive filter allowed it to compete and even outperform the benchmark filters. [ABSTRACT FROM AUTHOR]