The aim of this paper is to show both analytically and numerically the existence of a subwavelength phononic bandgap in bubble phononic crystals. The key is an original formula for the quasi-periodic Minnaert resonance frequencies of an arbitrarily shaped bubble. The main findings in this paper are illustrated with a variety of numerical experiments.Mathematics Subject Classification (MSC2000): 35R30, 35C20.
Pedestrian dead reckoning (PDR) systems based on a microelectromechanical-inertial measurement unit (MEMS-IMU) providing advantages of full autonomy and strong anti-jamming performance are becoming a feasible choice for pedestrian indoor positioning. In order to realize the accurate positioning of pedestrians in a closed environment, an improved pedestrian dead reckoning algorithm, mainly including improved step estimation and heading estimation, is proposed in this paper. Firstly, the original signal is preprocessed using the wavelet denoising algorithm. Then, the multi-threshold method is proposed to ameliorate the step estimation algorithm. For heading estimation suffering from accumulated error and outliers, robust adaptive Kalman filter (RAKF) algorithm is proposed in this paper, and combined with complementary filter to improve positioning accuracy. Finally, an experimental platform with inertial sensors as the core is constructed. Experimental results show that positioning error is less than 2.5% of the total distance, which is ideal for accurate positioning of pedestrians in enclosed environment.
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