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This paper proposes a novel sensor fusion approach using Ultra Wide Band (UWB) wireless radio and an Inertial Navigation System (INS), which aims to reduce the accumulated error of low-cost Micro-Electromechanical Systems (MEMS) Inertial Navigation Systems used for real-time navigation and tracking of mobile robots in a closed environment. A tightly-coupled model of INS/UWB is established within the integrated positioning system. A two-dimensional kinematic model of the mobile robot based on kinematics analysis is then established, and an Auto-Regressive (AR) algorithm is used to establish third-order error equations of the gyroscope and the accelerometer. An Improved Adaptive Kalman Filter (IAKF) algorithm is proposed. The orthogonality judgment method of innovation is used to identify the “outliers”, and a covariance matching technique is introduced to judge the filter state. The simulation results show that the IAKF algorithm has a higher positioning accuracy than the KF algorithm and the UWB system. Finally, static and dynamic experiments are performed using an indoor experimental platform. The results show that the INS/UWB integrated navigation system can achieve a positioning accuracy of within 0·24 m, which meets the requirements for practical conditions and is superior to other independent subsystems.

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The spatial scaling laws of velocity kinetic energy spectrum for compressible turbulence flow and its density-weighted counterpart have been formulated in terms of wavenumber, dissipation rate and Mach number by using dimensional analysis. We have applied the Barenblatt's incomplete similarity theory to both kinetic and density-weighted energy spectrum and showed that, within the initial subrange, both energy spectrums approach the -5/3 power law of the wavenumber, when the Mach number M tends to be naught, unity and infinity, respectively.