where xt+1 is the position and orientation of the robot (with respect to a reference frame) at time t + 1, with (ξ, η) giving the x and y coordinates and θ the angle (with respect to the x-axis) that the robot is facing. The robot has two drive wheels, of radius r on an axle of length d. During time period t the right wheel is believed to rotate at a velocity of φRt and the left at a velocity of φLt. In this example, these velocities are fixed with φRt = 0.4 and φLt = 0.1. The state update function, F , calculates where the robot should be at each time point, given its previous position. However, in reality, there is some random fluctuation in the velocity of the wheels, for example, due to slippage. Therefore the actual position of the robot and the position given by equation F will differ. The magnitude of these random fluctuations is included in the model through Σx.

Unscented Kalman Filterの計測への応用に関する研究

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This paper conducts performance evaluation for the ultra-tight integration of Global positioning system (GPS) and inertial navigation system (INS) by use of the fuzzy adaptive strong tracking unscented Kalman filter (FASTUKF). An ultra-tight GPS/INS integration architecture involves fusion of the in-phase and quadrature components from the correlator of the GPS receiver with the INS data. These two components are highly nonlinearly related to the navigation states. The strong tracking unscented Kalman filter (STUKF) is based on the combination of an unscented Kalman filter (UKF) and strong tracking algorithm (STA) to perform the parameter adaptation task for various dynamic characteristics. The STA is basically a nonlinear smoother algorithm that employs suboptimal multiple fading factors, in which the softening factors are involved. In order to resolve the shortcoming in a traditional approach for selecting the softening factor through personal experience or computer simulation, the Fuzzy Logic Adaptive System (FLAS) is incorporated for determining the softening factor, leading to the FASTUKF. Two examples are provided for illustrating the effectiveness of the design and demonstrating effective improvement in navigation estimation accuracy and, therefore, the proposed FASTUKF algorithm can be considered as an alternative approach for designing the ultra tightly coupled GPS/INS integrated navigation system.

Performance enhancement for ultra-tight GPS/INS integration using a fuzzy adaptive strong tracking unscented Kalman filter

This paper presents a sensor fusion method for the Ultra-Tightly Coupled (UTC) Global Positioning System (GPS)/Inertial Navigation System (INS) integrated navigation. The UTC structure, also known as the deep integration, exhibits many advantages, e.g., disturbance and multipath rejection capability, improved tracking capability for dynamic scenarios and weak signals, and reduction of acquisition time. This architecture involves the integration of I (in-phase) and Q (quadrature) components from the correlator of a GPS receiver with the INS data. The Particle Filter (PF) exhibits superior performance as compared to an Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) in state estimation for the nonlinear, non-Gaussian system. To handle the problem of heavy-tailed probability distribution, one of the strategies is to incorporate the UKF into the PF as the proposal distribution, leading to the Unscented Particle Filter (UPF). The combination of an adaptive UPF and Fuzzy Logic Adaptive System (FLAS) is adopted for reducing the number of particles with sufficiently good results. The GPS tracking loops may lose lock due to the signals being weak, subjected to excessive dynamics or completely blocked. One of the principal advantages of the UTC structure is that a Doppler frequency derived from the INS is integrated with the tracking loops to improve the receiver tracking capability. The Doppler frequency shift is calculated and fed to the GPS tracking loops for elimination of the effect of stochastic errors caused by the Doppler frequency. In this paper, several nonlinear filtering approaches, including EKF, UKF, UPF and ‘FLAS assisted UPF’ (FUPF), are adopted for performance comparison for ultra-tight integration of GPS and INS. It is assumed that no outage occurs such that the inertial sensor errors can be properly corrected and accordingly the aiding information is working well. Two examples are provided for performance assessment for the various data fusion methods. The FUPF algorithm with Doppler velocity aiding demonstrates remarkable improvement, especially in the high dynamic environments, in navigation estimation accuracy with reduction of number of particles.

/pdf/a-novel-design-for-the-ultra-tightly-coupled-gps-ins-525if2wv64.pdf

Chi-Fan Yang

Papers

Performance enhancement for ultra-tight GPS/INS integration using a fuzzy adaptive strong tracking unscented Kalman filter

A Novel Design for the Ultra-Tightly Coupled GPS/INS Navigation System