Inside GNSS Media & Research

MAR-APR 2018

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42 Inside GNSS M A R C H / A P R I L 2 0 1 8 ter bases on quantities of an inertial measurement unit (IMU), which are tightly coupled with observables of GPS and Gali- leo inside a filter algorithm. In this context, tightly coupled means the processing of inertial measurements corrected by the raw GNSS (Global Navigation Satellite System) observ- ables with lower sample rate. In contrast, a loosely coupled filter determines its GNSS-only position and velocity first to correct IMU measurement in a straightforward manner. A tightly coupled filter allows a state correction even if less than four satellites are available. Due to the usage of satellite raw data, it is possible to evaluate each GNSS observable, to cor- rect or even to exclude it. e dual-constellation mode in general enhances the satel- lite availability because of an increased total number of avail- able satellites and therefore, improves the geometrical constel- lation. Dual-frequency enables precise first-order ionospheric path delay elimination. Multiple real-world tests were carried out comparing the attained accuracy of the dual-constellation aided filter to differential corrected GNSS observables (DGPS). Results show that a 2D accuracy of up to 0.6 meters is achieved using the dual-constellation mode, which is almost as accurate as a filter using differentially corrected GPS. Tightly Coupled Navigation Filter Our tightly coupled filter bases on IMU quantities, where 3D accelerometer and 3D gyroscope measurements at a rate of 100 hertz are used within a well-known strap-down algorithm to propagate the filter states. e navigation filter estimates 18 states in total: where position p, velocity v, and biases of the accelerometers b a and gyroscopes b g incorporate three components each, atti- tude and heading are defined as a quaternion q, and the GNSS receiver clock error consists of an offset c b and a dri c d com- ponent. To provide long-term stability of the state propagation step, GNSS observables at a rate of 10 hertz are used to correct the driing filter states. During a GNSS pre-processing step the received satellite ephemeris is used to calculate satellite posi- tions at the time of signal transmission. Pseudo-ranges, delta- ranges and satellite positions are used within an error-state extended Kalman filter (EKF), which estimates the error of the current propagated state vector based on a measurement model and updates the estimated state error and covariance matrix P. is results in a 6-DOF nonlinear model as follows: Here, k is the time index, x is the state vector of the sys- tem, w is the process noise, z is the measurement, and v is the measurement noise. w and v are assumed to be normally dis- tributed with a mean of zero, where Q is the covariance matrix of the process noise (in this case the IMU noise) and R is the covariance matrix of the measurement noise included in GNSS observables. F, G and H are the state transition, noise and mea- surement matrices, respectively. e usage of a digital receiver time pulse (pulse per second; PPS) allows measuring the time delay between measurement epoch and data reception on the target platform. It enables the synchronization of IMU data with GNSS observables. By intro- ducing a data buffer for the IMU measurements and the past states, the Kalman filter update step can be performed with the (past) state at the time of measurement with a subsequent propagation to the present time. is approach improves the accuracy for highly dynamic movements. Satellite Data Pre-Processing Our EKF requires satellite position, relative velocity, and pseu- do- and delta-ranges for all observed satellites. erefore, satel- lite raw data is pre-processed to calculate the required system states for the EKF. Figure 1 sketches the applied structure of GNSS pre-processing. e satellite signals are disturbed by several environmen- tal influences causing biased pseudo-range measurements. e main influences can be summarized as ionospheric and tropo- spheric delays. e observed pseudo-range ρ r can be described with the equation: It is the sum of the real range , the satellite and receiver clock errors c S and c r , the ionosphere error , the troposphere error T r and additive measurement noise v ρ . M ρ is the multipath error, which is not corrected currently. e receiver clock error c r is dynamically estimated by the EKF. Both the GPS and the Galileo satellites transmit Kepler parameters. erefore, position and velocity calculation and clock correction algorithms for GPS and Galileo are identical. FIGURE 1 Structure of the GNSS pre-processing. Michael Breuer, Thomas Konrad, and Dirk Abel. High precision localisation in customised gnss receiver for railway applications. In Proceedings of the 29th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2016), 2016. R AILWAY APPLIC ATIONS

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