With the advancement of sensor technology, the disablement in 2000 of selective availability (a corrupting signal superimposed GPS broadcast signals to reduce accuracy), and the decreasing costs of computational equipment, a large number of navigational projects are becoming feasible. This thesis investigates the potential advantages for combining position based measurements (such as GPS), with acceleration based readings. The motive for this analysis was to explore localisation techniques as well as investigation the levels of achievable accuracy with a practical implementation.
The physical implementation for the study combines two complementary navigational technologies (the Global Positioning System or GPS and an inertial navigation system or INS) to track the position and velocity of a vehicle. This involves extracting data from a GPS receiver and an Inertial Measurement Unit (IMU), and processing the data with filtering techniques to estimate the navigation state.
Before measurements of the two systems could be directly filtered, a number of transformations and estimations needed to be undertaken. Firstly, GPS outputs in the form of Geodetic coordinates in NMEA-0183 sentence form, need to be decoded and then transformed into the desired format for further processing. The Geodetic coordinates are then converted into the navigation frame (N,E,D) for direct comparison with the state model
The GPS filter implementation also requires estimates of the system accuracy in the form of the measurement noise covariance. Experimentation was completed for the specific GPS card in order to characterise its error. This was undertaken through a number of stand-alone mobile tests that calculated the error of each measurement, producing an error distribution with a corresponding variance.
Since the IMU measurements are of linear and angular accelerations over three axes, integration methods must be undertaken to provide state estimates. The INS mechanisation equations utilising these measurements, are solved via the 4th order Runge-Kutta approximation providing state estimates at each time period. An appreciation for the error of the Crossbow DMU-FOG IMU was ascertained through calibration and noise analysis. The results were quite volatile, including low resolution for Y and Z axis measurements and skewness in the Z measurements. There was also evidence in cross-correlation in the covariance matrix for a static test.
Since a packaged GPS card was used, a loosely coupled filter approach had to be implemented. This was undertaken in two forms; the standard and extended Kalman filters. The standard filter utilised error state equations to predict the state estimate and update covariance. The extended filter incorporated the non-linear mechanization equations via the Runge-Kutta algorithm for state prediction. However, the Jacobian matrix estimate that is usually associated with the extended Kalman filter was not utilised. Rather, the error state model which represents a general linearised model was used for covariance propagation.
The states of the INS integration were passed through a Kalman filter using measurements of GPS position each second to update the state estimate. This involved a constant velocity assumption to provide GPS measurement estimates at the same rate as the INS, providing high speed filter updates, essential for many engineering applications.
A number of combined system experiments were undertaken in order to evaluate the processing models developed, as well as evaluating the merit of combining the two approaches. The one-dimensional test was inhibited by a number of experimental problems, corrupting the results. However, the full state modelling managed to reveal a number of trends. When the INS was unaided it produced unbounded error growth highlighting the need for position aiding with consumer-grade IMU’s. The velocity estimates suffered some volatility, however, they were updated at a much higher rate then the GPS system could provide. Additionally, GPS velocity estimates from position have the constant velocity assumption over a long period of time, making it useless for many control based applications.
There was very little difference between the results of the standard Kalman filter and the extended filter based on the non-linear differential equations. Hence, the error state standard Kalman filter provides the most desirable result as it involves less computation. However, more comprehensive experimentation is needed to make a recommendation in regard to the two models.
The experimental results forming the basis of the analysis were subject to the significant limitations of a low update rate of IMU data and limited testing time from the lack of stability of the GPS data extraction. Despite the experimental problems, the results still support the theory of the advantages of combined systems over either stand-alone option, and a framework is in place for any further investigation.