Degree: PhD or MSc (by research)

Key-words: GPS,  stochastic modelling, Kalman filtering, least squares, quality control 

Entry: Bachelors degree (preferably 1st class honours) or higher in geodesy, physics, mathematics, statistics, or related engineering / science discipline with strong mathematical background.

Supervisors:  A/Prof Mike Stewart. and Dr Nigel Penna  

Project Funding: Curtin University, Australian Research Council (requested)

Student Funding: Student is required to apply for APA, IPRS or other scholarship. Possible ARC scholarship (requested).

Collaboration: 

Resources:  Sun workstation, Bernese and in-house GPS software.

Starting Date: Unrestricted.

Computation of parameters (eg station coordinates) from raw GPS observations uses estimation theory that generally assumes the nature of the errors associated with the input data are known. Hence Gauss’s law of propagation of errors can be applied to the estimation process to derive reliability estimates of the computed parameters. In practice, however, the errors on raw GPS observations are difficult to model and reliability estimates can themselves be somewhat unrealistic.

The complexity of GPS error estimation is due to the large number of systematic error sources that can contaminate the raw data (eg Bock et al, 1986). Raw GPS data are correlated both spatially and temporally and therefore both the magnitude of residual systematic errors and the correlation between observations must be modelled before realistic reliability estimates can be derived. Recently, the improvement of stochastic modelling for GPS positioning (ie derivation of output coordinate quality) has become an important research topic. A routine technique is to approximate the standard deviations of GPS data, which are considered to be dependent on the elevation angles of the tracked satellites, using an exponential formula (eg Han, 1997). Similar exponential formulae have been proposed using the signal-to-noise ratio of raw GPS data to empirically indicate the quality of satellite data (eg Brunner et al, 1999). As these techniques are somewhat empirical, their statistical justification is theoretically dubious as they ignore correlations between raw observations. Furthermore, neither signal-to-noise ratios nor elevation angle models necessarily bear any resemblance to the ‘true’ error distribution of the raw data (Satirapod and Wang, 2000).

To date, no GPS data processing software suites assume stochastic models of raw GPS observations any more complex than the ‘elevation angle dependent models’. The Curtin University research team led by A/Prof Stewart has proposed several possible solutions. For general GPS baseline stochastic modelling, the Curtin team has applied a commonly used statistical technique, Minimum Norm Quadratic Unbiased Estimation (MINQUE) to construct a covariance matrix of GPS observations by estimating all the variance-covariance components and applying this to error estimation on static GPS baselines (Wang et al, 1998). This technique has been successfully used for quality estimation of short GPS baseline vectors. However, it is untested on regional-scale GPS networks. For kinematic GPS, the Curtin team has proposed a technique using an innovation-based adaptive Kalman filter, based on the adaptation of the measurement covariance matrix (Wang et al, 1998b). However, this type of adaptive Kalman filter is sensitive to the determination of an optimal window size which is strongly dependent on the nature of the errors in the raw data.

For this project students with strong mathematical, statistical, computing or engineering backgrounds are encouraged to apply.