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On the Treatment of Noise and Conspiring Bias in Dual-Frequency Differential Global Navigation Satellite Systems

Bruckner, Dean C.

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2010, Doctor of Philosophy (PhD), Ohio University, Electrical Engineering (Engineering and Technology).

Four primary contributions are made to the treatment of noise and conspiring bias for dual frequency differential Global Satellite Navigation Systems (GNSSs). These contributions enhance accuracy and protection levels for aircraft precision approach and landing operations and similar applications.

A statistical characterization is presented of Global Positioning System (GPS) user range error as an uncorrelated, normally distributed random variable with non-zero mean over the length of the aircraft precision approach operation. This leads directly to modeling GPS error in the position domain as multivariate normal with non-zero mean.

Based on this model, a vertical composite protection level VPLc and a horizontal composite protection level HPLc are each implemented as univariate normal distributions with non-zero means. A method is presented by which exact values – that is, values accurate to a user-defined error tolerance and consistent with statistical assumptions – of VPLc and HPLc are obtained, and by which computationally efficient approximations may be evaluated. A statistical quadratic form under the multivariate normal distribution is then used to derive a new class of protection levels based on the probability enclosed within a radius defined in two or more dimensions. A central chi-square representation of this quadratic form is also presented, and is incorporated into a six-step computational procedure for the two-dimensional composite radial protection level RPLc. This procedure is extended to the composite spherical protection level (SPLc) and the ellipsoidal protection level (EPLc).

Two additional algorithms are presented for dual-frequency differential Global Positioning System (GPS) use. Performance improvements are achieved first through the exchange of pseudorange noise and multipath for reducible biases using a modified Code Noise and Multipath (CNMP) algorithm applied both to reference station and aircraft ranging measurements. In this algorithm, the second frequency is used only to correct the code-minus-carrier (CMC) observable; other ionosphere errors are removed in differential processing. The corrected pseudorange measurements are then combined using a single-frequency carrier phase position domain smoothing (CPDS) algorithm. Composite vertical and horizontal protection levels for the H0 hypothesis are calculated.

The algorithms are implemented in a processing architecture suitable for short-baseline differential operations and termed Dual-Frequency Differential 1 (DFD1). They are then tested on recorded flight test data that includes six aircraft precision approaches. Performance is compared to the LAAS single-frequency architecture. Results over the entire flight data set show an improvement in vertical navigation system accuracy from 0.80 m to 0.32 m (95%), and in horizontal accuracy from 0.41 m to 0.33 m (95%). Mean reductions of the vertical and horizontal protection levels by 60% and 57%, respectively, are observed. Similarly, dramatic improvement is seen in all measures for the six 150-s approaches within this flight, including reduction in 95% error from 0.56 m to 0.26 m vertically and from 0.28 m to 0.14 m horizontally. These all demonstrate the effectiveness of the composite protection levels and the CNMP and CPDS algorithms within the DFD1 architecture.

This architecture uses C/A code on L1 and carrier phase measurements differenced over time on L1 and L2, but does not resolve integer ambiguities. Nonetheless, it achieves the same level of |μ| + 2σ navigation system error (NSE) performance in these flight tests as in all published studies of similar class systems known to the author that employ differential kinematic carrier phase architectures between ground and air and require ambiguity resolution.

Frank van Graas, PhD (Advisor)
Maarten Uijt de Haag, PhD (Committee Member)
Michael Braasch, PhD (Committee Member)
James Rankin, PhD (Committee Member)
Jacqueline Glasgow, PhD (Committee Member)
John Coulter, Colonel USAF (Committee Member)
216 p.

Recommended Citations

Citations

  • Bruckner, D. C. (2010). On the Treatment of Noise and Conspiring Bias in Dual-Frequency Differential Global Navigation Satellite Systems [Doctoral dissertation, Ohio University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1262040825

    APA Style (7th edition)

  • Bruckner, Dean. On the Treatment of Noise and Conspiring Bias in Dual-Frequency Differential Global Navigation Satellite Systems. 2010. Ohio University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1262040825.

    MLA Style (8th edition)

  • Bruckner, Dean. "On the Treatment of Noise and Conspiring Bias in Dual-Frequency Differential Global Navigation Satellite Systems." Doctoral dissertation, Ohio University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1262040825

    Chicago Manual of Style (17th edition)