Research Roundup: Design and evaluation of integrity algorithms for PPP in kinematic applications

April 22, 2019  - By
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By Kazuma Gunning, Juan Blanch and Todd Walter, Stanford University, and Lance de Groot and Laura Norman, Hexagon Positioning Intelligence

UAV and autonomous platforms can greatly benefit from an assured position solution with high integrity error bounds. The expected high degree of connectivity in these vehicles will allow users to receive real-time precise clock and ephemeris corrections, which enable the use of precise point positioning (PPP) techniques.

Until now, these techniques have mostly been used to provide high accuracy, rather than focusing on high-integrity applications. The authors apply the methodology and algorithms used in aviation to determine position error bounds with high integrity (or protection levels) for a PPP position solution.

PPP techniques can provide centimeter accuracy without local reference stations in kinematic applications. These techniques have so far mostly been used to provide high accuracy, and it is only recently that they have been proposed to provide integrity, that is, position error bounds with a very low probability of exceeding them.

There has been preliminary work on the application of integrity to PPP, but it remains a challenge to translate the benefits of PPP to accuracy while maintaining high integrity. Most of the integrity work in PPP and real-time kinematic (RTK) has dealt more with the ambiguity resolution process under nominal error conditions and less on the integrity of the position solution under fault conditions.

The authors overview their PPP filter implementation, and describe the threat model as well as two classes of integrity algorithms: solution separation and sum of squared residuals based (also called residual-based [RB], a misnomer, as all autonomous integrity monitors are based on the residuals.)

They present data sets used to evaluate the algorithms, compare the protection levels (PLs) obtained with different algorithms, and present the results obtained with the most promising PL formulation in four different data sets: static, dynamic in open-sky conditions, dynamic in midtown suburban conditions, and in flight.

Concluding, they state: “We have formulated RAIM protection-level formulas using either solution separation or the sum of residual squares. Both formulations consist of straightforward adaptations of snapshot RAIM to a Kalman filter solution.

“For solution separation, we have shown an implementation where the computational cost of running a bank of filters is far from being proportional to the cost of one filter. Instead, we could run 50 additional filters for the cost of one.

“For residual based RAIM we have developed a set of formulas to update the sum of square residuals from one time step to the next one. Because this test statistic is exactly the same as the one used in snapshot RAIM (when we consider the problem as a batch least squares), we could use the formula that ties the slope of a fault mode to the standard deviation of the solution separation. The slope can therefore also be updated recursively.”

Finally, “we have refined the PPP filter, added one scenario (suburban driving conditions), and examined the effect of considering multiple faults in the formulation of the test statistics and the protection levels. The results are very promising: protection levels below 2 m appear to be achievable, and the computation load is lower than expected.”

This paper was presented at ION-GNSS+ 2018. See browse.cfm.

About the Author: Tracy Cozzens

Senior Editor Tracy Cozzens joined GPS World magazine in 2006. She also is editor of GPS World’s newsletters and the sister website Geospatial Solutions. She has worked in government, for non-profits, and in corporate communications, editing a variety of publications for audiences ranging from federal government contractors to teachers.