Integrity Risk Minimisation in RAIM Part 2: Optimal Estimator Design

Mathieu Joerger, Steven Langel, Boris Pervan

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


This paper is the second part of a two-part research effort to find the optimal detector and estimator that minimise the integrity risk in Receiver Autonomous Integrity Monitoring (RAIM). Part 1 shows that for realistic navigation requirements, the solution separation RAIM method can approach the optimal detection region when using a least-squares estimator. This paper constitutes Part 2. It presents new methods to design Non-Least-Squares (NLS) estimators, which, in exchange for a slight increase in nominal positioning error, can substantially lower the integrity risk. A first method is formulated as a multi-dimensional minimisation problem, which directly minimises integrity risk, but can only be solved using a time-consuming iterative process. Parity space representations are then exploited to develop a computationally-efficient, near-optimal NLS-estimator-design method. Performance analyses for an example multi-constellation Advanced RAIM (ARAIM) application show that this new method enables significant integrity risk reduction in real-time implementations where computational resources are limited.

Original languageEnglish (US)
Pages (from-to)709-728
Number of pages20
JournalJournal of Navigation
Issue number4
StatePublished - Jul 1 2016


  • RAIM
  • Risk Minimisation

ASJC Scopus subject areas

  • Oceanography
  • Ocean Engineering


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