{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T01:12:24Z","timestamp":1774314744642,"version":"3.50.1"},"reference-count":33,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2020,9,21]],"date-time":"2020-09-21T00:00:00Z","timestamp":1600646400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Youth Innovation Promotion Association, Chinese Academy of Science","award":["Y50301A1BY"],"award-info":[{"award-number":["Y50301A1BY"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The residual-based (RB) receiver autonomous integrity monitoring (RAIM) detector is a widely used receiver integrity enhancement technology that has the ability to rapidly respond to outliers. However, the sensitivity and vulnerability of the residuals to the outliers are the weaknesses of the method especially in the case of multi-outlier modes. It is an effective method for enhancing the validity of residuals by robust estimation instead of least squares (LS) estimation. In this paper, a modified RB RAIM detector based on a robust MM estimation with a higher detection performance under multi-outlier modes is presented. A fast subset selection method based on the characteristic slope that could reduce the number of subsets to be calculated is also presented. The experimental results show that the proposed algorithm maintains a more robust performance than the RB RAIM detector based on the LS estimator and M estimator with an IGG III function especially with the increase in the number of outliers. The proposed fast subset selection method can reduce the calculation time by at least 80%, demonstrating the practical application value of the algorithm.<\/jats:p>","DOI":"10.3390\/s20185407","type":"journal-article","created":{"date-parts":[[2020,9,21]],"date-time":"2020-09-21T08:18:01Z","timestamp":1600676281000},"page":"5407","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["A Modified Residual-Based RAIM Algorithm for Multiple Outliers Based on a Robust MM Estimation"],"prefix":"10.3390","volume":"20","author":[{"given":"Wenbo","family":"Wang","sequence":"first","affiliation":[{"name":"Aerospace Information Research Institute, Chinese Academy of Science, Beijing 100864, China"},{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100864, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ying","family":"Xu","sequence":"additional","affiliation":[{"name":"Aerospace Information Research Institute, Chinese Academy of Science, Beijing 100864, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1503","DOI":"10.1007\/s10291-017-0627-4","article-title":"Integrity and continuity allocation for the RAIM with multiple constellations","volume":"21","author":"Liang","year":"2017","journal-title":"GPS Solut."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"22854","DOI":"10.3390\/s150922854","article-title":"Vision-Aided RAIM: A New Method for GPS Integrity Monitoring in Approach and Landing Phase","volume":"15","author":"Fu","year":"2015","journal-title":"Sensors"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"075001","DOI":"10.1088\/1361-6501\/ab1836","article-title":"On hypothesis testing in RAIM algorithms: Generalized likelihood ratio test, solution separation test and a possible alternative","volume":"30","author":"Imparato","year":"2019","journal-title":"Meas. Sci. Technol."},{"key":"ref_4","first-page":"45","article-title":"Development and Modernization of GNSS","volume":"73","author":"Zrinjski","year":"2019","journal-title":"Geod. List"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1508","DOI":"10.3390\/s17071508","article-title":"Does RAIM with Correct Exclusion Produce Unbiased Positions?","volume":"17","author":"Peter","year":"2017","journal-title":"Sensors"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1281","DOI":"10.1017\/S0373463318000383","article-title":"Fault Exclusion in Multi-Constellation Global Navigation Satellite Systems","volume":"71","author":"Yawei","year":"2018","journal-title":"J. Navig."},{"key":"ref_7","unstructured":"Joerger, M., Chan, F.C., Langel, S., and Pervan, A.B. (2012, January 17\u201321). Raim Detector and Estimator Design to Minimize the Integrity Risk. Proceedings of the International Technical Meeting of the Satellite Division of the Institute of Navigation, Nashville, TN, USA."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"105942","DOI":"10.1016\/j.asoc.2019.105942","article-title":"A gradient boosting decision tree based GPS signal reception classification algorithm","volume":"86","author":"Sun","year":"2019","journal-title":"Appl. Soft Comput."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"17329","DOI":"10.3390\/s150717329","article-title":"NLOS Correction\/Exclusion for GNSS Measurement Using RAIM and City Building Models","volume":"15","author":"Hsu","year":"2015","journal-title":"Sensors"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1235","DOI":"10.1109\/TAES.2010.5545186","article-title":"RAIM with optimal integrity and continuity allocations under multiple failures","volume":"46","author":"Blanch","year":"2010","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_11","first-page":"47","article-title":"GNSS Receiver Autonomous Integrity Monitoring (RAIM) for multiple outliers","volume":"4","author":"Hewitson","year":"2006","journal-title":"Eur. J. Navig."},{"key":"ref_12","unstructured":"Blanch, J., Walter, T., and Enge, P. (2014, January 27\u201329). Exclusion for Advanced RAIM: Requirements and a Baseline Algorithm. Proceedings of the International Technical Meeting of the Institute of Navigation, San Diego, CA, USA."},{"key":"ref_13","unstructured":"Rippl, M. (February, January 30). Real Time Advanced Receiver Autonomous Integrity Monitoring in DLR\u2019s Multi-Antenna GNSS Receiver. Proceedings of the International Technical Meeting of the Institue of Navigation, DLR, Newport Beach, CA, USA."},{"key":"ref_14","unstructured":"Blanch, J., Walter, T., Enge, P., Lee, Y., Pervan, B., Rippl, M., and Spletter, A. (2012, January 17\u201321). Advanced Raim User Algorithm Description: Integrity Support Message Processing, Fault Detection, Exclusion, and Protection Level Calculation. Proceedings of the 25th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2012), Nashville, TN, USA."},{"key":"ref_15","unstructured":"Rippl, M., Schroth, G., Belabbas, B., and Meurer, M. (2009, January 22\u201325). A Probabilistic Assessment on the Range Consensus (RANCO) RAIM Algorithm. Proceedings of the Ion International Technical Meeting, DLR, Savannah, GA, USA."},{"key":"ref_16","unstructured":"Schroth, G., Rippl, M., Ene, A., Blanch, J., Belabbas, B., Walter, T., Enge, P., and Meurer, M. (2008, January 16\u201319). Enhancements of the Range Consensus Algorithm (RANCO). Proceedings of the International Technical Meeting of the Satellite Division of the Institute of Navigation, Savannah, GA, USA."},{"key":"ref_17","unstructured":"Juan, B., Todd, W., and Per, E. (February, January 29). Fixed Subset Selection to Reduce Advanced RAIM Complexity. Proceedings of the International Technical Meeting of the Institute of Navigation, Reston, VA, USA."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1443","DOI":"10.1007\/s10291-017-0658-x","article-title":"Reduced ARAIM monitoring subset method based on satellites in different orbital planes","volume":"21","author":"Ge","year":"2017","journal-title":"GPS Solut."},{"key":"ref_19","unstructured":"Blanch, J., Walter, T., and Enge, P. (2015, January 26\u201328). Efficient Multiple Fault Exclusion with a Large Number of Pseudorange Measurements. Proceedings of the 2015 International Technical Meeting of the Institute of Navigation, Dana Point, CA, USA."},{"key":"ref_20","unstructured":"Walter, T., Blanch, J., and Enge, P. (2014, January 27\u201329). Reduced Subset Analysis for Multi-Constellation Araim. Proceedings of the 2014 International Technical Meeting of the Institute of Navigation, San Diego, CA, USA."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"709","DOI":"10.1017\/S0373463315000995","article-title":"Integrity Risk Minimization in RAIM Part 2: Optimal Estimator Design","volume":"69","author":"Mathieu","year":"2016","journal-title":"J. Navig."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1002\/j.2161-4296.2006.tb00370.x","article-title":"RAIM-FDE revisited: A new breakthrough in availability performance with NIORAIM (novel integrity-optimized RAIM)","volume":"53","author":"Hwang","year":"2006","journal-title":"Navigation"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1505","DOI":"10.1016\/j.cja.2019.12.012","article-title":"Correlation-weighted least squares residual algorithm for RAIM","volume":"33","author":"Song","year":"2020","journal-title":"Chin. J. Aeronaut."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.geog.2016.04.004","article-title":"GNSS receiver autonomous integrity monitoring (RAIM) algorithm based on robust estimation","volume":"7","author":"Yang","year":"2016","journal-title":"Geod. Geodyn."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1111\/rssb.12364","article-title":"Robust Estimation via Robust Gradient Estimation","volume":"82","author":"Adarsh","year":"2020","journal-title":"J. R. Statal Soc. Ser. B"},{"key":"ref_26","unstructured":"Wang, J., and Wang, J. (2007, January 4\u20136). Mitigation the Effects of Multiple Outliers on GNSS Navigation with M-Estimation Schemes. Proceedings of the IGNSS Symposium 2007, Sydney, Australia."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1007\/s11425-016-0285-1","article-title":"Finite sample breakdown point of Tukey\u2019s halfspace median","volume":"60","author":"Liu","year":"2017","journal-title":"Sci. China Math."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1017\/S0373463309990142","article-title":"A comparison of outlier detection procedures and robust estimation methods in GPS positioning","volume":"62","author":"Knight","year":"2009","journal-title":"J. Navig."},{"key":"ref_29","first-page":"7","article-title":"Robust Linear Discriminant Analysis with Highest Breakdown Point Estimator","volume":"10","author":"Sharipah","year":"2018","journal-title":"J. Telecommun. Electron. Comput. Eng."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Akram, M.A., Liu, P., Wang, Y., and Qian, J. (2018). GNSS Positioning Accuracy Enhancement Based on Robust Statistical MM Estimation Theory for Ground Vehicles in Challenging Environments. Appl. Sci., 8.","DOI":"10.3390\/app8060876"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.csda.2016.01.016","article-title":"A practical approximation algorithm for the LTS estimator","volume":"99","author":"Mount","year":"2016","journal-title":"Comput. Stats Data Anal."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"70102","DOI":"10.1109\/ACCESS.2019.2917377","article-title":"A modified LSR algorithm based on the critical value of characteristic slopes for RAIM","volume":"7","author":"Zhao","year":"2019","journal-title":"IEEE Access"},{"key":"ref_33","first-page":"1","article-title":"Combining Machine Learning and Dynamic Time Wrapping for Vehicle Driving Event Detection Using Smartphones","volume":"99","author":"Sun","year":"2019","journal-title":"IEEE Trans. Intell. Transp. Syst."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/18\/5407\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:12:02Z","timestamp":1760177522000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/18\/5407"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,21]]},"references-count":33,"journal-issue":{"issue":"18","published-online":{"date-parts":[[2020,9]]}},"alternative-id":["s20185407"],"URL":"https:\/\/doi.org\/10.3390\/s20185407","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9,21]]}}}