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When the extended Kalman filter (EKF) is applied for underwater cooperative localization, the outliers in the sensor observations cause unknown errors in the measurement system due to deep-sea environmental factors, which are difficult to calibrate and cause a significant reduction in the co-location accuracy of AUVs, and can even cause problems with a divergence of estimation error. In this paper, we proposed a cooperative navigation method of the EKF algorithm based on the combined observation of multiple AUVs. Firstly, the corresponding cooperative navigation model is established, and the corresponding measurement model is designed. Then, the EKF model based on combined observation is designed and constructed, and the unknown error is eliminated by introducing a previously measured value. Finally, simulation tests and lake experiments are designed to verify the effectiveness of the algorithm. The results indicate that the EKF algorithm based on combined observation can approximately eliminate errors and improve the accuracy of cooperative localization when the unknown measurement error cannot be calibrated by common EKF methods. The effect of state estimation is improved, and the accuracy of co-location can be effectively improved to avoid serious declines in\u2014and divergence of\u2014estimation accuracy.<\/jats:p>","DOI":"10.3390\/rs15020533","type":"journal-article","created":{"date-parts":[[2023,1,17]],"date-time":"2023-01-17T02:58:16Z","timestamp":1673924296000},"page":"533","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Cooperative Navigation Algorithm of Extended Kalman Filter Based on Combined Observation for AUVs"],"prefix":"10.3390","volume":"15","author":[{"given":"Guangrun","family":"Sheng","sequence":"first","affiliation":[{"name":"School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China"},{"name":"Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology, Ministry of Education, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xixiang","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China"},{"name":"Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology, Ministry of Education, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yehua","family":"Sheng","sequence":"additional","affiliation":[{"name":"Key Laboratory of Virtual Geographic Environment, Ministry of Education of PRC, Nanjing Normal University, Nanjing 210023, China"},{"name":"Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing Normal University, Nanjing 210023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiangzhi","family":"Cheng","sequence":"additional","affiliation":[{"name":"School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China"},{"name":"Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology, Ministry of Education, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hao","family":"Luo","sequence":"additional","affiliation":[{"name":"School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China"},{"name":"Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology, Ministry of Education, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"075109","DOI":"10.1063\/5.0007538","article-title":"A novel Rauch\u2013Tung\u2013Streibel smoothing scheme based on the factor graph for auto omous underwater vehicles","volume":"91","author":"Ma","year":"2020","journal-title":"Rev. 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