Modern Approaches in Nonlinear Filtering Theory Applied to Original Problems of Aerospace Integrated Navigation Systems with non-Gaussian noises

Benzerrouk, Hamza.M. Modern Approaches in Nonlinear Filtering Applied to Aerospace Integrated Navigation Systems with Non-Gaussian noises Saint Petersburg: Saint Petersburg State University, 2014, 49 p.(+included articles) Saint Petersburg State University Studies in Mathematics, Vol. 4 ISBN 978-5-288-05530-0, ISSN 2308-3476 In integrated navigation systems, the problem of data fusion from multiple sensors is a challenging problem and the methods involved to solve such complex problems are based on Kalman filtering theory and its nonlinear variants algorithms. The challenges in this field are how to obtain the best estimation accuracy and stability of the mathematical methods used in solving state estimation problems, especially in denied measurement environments. Mathematically, this leads with solving the problem of nonlinear estimation in the presence of non-Gaussian noises and then needs new formulations of the previous and modern approaches in nonlinear filtering algorithms, with also the proposal of novel approximations of the lower bounds of estimation. In the linear estimation problems with white Gaussian noises in the system and the measurement, Cramer Rao Lower Bound CRLB is well known to be the optimal lower bound of estimation, however if the noises are correlated or are non-Gaussian, the mathematical problem becomes more complex and all well know techniques and methods in the Gaussian space are transformed into robust or adaptive forms. This dissertation work is devoted to such severe conditions of noises where measurements are assumed affected by non-Gaussian noise, especially Gaussian mixture density. The second part of this contribution is a practical such as in many applications of autonomous navigation; Unmanned Aerial vehicle UAV or Unmanned Marine vehicle UMV for survey missions, photogrammetric, traffic survey,. etc, the sensors embedded and integrated onboard suffer from intentional and/or unintentional disturbances such as spoofing, jamming, multipath signals which induces a phenomena of measurement outliers. Especially with the use of GNSS signal composed by the previous and modern satellite constellations including “GPS, GLONASS, Galileo and Beidou”, and the merging new information technology frequencies used by peoples in urban environment like Smartphones, GSM, WiFi, Bluetooth, onboard the aircrafts, during walking in the city, some interferences problems occur sometimes without any intentional meaning, and cause a major degradation in the navigation process. Interesting and original applications in this dissertation are related to short duration Navigation of UAV, Robot navigation and pedestrian navigation in the city in degraded GNSS environment. Because of the emergence of low cost sensors such as MEMS based sensors including accelerometers, gyroscopes, magnetometers, baro altimeters, and compass, all integrated on mobile phones such as new Android based Smartphones, it is interesting to transform the actual fusion algorithm based on modern nonlinear filtering used in those technologies and develop robust forms of these algorithms against denied GNSS environment and keep the use of such devices for important matters such as blind peoples tracking and navigation in the city, autonomous robots for multi purposes in the human life and especially to improve the quality of existing tracking systems present with millions of devices in the world market and used for Aircrafts tracking and fleet management, ships, boats, cars, and also peoples tracking for safety purposes in additional to all parallel Space applications. Finally a novel and original theoretical and practical example on the basis of “Iridium Satellite Only Based Positioning System during GNSS missing” is giving as a real perspective for both mathematical studies and for technological development of a navigation solution on the surface of the earth in ocean, desert and even in urban environment. Analogue solution is then extrapolated to another original navigation problem devoted to astronauts and robonauts navigation on the surface of Mars planet using Phobos or Phobos/Deimos “natural satellites” instead of launching 06–08 artificial satellite on the orbit of Mars. This work has been object of 37 publications with 09 papers indexed SCOPUS and 01 paper accepted after revision in ISI THOMSON Journal.