Orientation estimation of radar platforms using MEMS-based inertial sensors

A radar observes its surroundings relative to itself in terms of distance and angles. In order to calculate a target’s absolute position it is therefore crucial to know the radar’s own position and especially its orientation. This is because even a fractional error in the assumed orientation of the radar highly impacts estimated target position. This demand for high accuracy in orientation can be solved by using expensive inertial sensors. But because of their high price and recent developments in sensor hardware technology it has become interesting to investigate the capability of cheaper sensors based on micro electromechanical systems (MEMS) technology. In this thesis, a MEMS based inertial navigation system (INS) is evaluated and compared in relation to a considerably more expensive INS, which typically can be found in radar systems. The evaluation of the different systems is performed on a non-moving mobile radar system in which the radar antenna is mounted on what can be described as a mast-like construction in order to increase its range. Even if the radar system can be considered as stationary there is still be some minor movement of the radar antenna due to that the mast is mounted on sways back and forth as an effect of the rotating antenna, which is not perfectly balanced. This swaying movement causes the orientation of the radar antenna to vary periodically within a range of angles. In order to not only evaluate the MEMS INS but also investigate how its performance can be enhanced for radar applications, the authors have designed a Kalman filter that tries to make use of the periodic behaviour. The results show that the designed periodic filter outperforms the existing MEMS INS (under periodic movement). The presented periodic filter design also offers some unique advantages with respect to typical filters used for estimating orientation. Even if the periodic filter described in this thesis does not describe a complete design, including adaptivity to a wider range of periodic behaviours that can change over time, it does suggest that the fundamental design is valid and is suitable for at least a mode of operation if not as a complete filter solution. Sammanfattning En radar observerar sin omgivning relativt sin egen position och orientering. För att beräkna ett m̊als absoluta position är det därför extremt viktigt att veta radarns position och i synnerhet orientering. Detta eftersom även ett mycket litet fel i antagen orientering har stor p̊averkan p̊a m̊alets skattade position. Dessa höga krav p̊a noggrannhet kan uppfyllas genom att använda dyra tröghetsnavigeringsensorer. P̊a grund av det höga priset och utveckling inom sensor-h̊ardvara är det intressant att undersöka hur billigare sensorer baserade p̊a MEMS teknologi st̊ar sig mot de dyrare systemen. I den här rapporten utvärderas ett tröghetsnavigeringsystem och jämförs med ett betydligt dyrare system som typiskt används i radarsystem. Utvärderingen utförs p̊a ett stillast̊aende mobilt radarsystem där radarantennen är monterad p̊a en mastlik konstruktion för att öka räckvidden. Även om radarsystemet kan anses stationärt finns det fortfarande en rörelse p̊a antennen eftersom masten svänger fram och tillbaka. Detta p̊a grund av att antennenen inte är perfekt balanserad och snurrar. Svängningen f̊ar orienteringen för radarantennen att variera periodiskt inom ett spann p̊a vinklar. Utöver att utvärdera MEMS INS:en har författarna utvecklat ett Kalman filter som använder den periodiska rörelsen för att förbättra mätvärdena. REsultaten visar att det designade filtret är bättre än den färdiga MEMS INS lösningen(givet en periodisk rörelse). Det periodiska filtret erbjuder även unika fördelar jämfört med typiska filter för orientering. Även om det periodska filtret i den här rapporten inte beskriver en komplett lösning, visar det att det grundläggande konceptet fungerar och är möjlig för åtminstone en del av en komplett lösning. Acknowledgements We, the authors, would like to state our most sincere appreciation to Jonas Nordh at Saab for all the assistance provided during the thesis. Without you and your contacts we not have had the possibility to carry out the thesis with anywhere near all the practical elements which made the experience so great. We would also like to thank others at Saab who assisted us during our practical trials and their facilitation: Fredrik H̊akansson, Krister Lyden, Stellan Karlsson, Mats Hansson and Christian Trané. Finally we would also like to thank Lennart Svensson at Chalmers University of Technology for all his constructive critique and discussions. Jonathan Lidqvist and Björn Skoglund, Göteborg 17/6/15 Notation Abbreviations ARW Angular random walk AVAR Allan variance BMFLC Bandlimited multiple fourier linear combiner DCM Direct cosine matrix EKF extended Kalman filter FLC Fourier linear combiner FOG fiberoptic gyroscope IMU inertial measurement unit INS inertial navigation system LMS Least mean squares MEMS micro-machined electro mechanical sensors NED North-east-down RLG ring laser gyro RMSD Root mean square deviation Capital Letters A amplitude D process noise covariance matrix E measurement noise covariance matrix F transition matrix H measurement model K Kalman gain O observation matrix P state covariance matrix Q quaternion rotation matrix R rotation matrix Small Letters a odd Fourier coefficient b even Fourier coefficient e error f motion function g gravity vector h measurement function q quaternion vector w amplitude weight vector x state vector x x-axis y measurement vector y y-axis z z-axis Greek Letters α misalignment angle ω frequency θ roll angle φ pitch angle ψ heading angle Θ orientation vector δ process noise ε measurement noise μ bias φ phase Subscripts k current time ς number of roll frequencies τ number of pitch frequencies ν number of heading frequencies Superscripts acc accelerometer gyr gyroscope p periodic s stationary t translational ref reference system sbg SBG sensor Diacritical marks ˆ approximation or estimate ̇ time derivative