GPS/INS
GPS/INS is the use of GPS satellite signals to correct or calibrate a solution from an inertial navigation system (INS). The method is applicable for any GNSS/INS system.
Overview
= GPS/INS method =
The GPS gives an absolute drift-free position value that can be used to reset the INS solution or can be blended with it by use of a mathematical algorithm, such as a Kalman filter. The angular orientation of the unit can be inferred from the series of position updates from the GPS. The change in the error in position relative to the GPS can be used to estimate the unknown angle error.
The benefits of using GPS with an INS are that the INS may be calibrated by the GPS signals and that the INS can provide position and angle updates at a quicker rate than GPS. For high dynamic vehicles, such as missiles and aircraft, INS fills in the gaps between GPS positions. Additionally, GPS may lose its signal and the INS can continue to compute the position and angle during the period of lost GPS signal. The two systems are complementary and are often employed together.{{cite book|last=Grewal|first=M. S.|title=Global Positioning, Inertial Navigation & Integration|year=2007|publisher=John Wiley & Sons|location=New York|author2=L. R. Weill |author3=A. P. Andrew }}
Applications
GPS/INS is commonly used on aircraft for navigation purposes. Using GPS/INS allows for smoother position and velocity estimates that can be provided at a sampling rate faster than the GPS receiver. This also allows for accurate estimation of the aircraft attitude (roll, pitch, and yaw) {{citation needed|reason=GPS wont provide attitude that easily, only position/velocity|date=May 2016}} angles. In general, GPS/INS sensor fusion is a nonlinear filtering problem, which is commonly approached using the extended Kalman filter (EKF){{cite journal|last=Kalman|first=R. E.|author2=R. S. Bucy|title=New Results in Linear Filtering and Prediction Theory|journal= Journal of Basic Engineering|year=1961|volume=83|pages=95–108|doi=10.1115/1.3658902|s2cid=8141345 }} or the unscented Kalman filter (UKF).{{cite book|last=Julier|first=S.|author2=J. Uhlmann|editor-first1=Ivan |editor-last1=Kadar |chapter=New extension of the Kalman filter to nonlinear systems |title=Signal Processing, Sensor Fusion, and Target Recognition VI|year=1997|volume=3068|pages=182–193|doi=10.1117/12.280797|s2cid=7937456}} The use of these two filters for GPS/INS has been compared in various sources,{{cite journal|last=Crassidis|first=J. L.|title=Sigma-Point Kalman Filtering for Integrated GPS and Inertial Navigation|journal=AIAA Guidance, Navigation, and Control Conference and Exhibit, San Francisco, CA|year=2005|doi=10.2514/6.2005-6052|isbn=978-1-62410-056-7|s2cid=12664565}}{{cite journal|last=Fiorenzani|first=T.|display-authors=etal|title=Comparative Study of Unscented Kalman Filter and Extended Kalman Filter for Position/Attitude Estimation in Unmanned Aerial Vehicles|journal=Iasr-CNR|year=2008|volume=08-08}}{{cite journal|last=Wendell|first=J.|author2=J. Metzger |author3=R. Moenikes |author4=A. Maier |author5=G. F. Trommer |title=A Performance Comparison of Tightly Coupled GPS/INS Navigation Systems Based on Extended and Sigma-Point Kalman Filters|journal=Journal of the Institute of Navigation|year=2006|volume=53|issue=1}}{{cite journal|last=El-Sheimy|first=Naser |author2=Eun-Hwan Shin |author3=Xiaoji Niu|title=Kalman Filter Face-Off: Extended vs. Unscented Kalman Filters for Integrated GPS and MEMS Inertial|journal=Inside GNSS|date=March 2006|pages=48–54}}{{cite journal|last=St. Pierre|first=M.|author2=D. Ing|title=Comparison between the unscented Kalman filter and the extended Kalman filter for the position estimation module of an integrated navigation information system|journal=2004 IEEE Intelligent Vehicles Symposium, Parma, Italy|date=June 2004}}{{cite journal|last=Gross|first=Jason|author2=Yu Gu |author3=Srikanth Gururajan |author4=Brad Seanor |author5=Marcello R. Napolitano |title=A Comparison of Extended Kalman Filter, Sigma-Point Kalman Filter, and Particle Filter in GPS/INS Sensor Fusion|journal=AIAA Guidance, Navigation, and Control Conference, Toronto, Canada|date=August 2010|doi=10.2514/6.2010-8332|isbn=978-1-60086-962-4}}{{cite journal|last=Gross|first=Jason N.|author2=Yu Gu |author3=Matthew Rhudy |author4=Srikanth Gururajan |author5=Marcello Napolitano |title=Flight Test Evaluation of GPS/INS Sensor Fusion Algorithms for Attitude Estimation|journal=IEEE Transactions on Aerospace and Electronic Systems|date=July 2012|volume=48|issue=3|pages=2128–2139|doi=10.1109/taes.2012.6237583|s2cid=393165}} including a detailed sensitivity analysis.{{cite journal|last=Rhudy|first=Matthew|author2=Yu Gu |author3=Jason Gross |author4=Marcello Napolitano |title=Sensitivity Analysis of EKF and UKF in GPS/INS Sensor Fusion|journal=AIAA Guidance, Navigation, and Control Conference, Portland, OR|date=August 2011|doi=10.2514/6.2011-6491|isbn=978-1-60086-952-5}} The EKF uses an analytical linearization approach using Jacobian matrices to linearize the system, while the UKF uses a statistical linearization approach called the unscented transform which uses a set of deterministically selected points to handle the nonlinearity. The UKF requires the calculation of a matrix square root of the state error covariance matrix, which is used to determine the spread of the sigma points for the unscented transform. There are various ways to calculate the matrix square root, which have been presented and compared within GPS/INS application.{{cite journal|last=Rhudy|first=Matthew|author2=Yu Gu |author3=Jason Gross |author4=Marcello R. Napolitano |title=Evaluation of Matrix Square Root Operations for UKF within a UAV-Based GPS/INS Sensor Fusion Application|journal=International Journal of Navigation and Observation|date=December 2011|volume=2011|doi=10.1155/2011/416828|doi-access=free}} From this work it is recommended to use the Cholesky decomposition method.
In addition to aircraft applications, GPS/INS has also been studied for automobile applications such as autonomous navigation,{{cite journal|last=Petovello|first=M. G.|author2=M. E. Cannon |author3=G. Lachapelle |author4=J. Wang |author5=C. K. H. Wilson |author6=O. S. Salychev |author7=V. V. Voronov |title=Development and Testing of a Real-Time GPS/INS Reference System for Autonomous Automobile Navigation|journal=Proc. Of ION GPS-01, Salt Lake City, UT|date=September 2001}}{{cite journal|last=El-Sheimy|first=Naser |author2=Eun-Hwan Shin |author3=Xiaoji Niu|title=Kalman Filter Face-Off: Extended vs. Unscented Kalman Filters for Integrated GPS and MEMS Inertial|journal=Inside GNSS|date=March 2006|pages=48–54}} vehicle dynamics control,{{cite journal|last=Ryu|first=Jihan|author2=J. Christian Gerdes|title=Integrating Inertial Sensors With Global Positioning System (GPS) for Vehicle Dynamics Control|journal=Journal of Dynamic Systems, Measurement, and Control|date=June 2004|volume=126|issue=2|pages=243–254|doi=10.1115/1.1766026}} or sideslip, roll, and tire cornering stiffness estimation.{{cite journal|last=Bevly|first=David M.|author2=Jihan Ryu |author3=J. Christian Gerdes |title=Integrating INS Sensors With GPS Measurements for Continuous Estimation of Vehicle Sideslip, Roll, and Tire Cornering Stiffness|journal=IEEE Transactions on Intelligent Transportation Systems|date=December 2006|volume=7|issue=4|pages=483–493|doi=10.1109/tits.2006.883110|s2cid=206739497}}{{cite journal|last=Ryu|first=Jihan|author2=Eric J. Rosseter |author3=J. Christian Gerdes |title=Vehicle Sideslip and Roll Parameter Estimation Using GPS|journal=AVED 2002 6th Int. Symposium on Advanced Vehicle Control, Hiroshima, Japan|year=2002}} Integrating inertial navigation systems with high-precision GNSS technologies, such as real-time kinematic (RTK) and precise point positioning (PPP), enhances the accuracy of autonomous vehicle navigation by providing high-precision localization.{{Cite web |date=August 2019 |title=High-Precision Localization for the Autonomous Sensor Suite |url=https://www.swiftnav.com/sites/default/files/whitepapers/high_precision_localization_white_paper.pdf |access-date=March 17, 2025 |website=www.swiftnav.com}}