GPS/INS

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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.

Contents

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. [1]

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 ] angles. In general, GPS/INS sensor fusion is a nonlinear filtering problem, which is commonly approached using the extended Kalman filter (EKF) [2] or the unscented Kalman filter (UKF). [3] The use of these two filters for GPS/INS has been compared in various sources, [4] [5] [6] [7] [8] [9] [10] including a detailed sensitivity analysis. [11] 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. [12] 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, [13] [14] vehicle dynamics control, [15] or sideslip, roll, and tire cornering stiffness estimation. [16] [17]

See also

Related Research Articles

Dead reckoning process of calculating ones current position by using a previously determined position

In navigation, dead reckoning is the process of calculating one's current position by using a previously determined position, or fix, by using estimation of speed and course over elapsed time. The corresponding term in biology, used to describe the processes by which animals update their estimates of position or heading, is path integration.

Kalman filter Algorithm that estimates unknowns from a series of measurements over time

In statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, containing statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more accurate than those based on a single measurement alone, by estimating a joint probability distribution over the variables for each timeframe. The filter is named after Rudolf E. Kálmán, one of the primary developers of its theory.

An attitude and heading reference system (AHRS) consists of sensors on three axes that provide attitude information for aircraft, including roll, pitch and yaw. These are sometimes referred to as MARG sensors and consist of either solid-state or microelectromechanical systems (MEMS) gyroscopes, accelerometers and magnetometers. They are designed to replace traditional mechanical gyroscopic flight instruments.

Sensor fusion

Sensor fusion is combining of sensory data or data derived from disparate sources such that the resulting information has less uncertainty than would be possible when these sources were used individually. The term uncertainty reduction in this case can mean more accurate, more complete, or more dependable, or refer to the result of an emerging view, such as stereoscopic vision.

The fast Kalman filter (FKF), devised by Antti Lange, is an extension of the Helmert-Wolf blocking (HWB) method from geodesy to safety-critical real-time applications of Kalman filtering (KF) such as GNSS navigation up to the centimeter-level of accuracy and satellite imaging of the Earth including atmospheric tomography.

Satellite navigation Any system that uses satellite radio signals to provide autonomous geo-spatial positioning

A satellite navigation or satnav system is a system that uses satellites to provide autonomous geo-spatial positioning. It allows small electronic receivers to determine their location to high precision using time signals transmitted along a line of sight by radio from satellites. The system can be used for providing position, navigation or for tracking the position of something fitted with a receiver. The signals also allow the electronic receiver to calculate the current local time to high precision, which allows time synchronisation. These uses are collectively known as Positioning, Navigation and Timing (PNT). Satnav systems operate independently of any telephonic or internet reception, though these technologies can enhance the usefulness of the positioning information generated.

A navigation system is a computing system that aids in navigation. Navigation systems may be entirely on board a vehicle or vessel bridge, or they may be located elsewhere and communicate via radio or other signals with a vehicle or vessel, or they may use a combination of these methods.

A radar tracker is a component of a radar system, or an associated command and control (C2) system, that associates consecutive radar observations of the same target into tracks. It is particularly useful when the radar system is reporting data from several different targets or when it is necessary to combine the data from several different radars or other sensors.

GNSS augmentation method of improving a navigation system

Augmentation of a global navigation satellite system (GNSS) is a method of improving the navigation system's attributes, such as accuracy, reliability, and availability, through the integration of external information into the calculation process. There are many such systems in place and they are generally named or described based on how the GNSS sensor receives the external information. Some systems transmit additional information about sources of error, others provide direct measurements of how much the signal was off in the past, while a third group provides additional vehicle information to be integrated in the calculation process.

An indoor positioning system (IPS) is a network of devices used to locate people or objects where GPS and other satellite technologies lack precision or fail entirely, such as inside multistory buildings, airports, alleys, parking garages, and underground locations. A large variety of techniques and devices are used to provide indoor positioning ranging from reconfigured devices already deployed such as smartphones, WiFi and Bluetooth antennas, digital cameras, and clocks; to purpose built installations with relays and beacons strategically placed throughout a defined space. IPS has broad applications in commercial, military, retail, and inventory tracking industries. There are several commercial systems on the market, but no standards for an IPS system. Instead each installation is tailored to spatial dimensions, building materials, accuracy needs, and budget constraints. Lights, radio waves, magnetic fields, acoustic signals, and behavioral analytics are all used in IPS networks. IPS can achieve position accuracy of 2cm, which is on par with RTK enabled GNSS receivers that can achieve 2cm accuracy outdoors.

In estimation theory, the extended Kalman filter (EKF) is the nonlinear version of the Kalman filter which linearizes about an estimate of the current mean and covariance. In the case of well defined transition models, the EKF has been considered the de facto standard in the theory of nonlinear state estimation, navigation systems and GPS.

UNSW School of Surveying and Geospatial Engineering

The UNSW School of Surveying and Geospatial Engineering (SAGE), part of the UNSW Faculty of Engineering, was founded in 1970 and disestablished in 2013.

Inertial navigation system navigation aid relying on systems contained within the vehicle to determine location

An inertial navigation system (INS) is a navigation device that uses a computer, motion sensors (accelerometers) and rotation sensors (gyroscopes) to continuously calculate by dead reckoning the position, the orientation, and the velocity of a moving object without the need for external references. Often the inertial sensors are supplemented by a barometric altimeter and occasionally by magnetic sensors (magnetometers) and/or speed measuring devices. INSs are used on mobile robots and on vehicles such as ships, aircraft, submarines, guided missiles, and spacecraft. Other terms used to refer to inertial navigation systems or closely related devices include inertial guidance system, inertial instrument, inertial measurement unit (IMU) and many other variations. Older INS systems generally used an inertial platform as their mounting point to the vehicle and the terms are sometimes considered synonymous.

Symmetry-preserving observers, also known as invariant filters, are estimation techniques whose structure and design take advantage of the natural symmetries of the considered nonlinear model. As such, the main benefit is an expected much larger domain of convergence than standard filtering methods, e.g. Extended Kalman Filter (EKF) or Unscented Kalman Filter (UKF).

The invariant extended Kalman filter (IEKF) is a version of the extended Kalman filter (EKF) for nonlinear systems possessing symmetries. It combines the advantages of both the EKF and symmetry-preserving filters. Instead of using a linear correction term based on a linear output error, the IEKF uses a geometrically adapted correction term based on an invariant output error; in the same way the gain matrix is not updated from a linear state error, but from an invariant state error. The main benefit is that the gain and covariance equations converge to constant values on a much bigger set of trajectories than equilibrium points that is the case for the EKF, which results in a better convergence of the estimation.

Attitude control is the process of controlling the orientation of an aerospace vehicle with respect to an inertial frame of reference or another entity such as the celestial sphere, certain fields, and nearby objects, etc.

Inertial measurement unit electronic device to measure a crafts velocity and orientation

An inertial measurement unit (IMU) is an electronic device that measures and reports a body's specific force, angular rate, and sometimes the orientation of the body, using a combination of accelerometers, gyroscopes, and sometimes magnetometers. IMUs are typically used to maneuver aircraft, including unmanned aerial vehicles (UAVs), among many others, and spacecraft, including satellites and landers. Recent developments allow for the production of IMU-enabled GPS devices. An IMU allows a GPS receiver to work when GPS-signals are unavailable, such as in tunnels, inside buildings, or when electronic interference is present. A wireless IMU is known as a WIMU.

The unscented transform (UT) is a mathematical function used to estimate the result of applying a given nonlinear transformation to a probability distribution that is characterized only in terms of a finite set of statistics. The most common use of the unscented transform is in the nonlinear projection of mean and covariance estimates in the context of nonlinear extensions of the Kalman filter. Its creator Jeffrey Uhlmann explained that "unscented" was an arbitrary name that he adopted to avoid it being referred to as the “Uhlmann filter.”

Pressure reference system

Pressure reference system (PRS) is an enhancement of the inertial reference system and attitude and heading reference system designed to provide position angles measurements which are stable in time and do not suffer from long term drift caused by the sensor imperfections. The measurement system uses behavior of the International Standard Atmosphere where atmospheric pressure descends with increasing altitude and two pairs of measurement units. Each pair measures pressure at two different positions that are mechanically connected with known distance between units, e.g. the units are mounted at the tips of the wing. In horizontal flight, there is no pressure difference measured by the measurement system which means the position angle is zero. In case the airplane banks, the tips of the wings mutually change their positions, one is going up and the second one is going down, and the pressure sensors in every unit measure different values which are translated into a position angle.

Positional tracking

Positional tracking detects the precise position of the head-mounted displays, controllers, other objects or body parts within Euclidean space. Positional tracking registers the exact position due to recognition of the rotation and recording of the translational movements. Since virtual reality is about emulating and altering reality it's important that we can track accurately how objects move in real life in order to represent them inside VR. Defining the position and orientation of a real object in space is determined with the help of special sensors or markers. Sensors record the signal from the real object when it moves or is moved and transmit the received information to the computer.

References

  1. ↑ Grewal, M. S.; L. R. Weill; A. P. Andrew (2007). Global Positioning, Inertial Navigation & Integration. New York: John Wiley & Sons.
  2. ↑ Kalman, R. E.; R. S. Bucy (1961). "New Results in Linear Filtering and Prediction Theory". Journal of Basic Engineering. 83: 95–108. doi:10.1115/1.3658902.
  3. ↑ Julier, S.; J. Uhlmann (1997). "A New Extension of the Kalman Filtering to Non Linear Systems". SPIE Proceedings Series. 3068: 182–193. doi:10.1117/12.280797.
  4. ↑ Crassidis, J. L. (2005). "Sigma-Point Kalman Filtering for Integrated GPS and Inertial Navigation". AIAA Guidance, Navigation, and Control Conference and Exhibit, San Francisco, CA. doi:10.2514/6.2005-6052. ISBN   978-1-62410-056-7.
  5. ↑ Fiorenzani, T.; et al. (2008). "Comparative Study of Unscented Kalman Filter and Extended Kalman Filter for Position/Attitude Estimation in Unmanned Aerial Vehicles". Iasr-CNR. 08-08.
  6. ↑ Wendell, J.; J. Metzger; R. Moenikes; A. Maier; G. F. Trommer (2006). "A Performance Comparison of Tightly Coupled GPS/INS Navigation Systems Based on Extended and Sigma-Point Kalman Filters". Journal of the Institute of Navigation. 53 (1).
  7. ↑ El-Sheimy, Naser; Eun-Hwan Shin; Xiaoji Niu (March 2006). "Kalman Filter Face-Off: Extended vs. Unscented Kalman Filters for Integrated GPS and MEMS Inertial". Inside GNSS : 48–54.
  8. ↑ St. Pierre, M.; D. Ing (June 2004). "Comparison between the unscented Kalman filter and the extended Kalman filter for the position estimation module of an integrated navigation information system". 2004 IEEE Intelligent Vehicles Symposium, Parma, Italy.
  9. ↑ Gross, Jason; Yu Gu; Srikanth Gururajan; Brad Seanor; Marcello R. Napolitano (August 2010). "A Comparison of Extended Kalman Filter, Sigma-Point Kalman Filter, and Particle Filter in GPS/INS Sensor Fusion". AIAA Guidance, Navigation, and Control Conference, Toronto, Canada. doi:10.2514/6.2010-8332. ISBN   978-1-60086-962-4.
  10. ↑ Gross, Jason N.; Yu Gu; Matthew Rhudy; Srikanth Gururajan; Marcello Napolitano (July 2012). "Flight Test Evaluation of GPS/INS Sensor Fusion Algorithms for Attitude Estimation". IEEE Transactions on Aerospace and Electronic Systems. 48 (3): 2128–2139. doi:10.1109/taes.2012.6237583.
  11. ↑ Rhudy, Matthew; Yu Gu; Jason Gross; Marcello Napolitano (August 2011). "Sensitivity Analysis of EKF and UKF in GPS/INS Sensor Fusion". AIAA Guidance, Navigation, and Control Conference, Portland, OR. doi:10.2514/6.2011-6491. ISBN   978-1-60086-952-5.
  12. ↑ Rhudy, Matthew; Yu Gu; Jason Gross; Marcello R. Napolitano (December 2011). "Evaluation of Matrix Square Root Operations for UKF within a UAV-Based GPS/INS Sensor Fusion Application". International Journal of Navigation and Observation. 2011. doi: 10.1155/2011/416828 .
  13. ↑ Petovello, M. G.; M. E. Cannon; G. Lachapelle; J. Wang; C. K. H. Wilson; O. S. Salychev; V. V. Voronov (September 2001). "Development and Testing of a Real-Time GPS/INS Reference System for Autonomous Automobile Navigation". Proc. Of ION GPS-01, Salt Lake City, UT.
  14. ↑ El-Sheimy, Naser; Eun-Hwan Shin; Xiaoji Niu (March 2006). "Kalman Filter Face-Off: Extended vs. Unscented Kalman Filters for Integrated GPS and MEMS Inertial". Inside GNSS : 48–54.
  15. ↑ Ryu, Jihan; J. Christian Gerdes (June 2004). "Integrating Inertial Sensors With Global Positioning System (GPS) for Vehicle Dynamics Control". Journal of Dynamic Systems, Measurement, and Control. 126 (2): 243–254. doi:10.1115/1.1766026.
  16. ↑ Bevly, David M.; Jihan Ryu; J. Christian Gerdes (December 2006). "Integrating INS Sensors With GPS Measurements for Continuous Estimation of Vehicle Sideslip, Roll, and Tire Cornering Stiffness". IEEE Transactions on Intelligent Transportation Systems. 7 (4): 483–493. doi:10.1109/tits.2006.883110.
  17. ↑ Ryu, Jihan; Eric J. Rosseter; J. Christian Gerdes (2002). "Vehicle Sideslip and Roll Parameter Estimation Using GPS". AVED 2002 6th Int. Symposium on Advanced Vehicle Control, Hiroshima, Japan.
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