# GPS and IMU in Photogrammetry

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The Global Positioning System (GPS), which is based on the NAVSTAR network, has provided the photogrammetry and remote sensing industry the centimeters-level accuracy that was required to position the camera in space for almost a decade. Another new technology that has made its way during the last few years to the photogrammetry and remote sensing community are inertial navigation systems (INS).

GPS may simply be viewed as a continuous series of radio signals broadcast from orbiting satellites to a radio receiver on the surface of the earth. These signals contain ephemeris information on the known position of the satellites, measurement data indicating the distance (range) to each satellite, and information describing the relative velocity of the satellites with respect to the receiver. A simple mathematical resection computation is used to determine a point’s position. GPS receivers use other constants broadcast by the satellite in its ephemeris to compute the X, Y, Z coordinates of each satellite for each instant (epoch) observations are made. When the distances to four or more satellites are measured, the X, Y, Z coordinates of the point occupied can be computed by resection formulas.

There are two types of GPS surveys, static surveys and kinematic surveys. GPS surveys are generally performed in so-called differential mode. This means that at least one receiver is placed at a point with precisely known coordinates, called the base or master station, while another receiver is positioned at a remote or roving point (camera station) with unknown coordinates. The vector that is solved is actually the coordinate differences from the base station to the remote station. This is referred to as relative positioning since the coordinate solution at the remote station is always relative to the known coordinates at the master. Differential or relative GPS surveys can be accurate to the meter, decimeter, or centimeter level depending on which receivers you are using and which mode you process in. Relative positioning is commonly used in aerial photography to navigate and position the aircraft more precisely.

Figure 1. Relative Kinematic GPS Positioning

Airborne GPS (ABGPS) is the name given to determining the accurate position of the photo-centers for aerial photographs. Accuracies as high as 2 to 5 cm can be achieved when the project covers a limited area and the GPS base station is located near the center of the project. Survey grade dual-frequency GPS receivers are required to achieve these high accuracies. The GPS receiver in the aircraft should also be equipped with the capability of recording the exact instant of exposure (event option). In some cases, the flight navigation system also records the photo-exposure times so that the event option in the GPS receiver would not be required. A camera equipped to output the exact time of the exposure midpoint is also required, and a cable connecting the camera to the airborne GPS receiver transmits this pulse from the camera to the GPS receiver where the time is recorded.

The optimum location for an ABGPS base station is at an airport near the center of the project area. Airports are excellent sites since there are few obstructions to block the satellite signals. Additionally, the aircraft GPS receiver will be able to quickly initialize (fix integer ambiguities) in a few minutes when the base station is located close to the aircraft. A base station can usually be left unattended at an airport, saving the cost of an operator.

GPS positioning is based on WGS84. A coordinate transformation to the national network coordinates is required. In addition to the transformation itself, the datum transfer has to be respected if this is not indirectly done with the reference point. In addition, the Geoid undulations have to be respected because the Z coordinates in WGS84 are ellipsoidal heights and not heights in the national coordinate system (orthometric heights), which are related to the Geoid. With a local transformation to control points, the effect of the Geoid can be minimized.

Today it is also possible to determine rotation angles of exterior orientation parameters with an Inertial Navigation System (INS). An INS comprises two main components. The first is the inertial measurement unit (IMU), which comprises three accelerometers, three gyros, and necessary electronics. The accelerometers are arranged as an orthogonal triad that measures the specific force vector experienced by the IMU. The gyros are likewise arranged into an orthogonal triad that measures the angular rate vector experienced by the IMU. High data rates are required to adequately sample short-term vibration dynamics as well as long-term vehicle dynamics. The second component is the navigation processor. It solves Newton’s equations for motion of the IMU on the rotating earth based on the measured accelerations and angular rates.

These systems can measure rotation angles with an accuracy up to +/-0.003° if the relation of the IMU system to the photogrammetric camera is determined within the block. Such accuracy is almost sufficient for all orthophoto production. However for large-scale mapping projects, additional control points or the combined block adjustment with GPS and IMU data are required. It is possible to determine shift and drift parameters of the GPS data (6 parameters) if at least two control points are available for each strip or if the project area is covered with at least two additional cross strips.

With the use of GPS and INS, the exterior orientation parameters are directly derived (Direct Georeferencing). Therefore, the number of control points required for a bundle block adjustment can be significantly reduced. Directly measured EO parameters from a well-planned mission and correctly operating GPS/IMU system are accurate enough to be used in many photogrammetric applications. However, the critical issue is the quality control and quality assurance (QC/QA) of the EO parameters.

The use of GPS and INS systems in photogrammetry can, on the one hand, support aerial triangulation (AT) packages by providing highly accurate exterior orientation parameters from the beginning and improve the quality and reliability of the orientation results. It is also possible to perform camera and/or self-calibration and simplify the point measurement process of automatic aerotriangulation by reducing the number of necessary tie points and the distribution of the tie point areas.