Spacemetric’s solutions are based on rigorous photogrammetric methods. An explicit mathematical formulation defines the image capture process by describing the relationship between individual pixels as imaged by the sensor’s detector array and their location on the Earth. A sensor model characterising the specific geometrical properties of an instrument provides an interface to the full range of photogrammetric functionality.

The many advantages of the rigorous photogrammetric approach include:

• Highest possible geometrical accuracy for given input data
• Lower operational costs because method is highly stable and requires less external data such as ground control points
• Support of true image orthocorrection with sub-pixel geolocation accuracy
• Modest efforts required to develop a sensor model makes full photogrammetric functionality readily available for any satellite or airborne sensor.

Optical sensor model

The line-of-sight model (LOS) describes in an analytical way how a pixel in a satellite image is projected onto the ground using a number of distinct sub-models that can be independently modified or replaced. It defines the relations between the sub-models and the flow of transformations involved (see figure at right).

Sensor model

The sensor model takes a pixel in the satellite image and computes its look vector u_S in the sensor coordinate system. It also computes the time for the instance of this look. The sensor model is initialised with parameters specific for the sensor design. It can be a generic model for a pushbroom scanner, which will have parameters such as focal length, detector positions in the focal plane and scan-line time interval. Alternatively, it can be a highly specialised model for a more complicated sensor. The sensor model is the sub-model that is most often modified when implementing a new satellite system.

Body model

The body model is used to rotate the look vector from the sensor coordinate system to the satellite body coordinate system. It is used to model either the intended off-nadir sensor mounts or the small misalignments in the nominal mount.

Attitude model

The attitude model is used to rotate the look vector from the body coordinate system to the flight coordinate system. The rotations between these systems are due to deviations in satellite attitude. This is a time-dependent variation, usually measured by devices such as Earth horizon detectors, gyroscopes or star trackers. The attitude model is initiated by a set of time-coded attitude and/or attitude rate measurements. The time of the look is used to calculate the transformation to be used.

Flight model

The flight model is used to rotate the look vector from the flight coordinate system to the Earth Centered Inertial (ECI) coordinate system. It is also used to calculate the position of the satellite. It employs orbital mechanics and is initiated by sets of parameters such as one or several ephemeris, several time-tagged position vectors or two-line elements. The time of the look is used to calculate the transformation and position to be used.

Astronomical model

The astronomical model is used to transform the position and look vectors from the ECI system to the Earth Centred Rotating (ECR) coordinate system. It is primarily a rotation of the x-axis from the Vernal Equinox to the Greenwich Meridian. The transformation is time-dependent and the time of the look is used to calculate the transformation to be used.

Intersection model

The intersection model calculates the intersection point between the look vector and an ellipsoidal Earth centred in the ECR system. The ellipsoidal height is also input to get a unique position. An atmospheric model is applied to correct for the deviation caused by atmospheric refraction.

Geodesy model

The geodesy model transforms the Earth intersection point, expressed in ECR coordinates, to a geographic coordinate (longitude, latitude, orthometric height). It uses a geoid model to account for the irregularities in the Earth zero potential surface. The result is a coordinate in the WGS84 system.

Map projection

The map projection transforms the geographic coordinate to a cartographic coordinate (x, y, h) by the use of a map projection that is suitable for the geographical area of the image. There are thousands of different map projections in use for different cartographic purposes all over the globe. Spacemetric's systems support several thousand coordinate reference systems worldwide as defined by EPSG. New user-defined projections can easily be added too.

Aero sensor model

A special case of the optical sensor model is supported for sensors on aerial platforms. The main difference is that the astronomical model is not needed. The platform moves in an Earth-fixed system.

SAR sensor model

The LOS model for SAR (Synthetic Aperture Radar) sensors is to a large extent based on the same generic components as in the optical case. The main difference is the intersection model, which is now dependent on the spacecraft and ground velocities.

Replacement sensor models

In some cases, data for the generation of a full analytical LOS model is not provided in the metadata for the raw satellite image. A replacement sensor model (RSM) can be used instead. Spacemetric uses two RSMs:

• Rational functional model (RFM). This is a rational polynomial of 3rd degree. As as example, coefficients for such models are supplied in the metadata for Ikonos and Quickbird (referred to as RPCs or Rational Polynominal Coefficients).
• 3rd degree polynomial. This height-dependent polynomial can also be used with sufficient accuracy for most satellite sensors.

The parameters to be adjusted in the RSM are selectable and can be weighted, just as for the parameters in the fully analytical models.

Various applications of line-of-sight models are documented in the scientific papers provided in the Technical Papers section.