A Study of Trajectory Models for Satellite Image Triangulation
Total Page：16
File Type：pdf, Size：1020Kb
265-276_07-096.qxd 2/16/10 3:36 PM Page 265 A Study of Trajectory Models for Satellite Image Triangulation In-seong Jeong and James Bethel Abstract metric camera. In common use, it generally encompasses Many Spaceborne imagery products are provided with both the internal camera geometry as well as any relevant metadata or support data having diverse types, representa- platform motions. For exploitation of a particular image, the tions, frequencies, and conventions. According to the vari- variables and parameters of that model must be assigned ability of metadata, a compatible physical sensor model numerical values, either from calibration, acquisition time approach must be constructed. Among the three components auxiliary sensors, triangulation, or some combination thereof. of the sensor model, i.e., trajectory model, projection equa- Generally, sensor models fall into two categories: models tions, and parameter subset selection, the construction of the based on the explicit physical characteristics of the system, position and attitude trajectory is closely linked with the and replacement models with generic, polynomial form availability and type of support data. In this paper, we show (RPCs), whose numerical values are obtained by means of a how trajectory models can be implemented based on support physical model. For the purposes of this paper, we will data from six satellite image types: QuickBird, Hyperion, exclude from consideration any polynomial based models SPOT-3, ASTER, PRISM, and EROS-A. Triangulation for each (rubber sheet warping) for which numerical parameters are image is implemented to investigate the feasibility and assigned without reference to a physical model. A physi- suitability of the different trajectory models. The results show cally-based, or rigorous, model has the advantage that all the effectiveness of some of the simple models while indicat- parameters have physical meaning. This is a more favorable ing that careful use of dense ephemeris information is environment for merging with other, related physical data necessary. These results are based on having a number of such as navigation sensors. high quality ground control points. For sensors that will be tested in this paper, many rigorous sensor models have been investigated: QuickBird (Weser et al., 2007; Robertson, 2003; Toutin, 2004), SPOT Introduction (Gugan and Dowman, 1988; Konecny et al., 1987; Makki, Experience has shown that there is a natural linkage 1991; Westin, 1990; Kim et al., 2007), ASTER (Dowman and between the type of metadata supplied with a raw, basic, Michalis, 2003), PRISM (Kocaman and Gruen, 2007) and or level-0 (no geometric correction) satellite image and the EROS-A (Chen and Teo, 2002; Tonolo and Poli, 2003; Westin models used for triangulation of that imagery. As technol- and Forsgren, 2001). Dowman and Michalis (2003) described ogy evolves, such metadata exhibits higher quality with a framework of the physical modeling process as consisting higher frequency sampling rates. Nevertheless, different of a satellite moving along a smooth elliptical orbit with vendors and suppliers make different choices about what image lines acquired sequentially, and with a provision to metadata to provide and about how to present it. Examples allow a dynamic scanning motion during the image capture. of such vendor choices include: reference coordinate Replacement models, on the other hand, may be easier system, Earth fixed or inertial, data frequency, ranging to implement in software, and have a faster execution time. from a few ephemeris points per image to hundreds, and For this approach, Rational Polynomial Coefficients (RPCs) parameterization of attitude data presented as Euler angles (Grodecki et al., 2003; Fraser et al., 2006) have been widely or as quaternions. Such diversity presents a challenge to used and studied. Some vendors, however, have used replace- sensor model developers in requiring a detailed study of ment models as means to avoid divulging proprietary informa- such metadata while constructing a compatible model. tion about physical characteristics of the system. This paper In an attempt to highlight these issues and to encourage a therefore will exclusively consider physical sensor models. movement toward standardization of metadata presentation, we have done a study involving imagery from six medium to Model Components in Satellite Photogrammetry high-resolution systems with the goal of evaluating different A rigorous, physical satellite sensor model can be thought of approaches for construction of the initial position and attitude as having three components: a time-dependent reference or trajectory and its refinement using the triangulation process. initial trajectory specification; a set of projection equations, usually over-parameterized; and an algorithm to select some subset of the trajectory and projection parameters for use in Satellite Sensor Model the actual estimation process. Note that when we speak of a The phrase sensor model refers to the mathematical relation- ships between image space and object space for a photogram- Photogrammetric Engineering & Remote Sensing Vol. 76, No. 3, March 2010, pp. 265–276. Geomatics Engineering, School of Civil Engineering, 0099-1112/10/7603–0265/$3.00/0 Purdue University, 550 Stadium Mall Drive, © 2010 American Society for Photogrammetry West Lafayette, IN, 47907 ([email protected]). and Remote Sensing PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING March 2010 265 265-276_07-096.qxd 2/16/10 3:36 PM Page 266 trajectory, it means a path through a six dimensional space model become parameter elements in the projection equations. including both position and attitude. Also, the trajectory model influences the parameter subset selection according to the quality of support data used to (Initial) Trajectory Model construct the trajectory. And clearly, the parameterization of As Dowman and Michalis (2003) summarized, unlike frame the projection equations limits the possible range of variables camera geometry, due to the dynamic nature of pushbroom present in the subset model. imaging geometry, each line has its own exterior orientation (EO) parameters. However, those parameters cannot be individ- ually considered in the model because information to recover Two Approaches for the Trajectory Model explicitly the parameters of all scan lines is insufficient. As suggested by Ebner (1999), there are generally two Therefore, we assume that the EO of adjacent lines is highly approaches for the trajectory model. These are (a) the orienta- correlated and may be modeled by a low order function. tion point approach, and (b) the orbital constraint approach. This calls for a model to specify an initial trajectory of both With the orientation point approach, at certain regular or position and attitude. This initial trajectory is important since irregular time intervals, position and attitude are determined subsequent estimation often entails making corrections or (usually by auxiliary sensors on the satellite) and provided as refinements to this initial path. The position and attitude orientation points, or ephemeris points. For any scan lines in along this trajectory should be a function of time, so that time- between the observed points, a low order piecewise interpola- tagged line numbers can be unambiguously referenced to it. A tion may be used to interpolate a position and attitude. Ebner trajectory model can be very complete and accurate with only (1999) points out that whereas this reduces the number of small corrections required, or it can be very rough or simplis- unknowns to a manageable number, it leaves much of the tic, with significant departures built up during the estimation trajectory un-tethered to any physical model for the motion. process. Such an initial trajectory can consist of, for example, The orbital constraint approach (Ohlhof et al., 1994) Kepler elements or a sequence of discrete positions and assumes that the imaging satellite moves along a smooth attitudes. One may have to distinguish between the camera mathematical curve. All scan line exposure stations would and the platform if they are not the same entity. Such a therefore be constrained on this orbit path. For a short arc, the trajectory model describes the initial approximation of the assumption of a “two-body” orbit may be used. This may be time varying exterior orientation of the camera system. parameterized with six elements of a state vector or, equiva- lently, six Kepler elements. For more extended arcs, additional Projection Equations force model parameters may be used. The basic idea of the As described, a rigorous sensor model tries to reflect the orbital constraint was originally introduced in the early days geometry and physics of how the image is formed based of satellite photogrammetry (Case, 1961). This concept has on the well-known collinearity condition. Unlike the been exploited in many published sensor models. frame camera model, the satellite sensor model should Regarding the attitude trajectory, older, strictly nadir contain sufficient parameters to accommodate any permis- looking cameras could derive attitude information from the sible scanning motions. These scanning motions may position trajectory and its relation to the Earth. For modern, be present in the initial trajectory or they may have to agile, body-scanning instruments, such assumptions are clearly be built up during the estimation process. Also, it is a not valid. These instruments completely decouple the scan- common strategy