Updating Solutions of the Rational Function Model Using Additional Control Information

shown that the RFM can achieve a very high fitting accuracy to The rational function model (RFM) is a sensor model that the physical and is capable of replacing the rigorallows users to peqorm ~rtho-~~ctificat i~~ and 30 feature sensor models for photogrammetric restitution (~adani, extraction from imagery without knowledge of the physical lg99; DOwman and Dolloff, 2000; Yang, 2000; Tao and Hu, sensor model. It is a fact that the RFM is determined by the 2001~). It was reported in Grodecki (2001) that the ~konos ravendor using a proprietary physical sensor model. The ac- tional differs no more than 0.04 pixel fromthe ~h~sicuracy of the RFM solutions is dependent on the availability cal withtheRMS error 0.01 pixel. and the usage of ground control points (GCPS). In order to The RFM solutions are determined by the data vendor usobtain a more accurate RFM solution, the user may be asked ing a proprietary physical enso or model. The accuracy of the to supply GCPS to the data vendor. However, control infor- RFM solutions is dependent on the availability and the usage of mation may not be available at the time of data processing the GCPS. If accurate RFM solutions are required, GCPs are needor cannot be supplied due to some reasons (e.g., politics or ed and are incorporated into the RFM solution process. In this confidentiality). This paper addresses a means to update or case, the user may be a~ked to supply the GCPs to the data venimprove the existing RFM solutions when additional GCP~ are dor. However, the GCPS may not be available at the time of procavailable, without knowing the physical sensor model. From essing or cannot be supplied due to some reasons (e-g., politics a linear estimation perspective, the above issue can be tackled or confidentiality). using a phased estimation theory. In this paper, two methods If additional GCPS are available, one may ask if it is possible are proposed: a batch iterative least-squares (BILS) method to update or improve the existing RFM solutions (provided, for and an incremental discrete Kalman filtering (IDKF) method. example, by the vendor). In this paper, we present an approach Detailed descriptions of both methods are given. The feasi- to update and/or improve the existing RFM solutions when adbility of these two methods is validated and their perform- ditional GCPs are available, given that the physical sensor ances are evaluated. Some results concerning the updating model is unknown. In the next section, we briefly describe the of Ikonos imagery are also discussed. RFM by introducing a least-squares solution as well as two computation scenarios for RFM determination. In the following