Sequential Bundle Adjustment Using Kalman Filtering and Optimal Smoothing
Vision aiding of the navigation solution has become an integral component of low-cost IMU/GPS subsystems providing direct georeferencing to remote sensing systems. The data workflow to recover the orientation parameters rigorously requires the simultaneous handling of large amounts of imagery and navigation data. In some situations, with small unmanned aerial vehicles, for example, a flight block of thousands of images is the norm. The normal matrix of the blended imagery and navigation data can be very large in size for regular computers to handle efficiently. We use a Kalman filtering approach to sequentially process the blended navigation and imagery data; georeferencing parameters are then computed for every exposure station. In overlapping areas of the imagery, the exposure stations and the overlapping object are coplanar; this forms the general update equation of the Kalman filter. In order to rigorously account for the simultaneous optimal solution of the state parameters, we backward smooth the filtered estimates using the stored covariance information. We solve the problem in a form of overlapping strips in two directions to account for the whole block of imagery. We also account for the hybrid nature of the observation equation formulation which has mixed observations and parameters through creating equivalent condition equations and use the general least-squares approach. We use this technique on imagery collected by a small unmanned aerial vehicle used in environmental research. The small format of the imagery resulting from the low flying altitude produces a large amount of images per flight mission. Because of the limitation on vehicle payload, a lightweight MEMS-based inertial unit augmented by low-cost precise GPS is used to directly georeference the acquired imagery. The benchmarked accuracy of the attitude information from the inertial unit is on the order of half a degree of root-mean-squared error. Simulation results show the possibility of improving the results by at least a factor of two by using image aiding. The condition of coplanar exposure stations and overlapped objects creates tighter relative models between the different images and between the different strips, resulting in a tighter adjustment of the whole block. The proposed technique should not only improve the accuracy of the image block, but also improve the algorithm computational efficiency drastically.
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