Pose versus state: Are sensor position and attitude sufficient for modern photogrammetry and remote sensing?

Abstract

We investigate the advantages of using what we call sensor state parameters or sensor state to describe the geometrical relationship between a sensor and the 3D space or the 4D time-space that extend the traditional image pose or orientation (position and attitude) to the image state. In our concept, at some point in time t, the sensor state is a 12-dimensional vector composed of four 3-dimensional subvectors p(t), ν(t), γ(t) and ω(t). Roughly speaking, p(t) is the sensor's position, ν (t) its linear velocity, γ(t) its attitude and ω(t) its angular velocity. It is clear that the state concept extends the pose or orientation ones and attempts to describe both a sensor's statics (p(t), γ(t)) and dynamics (ν (t),ω(t)). It is also clear that if p(t), γ (t) are known for all t within some time interval of interest, then ν (t) and ω(t) can be derived from the former. We present three methods to compute the state parameters, two for the continuous case and one for the discrete case. The first two methods rely on the availability of inertial measurements and their derived time-Position-Velocity-Attitude (tPVA) trajectories. The first method extends the INS mechanization equations and the second method derives the IMU angular velocities from INS mechanization equations' output data. The third method derives lineal and angular velocities from relative orientation parameters. We illustrate how sensor states can be applied to solve practical problems. For this purpose we have selected three cases: multi-sensor synchronization calibration, correction of image motion blur (translational and rotational) and accurate orientation of images acquired with focal-plane shutters.