Modeling of Image Formation in Multi-Spacecraft Interferometric Imaging Systems

Abstract

In this paper, we develop a detailed model of the process of image formation in MultiSpacecraft Interferometric Imaging Systems (MSIIS). We show that the Modulation Transfer Function of, and the noise corrupting, the synthesized optical instrument are dependent on the trajectories of the constituent spacecraft and obtain these explicit functional relationships. We show that "good" imaging using MSIIS is equivalent to painting a "large disk" with smaller "paintbrushes" while maintaining a minimum thickness of paint, given that the goal of imaging is the correct classification of the formed images. This implies that the trajectories of the constituent spacecraft have to be "dense" enough in a given region, while making sure that they are "slow" enough. This is illustrated through an example.

Design of minimum time maneuvers for multispacecraft interferometric imaging systems

“…In this section, we shall pose the problem of designing minimum time maneuvers for an MSIIS, such that the imaging constraints are satisfied. We shall first recount a few results from [4].…”

“…In a previous paper [4], we had shown that the imaging constraints on an MSIIS translate into trajectory constraints on the constituent spacecraft of the system. In this section, we shall pose the problem of designing minimum time maneuvers for an MSIIS, such that the imaging constraints are satisfied.…”

“…Hence, the need to consider minimum time trajectories. In a previous paper [4], we had shown that the noise process corrupting the process of image formation in an MSIIS depends on the trajectories of the constituent spacecraft. We had obtained conditions on the noise process such that, if they were satisfied, the probability of misclassifying any image formed by the MSIIS would be below a given threshold, given that the classification is done based upon a feature.…”

“…The topic of long baseline interferometry falls under the category of synthetic aperture optics [5], that was first developed in the context of synthetic aperture radar (SAR) [6]. For a discussion of the various metrics used in the optimization of these systems, refer to [4] and the references therein. We note here that all the abovementioned designs correspond to static optimization problems while the design of an MSIIS is a dynamic optimization problem.…”

Intelligent exploration of unknown environments with vision like sensors

“…The state space of any path planning problem can be expressed as the ordered pair (s, q(s)) where s represents the system state and q(s) represents the state of the environment at the state s. For example, in the case of a robot exploring an unknown terrain, s corresponds to the (x, y) co-ordinates of the robot and q(s) corresponds to the height of the terrain z(x, y) at the point (x, y). This methodology is not limited to only robotic path planning and is equally applicable to UAV navigation and multi-spacecraft imaging problems [1], [2]. The goal of the path planning strategy is to use all available information about the environment, until the current time instant, in order to plan the ìbest possibleî path.…”