On some mathematical problems in sensing and measurement

Sensing and measurement provides numerous, interesting, and essential problems of physical phenomena and man-made systems in real-worlds. This article describes various types of mathematical problems which we have encountered in developing the sensing and measurement technologies: 1) super resolution problem; 2) sound source localization; 3) exploiting self-similarity in sensors; 4) consistency maximization in gradient measurements; and 5) collaborative calibration architecture. These all can be seen as ones of the inversion problems in a general sense. The solutions of them give us plenty of insights on physical and biological systems as well as technological systems.