Joint Calibration and Tomographic Reconstruction for Time-of-Flight Sensor Systems

A typical time-of-flight (ToF) tomography method requires accurate information about the system’s calibration parameters in order to reconstruct the features of interest  within a region of interest (RoI). This paper proposes a constrained joint calibration and tomography (CJCT) method based on a separable least squares (SLS) approach for ToF tomographic systems. Contrary to the existing offline and online calibration methods, the proposed method utilizes prior information about the calibration parameters in the form of constraints. The imposed constraints allow for an efficient search for the minimum of the inherent SLS cost function by reducing the system and measurement ambiguities. Thus, the proposed CJCT method can find the optimum values for both tomography and calibration parameters more efficiently compared to unconstrained methods. The general applicability of the proposed method is demonstrated by evaluating it on two applications: tomographic reconstruction of the permittivity distribution in a RoI using ToF measurements from a high resolution millimeter-wave radar system, and the  temperature distribution inside an industrial blast furnace using measured and simulated acoustic ToF values. The simulation and experimental results show that the proposed method performs significantly better in terms of tomographic reconstruction accuracy compared to unconstrained methods.