The Fukushima Daiichi nuclear disaster occurred in the Great East Japan Earthquake. Inside the reactor, the material with high radioactivity scattered thoroughly, causing a severe condition, which requires a small number of measurement spots to use the detector. We propose a new system based on a plane model under several constraints to use fewer measurement spots and make less estimating error. We estimate the radiation source distribution using the maximum likelihood estimation method optimized by gradient descent. As a result, it is found that the proposed system performs less error than the previous system, with a limited number of measurement spots.