The Fukushima Daiichi nuclear disaster occurred during the Great East Japan Earthquake. Inside the reactor, materials with high radioactivity were scattered entirely, leading to a severe condition that restricted the number of measurement spots where the detector could be used. We propose a new system based on a plane model that uses fewer measurement spots and causes fewer estimation errors. We estimated the radiation source distribution using the maximum-likelihood estimation method optimized by gradient descent. Consequently, it was found that the proposed system, showed fewer errors than the previous system with a limited number of measurement spots.