A Spatial Interpolation Method Based on BP Neural Network with Bellman Equation

Spatial interpolation is a valuable technique that uses the data of a sample set to estimate the property values at unsampled locations. Neural networks for spatial interpolation can capture spatial trends effectively; however, they may not be optimal when a strong local correlation is present, which leads to unreliable outcomes. Neural Network Residual Kriging methods use Kriging to handle residuals, assuming strict conditions such as the stationarity of the random field and stable spatial variability. In many applications without these strict conditions, however, those Neural Network interpolation methods have limitations for obtaining highly accurate estimates. To address this problem, in this paper, we propose a new spatial interpolation method, called NNRB, based on the mechanisms of BP Neural Network with Bellman Equation. Firstly, our NNRB method employs a BP neural network for capturing nonlinear relationships and spatial trends in the data of a sample set. Secondly, NNRB uses Bellman Equation to handle residuals by accounting for interactions between multiple adjacent data and reducing the influence of distant data on the current data. Our NNRB method is utilized for a system of soil testing and formulated fertilization for intelligent agriculture. We compared NNRB with four state-of-the-art interpolation methods, and the results show that our NNRB method outperforms the three methods significantly and is highly competitive with one approach.