Modeling the spatial magnetic field precisely is the basis for the geomagnetism-based indoor localization and tracking system. Traditional magnetic constructing schemes ignore the distribution of magnetic field

which causes low accuracy of the constructing magnetic field. To deal with this problem

this paper presents a magnetic field modeling method based on the gradient of the magnetic potential and Gaussian processes. Firstly

the relationship between the gradient of the magnetic potential and magnetic field is introduced into the Gaussian processes. Furthermore

the sum of the squared exponential kernel spatial gradient and geomagnetic offset field distribution variance is used as the kernel function of the Gaussian processes. By transforming the constrained hyperparameters optimization problem into an unconstrained optimization problem

we employ the Rprop algorithm to estimate the hyperparameters. Finally

simulations are implemented to analyze the advantage of proposed method over traditional methods

and the impact of the hyperparameters on magnetic discernibility is also discussed. In addition

we carry out magnetic field constructing tests using a triaxial vector magnetic sensor in different environments

including small area relatively strong magnetic field distorted environment

strong magnetic field distorted environment

and open area weak magnetic field distorted environment

to validate the performance of the proposed method in different real environments. The results of the experiments prove that the proposed scheme works well in practical applications.