Get distance from magnetic disturbances

[oliv]

I'm currently working on the estimation of the velocity of a mobile in indoor environment. I show some interresting new perspective here: use the magnetic disturbances to estimate velocity) . This paper affirms that it is possible by using Maxwell's equations and adopting some hypothesis:

- The magnetic field is stationnary. According to Faraday's law of induction in the absence of electrical source dBi/dt = 0. In other words, the magnetic field is a function of the position only. We not Bi(X)

- The magnetic field is a potential field. According to Ampere's law, in the absence of electric and magnetic sources, curl(Bi) =0. Therefore, there exists a scalar function h(X) such that Mi = nabla h

- The divergence of the magnetic field is zero: div(Bi) = 0. Thanks to the previous propoerty, this implies laplacian of h equals hxx + hyy + hzz equals 0.

 

But I can not succeed in demonstrate the last equation from Maxwell's equations. Does anyone have an idea?

 

Thank you by advance.