Assuming that they are regular grids with known latitude and longitude vectors, Along, Alat, Blong, Blat, then the approximation that neglects curvature of the Earth would be
[X, Y] = meshgrid(Blat, Blong);
[Xq, Yq] = meshgrid(Alat, Along);
Bapprox = interp2(X, Y, B, Xq, Yq);
The interp2() would need the longitude vectors phase-unwrapped if they cross 180 to -180:
degrad = pi./180;
unwrappedBlong = unwrap(Blong .* degrad) ./ degrad;
If you do need to take the curvature of the Earth into account, then possibly mapprofile might turn out to be usable for you -- I am too tired at the moment to figure out what a refmatrix is.
If mapprofile is not suitable then perhaps someone has already built a routine. If not then intrplon might help.
