As odd as it sound when you want to permit nested attributes you do specify the attributes of nested object within an array. In your case it would be
Update as suggested by @RafaelOliveira
params.require(:measurement)
.permit(:name, :groundtruth => [:type, :coordinates => []])
On the other hand if you want nested of multiple objects then you wrap it inside a hash… like this
params.require(:foo).permit(:bar, {:baz => [:x, :y]})
Rails actually have pretty good documentation on this: http://api.rubyonrails.org/classes/ActionController/Parameters.html#method-i-permit
For further clarification, you could look at the implementation of permit and strong_parameters itself: https://github.com/rails/rails/blob/master/actionpack/lib/action_controller/metal/strong_parameters.rb#L246-L247