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An inverse equivalent current method with full probe correction capabilities and higher-order hierarchical surface current expansion functions is investigated. The approach works with electric and magnetic surface current densities and the triangular surface discretization is fully compatible with the usual models from integral equation solutions by the method of moments. Maximum efficiency and flexibility of the solution approach is achieved by employing an adapted version of the multilevel fast multipole method. Arbitrary measurement probes with arbitrary orientations and scanning over arbitrarily irregular surfaces can be accurately and efficiently processed. The capabilities of the method are demonstrated by a variety of results, where in particular badly miss-aligned measurement probes are considered.