Various resistivity logging tools, systems, and methods are disclosed. At least some tool embodiments include transmit and receive antennas that measure the electromagnetic response of the formation, at least one of which is tilted to provide a directional sensitivity. A processor converts the response (measured as a function of the tool's rotation angle) into a set of inversion parameters, which are then used to estimate the anisotropic properties of the formation. The set of inversion parameters includes at least one parameter based on an antipodal sum of the response signal, and may further include parameters based on an antipodal difference and an average of the signal response. Antipodal sum and difference values at different rotational orientations can be included in the set of inversion parameters, and they may be normalized to reduce environmental effects. Some tool embodiments collect the relevant formation measurements using parallel or perpendicular tilted antennas.