Shape memory alloys (SMAs) are a well-known class of smart materials which allow the design of compact and silent actuation mechanisms. A remarkable feature of SMAs is self-sensing, namely the possibility to reconstruct the actuator position information from electrical resistance measurements. In case of simple SMA actuators, such as spring-loaded wires, the relation between resistance and displacement is usually linear and thus simple to exploit for self-sensing. For more advanced actuator types, such as protagonist-antagonist SMA configurations, the resistance-displacement characteristic is often hysteretic and thus more difficult to invert in real-time. To deal with this issue, this work proposes a novel self-sensing method for protagonist-antagonist SMA actuators having a highly hysteretic resistance-displacement behavior. An online hysteresis compensation scheme, based on the modified Prandtl-Ishlinskii model, is implemented and used to linearize the resistance-displacement characteristic. A lab setup which allows characterization of antagonistic SMA system as well as implementation of self-sensing control architectures is also developed. Experimental results show how, when combined with a PI controller, the developed scheme permits to noticeably reduce the error in comparison to compensator-free self-sensing architectures.