The NANOGrav collaboration aims to detect low frequency gravitational waves by measuring the arrival times of radio signals from pulsars. A confirmation of such a gravitational wave signal requires timing tens of pulsars with a precision of better than 100 nanoseconds for around 10 – 25 years. A crucial component of the success of pulsar timing relies on understanding how the interstellar medium affects timing accuracy. Current pulsar timing models account only for the large-scale dispersion delays from the ISM. As a result, the relatively small-scale propagation effects caused by scattering are partially absorbed into the dispersion delay component of the model.
In this thesis we developed a model that accounted for both dispersion delay and scattering delay. In addition to the two observable quantities used in the NANOGrav model, we also included the slopes of those two observables. We then simulated data describing motion of a pulsar through the interstellar medium over 11 years. We used a weighted linear least squares formalism to solve the system of four equations and two parameters at every epoch of measurement in order to remove the effects of dispersion and scattering from the data as fully as possible. This model was successful at removing these effects.