We describe the development of new HF data assimilation capabilities for our ionospheric inversion algorithm called GPSII GPS Ionospheric Inversion. Previously existing capabilities of this algorithm included assimilation of GPS total electron content data as well as assimilation of backscatter ionograms. In the present effort we concentrated on developing assimilation tools for data related to HF propagation channels. Measurements of propagation delay, angle of arrival, and the ionosphere-induced Doppler from any number of known propagation links can now be utilized by GPSII. The resulting ionospheric model is consistent with all assimilated measurements. This means that ray tracing simulations of the assimilated propagation links are guaranteed to be in agreement with measured data within the errors of measurement. The key theoretical element for assimilating HF data is the raypath response operator RPRO which describes response of raypath parameters to infinitesimal variations of electron density in the ionosphere. We construct the RPRO out of the fundamental solution of linearized ray tracing equations for a dynamic magnetoactive plasma. We demonstrate performance and internal consistency of the algorithm using propagation delay data from multiple oblique ionograms courtesy of Defence Science and Technology Organization, Australia as well as with time series of near-vertical incidence sky wave data courtesy of the Intelligence Advanced Research Projects Activity HFGeo Program Government team. In all cases GPSII produces electron density distributions which are smooth in space and in time. We simulate the assimilated propagation links by performing ray tracing through GPSII-produced ionosphere and observe that simulated data are indeed in agreement with assimilated measurements.