A new technique for diagnostics of traveling ionospheric disturbances (TIDs) uses measurements of arrival angles and Doppler frequency shift variations of HF radio signals reflected from the ionosphere. This technique is a further improvement of a frequency-and-angular sounding method previously suggested. Here we solve the respective inverse problem of reconstructing TID parameters by using a physically realistic three-dimensional model of electron density waves propagating through an ionospheric layer. The developed diagnostic algorithms were tested through computer simulations demonstrating the high efficiency of the proposed method. We also reprocessed the data collected in an earlier experiment carried out at the Millstone Hill Observatory in March 2001 using the new algorithms. In that campaign, HF signal trajectory parameters were recorded using the Digisonde instrument as a receiver monitoring continuous transmission from the CHU station. Comparison of the TID parameters determined with the frequency-and-angular sounding method and simultaneous incoherent scatter radar observations showed good agreement between the two diagnostic techniques with the differences of no greater than 10%.