arXiv:2411.04364v5 Announce Type: replace Abstract: Localization methods designed for omnidirectional emitters degrade on directional sources, where directive beampatterns induce pronounced received signal strength (RSS) modulations. We present a direct position determination (DPD) approach that augments standard angle of arrival (AOA) and time difference of arrival (TDOA) measurements with RSS modulation to jointly estimate emitter position and beampattern parameters. Two algorithms reduce the four-dimensional search to two dimensions: a block coordinate ascent (BCA) method that alternates between position and beampattern subproblems, and a profile likelihood method that concentrates the beampattern parameters out via a generalized eigenvalue solve, a weighted least squares fit, and Newton refinement on the constrained Rayleigh quotient. We derive the Cram\'er--Rao lower bound (CRLB) and benchmark against an AOA-TDOA baseline and a prior-art approach that assumes known beamwidth and estimates only the orientation. The profile likelihood method approaches the CRLB, substantially outperforms all baselines at low signal-to-noise ratio (SNR), and remains robust under model mismatch with the assumed von Mises template. A sensitivity analysis shows performance peaks when receivers lie on the main-lobe edges where RSS gradients are maximized.