A multipath-based simultaneous localization and mapping (SLAM) scenario at time step n, involving two reflective surfaces, a single physical anchor (PA) with position p(1)pa, and a single mobile agent with position and orientation, pn and psin, respectively. The mobile agent is depicted with five individual antenna elements at positions p(h)n, defined by offset d(h) and angle psi(h). The reflecting surfaces can be represented by virtual anchors (VAs) or master virtual anchors (MVAs), e.g., p(1)11,va or p1,mva, respectively. A single-bounce VA represents the location of the mirror image of a PA on the corresponding reflective surface. A MVA represents the location of the mirror image of a common origin on the corresponding reflective surface, thus creating a unique MVA for each reflecting surface. For a second PA or double-bounce propagation path involving surface 1 (not shown), VA positions are different than p(1)11,va while the unique MVA position p1,mva remains the same. Note that u1 and u2 are the unit vectors perpendicular to surfaces 1 and 2, while e2 is an arbitrary vector from the origin to surface 2. Distance and angle for PA and VA at surface 1, i.e., (d00,n(1),varphi00,n(1)) and (d11,n(1),varphi11,n(1)), are also shown.
