Efficient 3D Indoor Visible Light Positioning via Stabilized Regularized Least Squares

We study indoor visible light positioning (VLP) in a fully three-dimensional setting under thermal noise and signal-dependent shot noise. Existing shot-noise-aware least-squares (LS) VLP methods largely rely on a fixed receiver height, so their key simplifications break down when the vertical coordinate is unknown. We derive a 3D likelihood-inspired surrogate, lift the nonlinear geometry into a weighted LS form, and add a geometry-aware regularizer that restores approximate consistency among redundant lifted variables. To make the iterative solver reliable in sparse layouts, we introduce room-feasible projection, consistent pilot reconstruction, clipped frozen weights, and damped objective-accepted updates. Each inner step remains a closed-form 4 × 4 linear solve. In deterministic synthetic simulations of an 8 × 8 × 3 m room with layouts containing 4, 9, and 16 light-emitting diodes (LEDs), high- and low-power regimes, and 400 test samples per scenario, the stabilized solver removes the catastrophic sparse-layout failures observed for the tested LS-family baselines and retains a 14×–23× runtime advantage over the nonlinear baseline. The nonlinear baseline often attains lower mean error in sparse and moderate layouts; the contribution here is the resulting speed–tail-control trade-off within the fixed-orientation line-of-sight model. The resulting estimator is intended for synthetic 3D VLP simulations; hardware validation is outside the present study.