  We consider 3-dimensional (3D) visible light positioning (VLP) based on
smartphone camera in an indoor scenario. Based on the positioning model in the
quantized pixel-domain, we characterize the 3D normalized positioning error
metric (NPEM) through the partial derivative of the positioning function, and
evaluate the NPEM for horizontal and non-horizontal receiver camera positions.
Moreover, under horizontal receiver terminal position, we explore the
relationship between the NPEM and the light-emitting diode (LED) cell layout,
approximate the relationship between the NPEM and the number of LEDs captured
by the camera, and evaluate the approximation accuracy according to the
simulated positioning error. Based on the approximation results, we optimize
the LED transmitter cell layout to minimize NPEM assuming structured square
cell layouts with certain distance parameters.
