The precise (location) tracking of automated guided vehicles will be key in enlarging the productivity, efficiency and safety in the connected warehouse or production infrastructure. Combining the modest price tag, the adequate coverage and the potential centimetre accuracy makes Visible Light Positioning (VLP) systems appealing as replacements for the current, high-cost, tracking systems. Model-fingerprinting-based received signal strength (RSS) VLP enables the required accuracy. It requires an elaborate optical channel model fingerprinted in a fine-grained, and predefined positioning grid. Depending on the grid's granularity, constructing the fingerprint database demands a significant computation and storage effort. This paper employs response adaptive or sequential experimental design to form sparse channel models, vastly reducing the storage and computation. It is shown that model-fingerprinting-based RSS only requires modelling less than 1 percent of the grid points, in an elementary positioning cell. The sparse model can be re-evaluated as a way to cope with environment changeover. Model recomputation as a way of compensating for LED ageing is also studied.