Knowing the plug-level power consumption of each appliance in a building can lead to drastic savings in energy consumption. Non-Intrusive Load Monitoring (NILM) is a method for disaggregating power loads in a building to the single appliance level, without using direct sensors or electric meters. This paper addresses the issues of NILM inaccuracy in the context of commercial and industrial buildings, by adding to the problem data from a low-cost, non-dedicated, smart sensor network. The SmartSense platform gathers environmental data and allows us to make an approximate guess on the states of some monitored appliances. The considered problem is the power estimation of each device states, subject to partial knowledge of the device states. The problem, formulated using linear algebra, is solved to estimate the power load values of these steady states on sliding windows of data with varying size. In this paper we show the principle and interest of the approach, its limited complexity, and its applicability to real datasets.