Fixed assets are an enterprise’s core means of production and a vital asset for the enterprise’s sustainability. Good fixed asset management not only helps to enhance asset utilization but also helps to prevent idleness and asset loss, both of which are vital in the success of the enterprise. To improve fixed asset management, it needs not only a good asset management system but also advanced asset monitoring and management technology. As a result, to address the issues of difficult positioning, tracking, and low management efficiency in enterprise’s asset management, this paper optimizes the commonly used the LANDMARC positioning algorithm and implements an improved algorithm based on Lagrange nonlinear interpolation. It is also used in fixed asset positioning management to overcome the problem of increasing the density of auxiliary tags to enhance positioning accuracy, which leads to higher costs and greater radio frequency interference. Simultaneously, a set of RFID-based fixed asset management systems was built and implemented, starting with the application requirements of enterprises and combining the optimization algorithm with FRID technology. Finally, a simulation experiment on the application of the Lagrange nonlinear interpolation algorithm in fixed asset positioning management is carried out and a comparison with other algorithms is performed. According to the simulation findings, the new algorithm has enhanced the positioning accuracy. The system can perform all-around dynamic tracking and positioning management of diverse assets, optimize the use efficiency and management level of assets, and improve the intelligent level of enterprise asset management.