Phase advance and β function are basic lattice functions characterizing the linear properties of an accelerator lattice. Accurate and efficient measurements of these quantities are important for commissioning and operating a machine. For rings with little coupling, we report a new method to measure these lattice functions based on the model-independent analysis technique, which uses beam histories of excited betatron oscillations measured simultaneously at a large number of beam position monitors. It is simple, fast, accurate, and robust. Measurements done at the storage ring of the Advanced Photon Source are reported. Comparisons among various methods are made.