This paper describes methods for dynamic measurement and correction of laser interferometer periodic nonlinearity down to the picometre level. A capacitive sensor is used as an external reference for measuring and calculating the periodic interferometer nonlinearity correction function. The experimental interferometer setup is a heterodyne interferometer with symmetrical paths to detectors and time-interval-based phase detection. The periodic nonlinearity is represented as harmonic Fourier components. The time evolution of the nonlinearity function is tracked during measurement. The method is verified by spatial and temporal repeatability of the measured nonlinearity. Linearization repeatability in the 10 pm range is observed.