This paper presents a real-time parameter identification algorithm for periodic signals, based on the recursive variable projection (RVP) algorithm. The recursive implementation enables the tracking of time-varying parameters. The signal model is linear with respect to the amplitude parameters while being nonlinear with respect to the phase and frequency. This feature motivates the use of a variable projection based approach. Its performance is tested using Monte Carlo simulations and the results are compared with those obtained by a multiobjective Gauss-Newton (MGN) algorithm. Furthermore, the RVP algorithm is applied to measurement data acquired by a MEMS accelerometer and it is demonstrated that it can successfully track time-varying linear and nonlinear parameters.