Systems and methods for an elevator. The elevator includes an elevator car to move along a first direction. A transmitter for transmitting a signal having a waveform. A receiver for receiving the waveform. A processor having memory is configured to represent the received waveform as a hybrid sinusoidal frequency modulated (FM)-polynomial phase signal (PPS) model. The hybrid sinusoidal FM-PPS model having PPS phase parameters representing a speed of the elevator car along a first direction and a sinusoidal FM phase parameter representing a vibration of the elevator car along a second direction. The processor solves the hybrid sinusoidal FM-PPS model to produce the speed of the elevator car or the vibration of the elevator car or both. A controller controls an operation of the elevator using the speed of the elevator car or the vibration of the elevator car, or both, to assist in an operational management of the elevator.