Session: P3A

Background: The Kalman filter is an effective tool for estimating a stochastic process in noise. Given a state-space model of a stochastic process, the Kalman filter recursively estimates state variables from noisy measurements by minimizing the sum of squared estimation errors. It is an optimal estimator for a Gauss random process and provides estimates of error variances. Its application for harmonic vibration detection may improve vibro-acoustography for tissue characterization in medical applications. Approach: The harmonic motion generated by the ultrasound radiation force of vibro-acoustography is represented in repetitive ultrasound pulse echoes. The motion at a given vibration frequency is modeled with a 2 order differential equation with random amplitude and phase, which are represented by two state variables in a discrete state equation. Kalman filter estimates the state variables from received ultrasound echoes and provides the estimation error covariance. Methods: In a water tank a piece of metal is vibrated by a mechanical actuator at 500 Hz with very low amplitude. The vibration is detected with a pulse echo ultrasound transducer and a laser vibrometer simultaneously. The pulse repetition frequency is 4 kHz and the center frequency of the transducer is 5 MHz. Sixty-five pulses are transmitted for each of nine different vibration amplitudes. Results: The Kalman filter successfully estimated the vibration amplitudes of displacements from 28.7 ± 7.3 nm to 3.83 ± 0.19 μm and vibration phases from 0 to ± 60◦ with average estimation errors from 1.6◦ to 7.3◦, respectively. Comparing the amplitude estimations with those measured by the laser vibrometer, we find that error percentages of eight data sets are from 0.5% to 13.6% and one of them is 30.7%. The comparison results match the error estimations given by the Kalman filter. Conclusion: The results indicate that the Kalman filter effectively estimates amplitude and phase of very small harmonic vibration for vibro-acoustography.