A novel Kalman filter based technique for calculating the time history of vertical displacement of a boat from measured acceleration

Abstract

Accelerometers are used to measure velocity and displacement in many applications such as ship motion, monitoring of civil and mechanical structure, seismology and machine condition monitoring. However, using direct numerical integration to calculate velocity and displacement from the acceleration signal is known to suffer from low frequency noise amplification and wind-up. In this paper, a Kalman filter based method is proposed for calculating displacement from measured acceleration. Integration wind-up is eliminated by incorporating an additional state variable, namely the integral of the displacement whose "measured" value is assumed to be equal to the known average value of the displacement. In many applications, such as those in marine environment, this average value can be assumed to be constant, usually conveniently assigned to be zero if non-linear behaviour and permanent deformations are deemed negligible. The paper describes the technique and investigates its performance under different conditions of amplitude and frequency of vibrations and sampling rate and validates it by conducting two laboratory experiments. In the first experiment the displacement of a small shaker is calculated from a relatively high frequency (tens of Hz) acceleration signal sampled at 1 kHz with a resolution of 1 g. The calculated displacement of the shaker is found to agree well with that measured using a high resolution laser. In the second experiment, the proposed method is applied to the calculation of the vertical displacement of a boat from a low frequency (less than 1 Hz) acceleration signal sampled at 5 Hz and a resolution of 0.01g. An experimental set up designed to mimic typical motion of a boat is used to validate the results. Although the method explained in this paper is used to calculate the vertical displacement of a boat, it can be applied for calculating the displacement in a wide range of applications with reciprocating movement.