A stochastic model of the time-of-flight noise in airborne sonar ranging systems

A stochastic model is developed for describing the statistical properties of the noise present in the time-of-flight (TOF) measurements made by in-air ultrasonic (US) transducers. The proposed method of analysis decomposes the TOF noise into three components with different physical origin and properties: a deterministic time-varying mean, a correlated random process and an uncorrelated random process. The physics of US waves propagating in air and the operating mode of typical sonar ranging systems are considered in orienting the choice of the model structure. The time-varying mean correlates with global thermal changes and drafts affecting the environment. The de-trended data are assumed to result from the sum of a correlated random component, due to inhomogeneities in the medium, such as temperature gradients and air turbulence, and an uncorrelated random component, mainly due to the wide band electronic noise superimposed on the echo signal. Autoregressive-moving average (ARMA) modelling techniques are used to capture the correlation structure with exponential decay of the piecewise stationary correlated random process. A method of adaptive segmentation allows to test for weak stationarity of this component. Kalman filtering techniques are used for its estimation. The adequacy of the representation in typical indoor environments is demonstrated by analyzing experimental data from Polaroid sensors.