Robust estimation techniques for target-motion analysis using passively sensed transient signals

On The Implementation Of A Transient Model For An Intelligent Target Motion Analysis System

“…In a real application, the time delay measurements are disturbed by noise, caused, for example, by the crosscorrelation function used for finding a common signal in a pair of sensors or by the environment (Carevic 2003). Therefore, the measured time delay t i is a linear combination of the real time delay i and a measurement error e i :…”

“…Carevic (2003) proposed a probability density function for modelling this error as independent random variables based on a two-component Gaussian-mixture model: It can be seen that the tails are much wider for the Gaussian-mixture distribution, which implies that there is always a certain measurement error. This noise makes it difficult for traditional Least Squares Methods to solve the TMA problem.…”

“…In order to obtain realistic results from the simulations, 1 in the probability density function (Equation 6) is modelled as a function of the target range R (Carevic 2003). Figure 3 shows the dependency of 1 σ on target range R. …”

“…Another source of errors is false readings or clutter (Carevic 2003). This clutter is usually assumed to be uniformly distributed over an area A and to follow a Poisson probability density function with a known parameter λ.…”

“…But because of the noisy data and possible outliers in the readings from the hydrophones, LS methods cannot be used directly to minimise the residuals. Often so-called M-estimators are used here, which replace the original error function with a symmetric positive-definite objective function (Carevic 2003). Other methods used are Maximum Likelihood and Bayes estimators.…”