| Summary: | Target tracking from non-invertible measurement sets, for example, incomplete spherical coordinates measured by asynchronous sensors in a sensor network, is a task of data fusion present in a lot of applications. Difficulties in tracking using extended Kalman filters lead to unstable behavior, mainly caused by poor initialization. Instead of using high complexity numerical batch-estimators, we offer an analytical approach to initialize the filter from a minimum number of observations. This directly pertains to multi-hypothesis tracking (MHT), where in the presence of clutter and/or multiple targets (i) low complexity algorithms are desirable and (ii) using a small set of measurements avoids the combinatorial explosion. Our approach uses no numerical optimization, simply evaluating several equations to find the state estimates. This is possible since we avoid an over-determined setup by initializing only from the minimum necessary subset of measurements. Loss in accuracy is minimized by choosing the best subset using an optimality criterion and incorporating the leftover measurements afterwards. Additionally, we provide the possibility to estimate only sub-sets of parameters, and to reliably model the resulting added uncertainties by the covariance matrix. We compare two different implementations, differing in the approximation of the posterior: linearizing the measurement equation as in the extended Kalman filter (EKF) or employing the unscented transform (UT). The approach will be studied in two practical examples: 3D track initialization using bearingsonly measurements or using slant-range and azimuth only.
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