Joint Multisensor Fusion and Tracking Using Distributed Radars
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This thesis deals with multisensor fusion in the presence of systematic errors in the context of target tracking. A typical target tracking problem consists of multiple sensors producing position measurements of multiple targets, for instance aircraft. The goal is to establish tracks on all targets that are observed by the sensors. A track usually consists of an id, such as a track number, target position, and target velocity. The systematic errors are modeled as measurement biases. If unaccounted for these biases may lead to inaccurate estimates of the target state (position and in particular velocity) and a single target may appear as several targets if the biases are large enough (ghost tracks). Furthermore, if all sensors are biased it is challenging to find an unbiased estimate of target state with respect to a coordinate system independent of the sensors. In this thesis the sensors are radars producing measurements in 3D. The systematic errors (biases) are called alignment bias, location bias and sensor bias. The first two are related to sensor deployment, as they describe errors in orientation (misalignment) and sensor placement (location). The sensor bias addresses errors caused by sensor imperfections. These biases are estimated relative to a sensor independent coordinate system and relative to a sensor of reference (master sensor). A novel distinction is made in this context, where a universal bias estimator (UBE) is used relative to sensor independent coordinates, while an absolute bias estimator (ABE) is used relative to a master sensor. The estimability of the biases is investigated using a novel estimability index, which quantifies whether a bias can be estimated more accurately with the available measurements. The estimability index is based on the Cramer-Rao Lower Bound. The study of estimability is used to determine a multisensor-multitarget scenario where several bias estimators are compared with respect to performance using a Monte Carlo simulation. The simulation includes alignment, location and sensor biases, and all sensors are affected. The estimators are evaluated in sensor independent coordinates and master sensor coordinates. Two Kalman Filter (KF) based estimators are used as references. A lower bound is represented by a KF where the bias values are known, while an upper bound is represented by a KF where the measurement noise is increased to reflect the biases present. The alignment, location and sensor biases contain three elements each, to a total of nine bias values to estimate per sensor. The UBE performs well (below the upper bound) in sensor independent coordinates when one of the sensor bias values are removed from the simulation, estimating eight bias values per sensor. Performance is close to the lower bound when the location bias only is removed, yielding six bias values per sensor. In master sensor coordinates the ABE has the best performance. However a simplified version has almost identical performance. It is called the Relative Bias Estimator (RBE), and it neglects the biases of the master sensor. This is a popular assumption in the literature, and this study confirms that this simplification should be preferred in an implementation. Possible extensions of this work are explored. First curved target motion is explored by letting the target move at constant altitude above the Earth. The curvature of the trajectory results in increased bias estimability. However, observing this curvature requires observing the target for a long time with high accuracy. This is challenging in practice, and therefore this path was not explored further. Second, extending the application to Air Traffic Control (ATC) is considered. At airports radars typically produce 2D measurements, so to extend the developed 3D bias estimators it is necessary to incorporate altitude measurements from the aircraft Mode C transponders with these 2D measurements. The altitude measurements are quantized and received with a coarse resolution which may have a negative impact on bias estimator performance since the vertical velocity estimate becomes unstable. Several estimators are developed to estimate altitude and vertical velocity, and these are tested on real measurement data for a performance comparison. The main contribution is the use of the Interacting Multiple Model (IMM) and Unscented Kalman Filter (UKF) based estimators on quantized real world measurements. The UKF produces the best performance for long term altitude predictions, meaning that its vertical velocity estimate is the most stable.