Flightpath reconstruction and systematic radar error estimation from multi-radar range-azimuth measurements

MURATREC is a facility for the off-line reconstruction of aircraft trajectories in an absolute reference frame. It is based on the processing of range and azimuth measurements of opportunity traffic in a multiradar environment. Its main features are the estimation of systematic radar errors, their covariance matrix and B-spline series approximating the reconstituted trajectories. Splines are used extensively in MURATREC because of their favourable approximative and computational properties. In this paper a description is given of the main algorithms. The systematic radar errors are computed with a batch-processing version of non-linear least-squares parameter estimation. The range and azimuth data are assembled into batches, each batch pertaining to one aircraft traversing the multi-radar coverage. A B-spline series approximating the 3-dimensional trajectory and updates of the radar errors are computed simultaneaously for each batch. Knowledge on the radar errors is propagated via their square-root information matrix as updated after processing each flight. The co-ordinate transformations between the reference frame and the local radarframes are based on the ellipsoid EURO-50 earth model. They are the main source of non-linearity in the estimation problem. Their description is omitted. Reconstitution of trajectories is essentially the same problem, however, without the systematic errors. Triangularization is implicitely performed in this manner if no height information is available. Results of validating MURATREC against high precision test flights are discussed. Absolute accuracies up to the radar resolution or better are obtained despite the weird error patterns that sometimes occur in live radar data.