Fast Robust Estimators for Linear Regression and Doppler-Bearing Tracking

Anders Rosenqvist

Department of Mathematical Statistics,
Lund Institute of Technology,
Lund University,

A pseudo-linear estimator for Doppler-bearing tracking, called DBPLE, is proposed. By applying it to individual legs a multi-leg tracker is created. The DBPLE is fast, explicit and stable. It is further almost free from bias and has a precision comparable to that of the computationally far more expensive maximum likelihood estimator, MLE. The DBPLE works well in most non-manoeuvring own-ship scenarios and asymptotic theory is used to investigate when. Under some conditions, especially if the own-ship manoeuvres, the DBPLE needs to be followed by another estimator to be effective. The MLE or an approximate likelihood estimator, ALE, inspired by the DBPLE, can play that role. All three estimators are studied in a variety of scenarios where the own-ship is manoeuvring as well as not.

A method for fast robust linear regression, the EP-method, is proposed and used to achieve robust manoeuvre detection. The calculations are based on least squares methods, inherit their equivariance features and are fast. The EP-method is also applied to various published data materials.

The Hough transform, frequently used for localization of lines and other patterns in digital images, is used to propose a new fast estimator for robust simple regression. It searches for the best parameters in a way that is inspired by the Fast Hough Transform, FHT. The resulting estimator can be interpreted as an M-estimator with a robust scale estimate. Its performance is tested using a simple linear regression experiment.

Key words:
Doppler-bearing tracking, pseudo-linear estimation, target motion analysis, passive ranging, robust linear regression, leverage point, outlier, image analysis, Hough transform.