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.