The focus of this work lies on multi-object estimation techniques, in particular the Probability
Hypothesis Density (PHD) filter and its variations. The PHD filter is a recursive, closed-form estimation
technique which tracks a population of objects as a group, hence avoiding the combinatorics
of data association and therefore yielding a powerful alternative to methods like Multi-Hypothesis
Tracking (MHT). Its relatively low computational complexity stems from strong modelling assumptions
which have been relaxed in the Cardinalized PHD (CPHD) filter to gain more flexibility, but
at a much higher computational cost. We are concerned with the development of two suitable
alternatives which give a compromise between the simplicity and elegance of the PHD filter and
the versatility of the CPHD filter. The first alternative generalises the clutter model of the PHD
filter, leading to more accurate estimation results in the presence of highly variable numbers of false
alarms; the second alternative provides a closed-form recursion of a second-order PHD filter that
propagates variance information along with the target intensity, thus providing more information
than the PHD filter while keeping a much lower computational complexity than the CPHD filter.
The discussed filters are applied on simulated data, furthermore their practicality is demonstrated
on live-cell super-resolution microscopy images to provide powerful techniques for molecule and
cell tracking, stage drift estimation and estimation of background noise
