  For pedestrians moving without spatial constraints, extensive research has
been devoted to develop methods of density estimation. In this paper we present
a new approach based on Voronoi cells, offering a means to estimate density for
individuals in small, unbounded pedestrian groups. A thorough evaluation of
existing methods, encompassing both Lagrangian and Eulerian approaches employed
in similar contexts, reveals notable limitations. Specifically, these methods
turn out to be ill-defined for realistic density estimation along a
pedestrian's trajectory, exhibiting systematic biases and fluctuations that
depend on the choice of parameters. There is thus a need for a
parameter-independent method to eliminate this bias. We propose a modification
of the widely used Voronoi-cell based density estimate to accommodate
pedestrian groups, irrespective of their size. The advantages of this modified
Voronoi method are that it is an instantaneous method that requires only
knowledge of the pedestrians' positions at a give time, does not depend on the
choice of parameter values, gives us a realistic estimate of density in an
individual's neighborhood, and has appropriate physical meaning for both small
and large human crowds in a wide variety of situations. We conclude with
general remarks about the meaning of density measurements for small groups of
pedestrians.
