A process parameter associated with a material contained in a vibrating
structure is estimated. A plurality of motion signals representing motion
at a plurality of locations of the vibrating structure are received. The
received plurality of motion signals are force filtered with a force
filter to produce a force-filtered motion signal that discriminates motion
attributable to a force of interest among a plurality of forces acting on
the vibrating structure. A process parameter associated with the material
contained in the vibrating structure is estimated from the force filtered
motion signal. Preferably, a plurality of motion signal values is
generated from the received plurality of motion signals, and force
filtering includes the step of applying a force filter matrix to the
plurality of motion signal values to produce a force filtered motion
signal value. A process parameter, such as mass flow, density or the like,
is then estimated from the force filtered motion signal value. According
to an aspect of the present invention, the force filter matrix represents
a product of a frequency response function matrix for the vibrating
structure, a force selectivity matrix and an inverse of the frequency
response function matrix. Methods for estimating structural motion, along
with related apparatus and computer program products, are also discussed.