  This paper presents two schemes to jointly estimate parameters and states of
discrete-time nonlinear systems in the presence of bounded disturbances and
noise and where the parameters belong to a known compact set. The schemes are
based on sampling the parameter space and designing a state observer for each
sample. A supervisor selects one of these observers at each time instant to
produce the parameter and state estimates. In the first scheme, the parameter
and state estimates are guaranteed to converge within a certain margin of their
true values in finite time, assuming that a sufficiently large number of
observers is used and a persistence of excitation condition is satisfied in
addition to other observer design conditions. This convergence margin is
constituted by a part that can be chosen arbitrarily small by the user and a
part determined by the noise levels. The second scheme exploits the convergence
properties of the parameter estimate to perform subsequent zoom-ins on the
parameter subspace to achieve stricter margins for a given number of observers.
The strengths of both schemes are demonstrated using a numerical example.
