ESPIRIT is a recently developed technique for high-resolution signal p
arameter estimation with applications to direction-of-arrival estimati
on and time series analysis. By exploiting invariances designed into t
he sensor array, parameter estimates are obtained directly, without kn
owledge of the array response and without computation or search of som
e spectral measure. The original formulation of ESPIRIT assumes there
is only one invariance in the array associated with each dimension of
the parameter space. However, in many applications, arrays that posses
s multiple invariances (e.g., uniform linear arrays, uniformly sampled
time series) are employed, and the question of which invariance to us
e naturally arises. More importantly, it is desirable to exploit the e
ntire invariance structure simultaneously in estimating the signal par
ameters. Herein, a subspace-fitting formulation of the ESPIRIT problem
is presented that provides a framework for extending the algorithm to
exploit arrays with multiple invariances. In particular, a multiple i
nvariance (MI) ESPIRIT algorithm is developed and the asymptotic distr
ibution of the estimates obtained. Simulations are conducted to verify
the analysis and to compare the performance of MI ESPIRIT with that o
f several other approaches. The excellent quality of the MI ESPIRIT es
timates is explained by recent results which state that, under certain
conditions, subspace-fitting methods of this type are asymptotically
efficient.