  In this paper, we present an approach to identify linear parameter-varying
(LPV) systems with a state-space (SS) model structure in an innovation form
where the coefficient functions have static and affine dependency on the
scheduling signal. With this scheme, the curse of dimensionality problem is
reduced, compared to existing predictor based LPV subspace identification
schemes. The investigated LPV-SS model is reformulated into an equivalent
impulse response form, which turns out to be a moving average with exogenous
inputs (MAX) system. The Markov coefficient functions of the LPV-MAX
representation are multi-linear in the scheduling signal and its time-shifts,
contrary to the predictor based schemes where the corresponding LPV
auto-regressive with exogenous inputs system is multi-quadratic in the
scheduling signal and its time-shifts. In this paper, we will prove that under
certain conditions on the input and scheduling signals, the $\ell_2$ loss
function of the one-step-ahead prediction error for the LPV-MAX model has only
one unique minimum, corresponding to the original underlying system. Hence,
identifying the LPV-MAX model in the prediction error minimization framework
will be consistent and unbiased. The LPV-SS model is realized by applying an
efficient basis reduced Ho-Kalman realization on the identified LPV-MAX model.
The performance of the proposed scheme is assessed on a Monte Carlo simulation
study.
