  System identification poses a significant bottleneck to characterizing and
controlling complex systems. This challenge is greatest when both the system
states and parameters are not directly accessible leading to a dual-estimation
problem. Current approaches to such problems are limited in their ability to
scale with many-parameter systems as often occurs in networks. In the current
work, we present a new, computationally efficient approach to treat large
dual-estimation problems. Our approach consists of directly integrating
pseudo-optimal state estimation (the Extended Kalman Filter) into a
dual-optimization objective, leaving a differentiable cost/error function of
only in terms of the unknown system parameters which we solve using numerical
gradient/Hessian methods. Intuitively, our approach consists of solving for the
parameters that generate the most accurate state estimator (Extended Kalman
Filter). We demonstrate that our approach is at least as accurate in state and
parameter estimation as joint Kalman Filters (Extended/Unscented), despite
lower complexity. We demonstrate the utility of our approach by inverting
anatomically-detailed individualized brain models from human
magnetoencephalography (MEG) data.
