Local Identification in Dynamic Networks using a Multi-Step Least Squares Method

For identification of a single module in a linear dynamic network with correlated disturbances different meth-ods are available in a prediction error setting. While indirect methods fully rely on the presence of a sufficient number of external excitation signals for achieving data-informativity, the local direct method with a MIMO predictor model can exploit also non-measured disturbance signals for data-informativity. However, a simple two-node example shows that this local direct method can also be conservative in terms of the number of ex-ternal excitation signals that is required. Inspired by a recently introduced multi-step method for full network identification, we present a multi-step least squares method for single module identification. In a first indirect step a model is estimated that is used to reconstruct the innovation on a set of output signals, which in a second step is used to directly estimate the module dynamics with a MISO predictor model. The resulting path-based conditions for data-informativity show that the multi-step method requires a smaller number of excitation signals for data-informativity than the local direct method.