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In contrast to Chap. 5 where the blind SIMO system identification problem is investigated, this chapter is devoted to the identification of MIMO systems. Compared with the blind identification of the SIMO system (or a polynomial vector), the blind identification of an MIMO system (or a polynomial matrix) turns out to be more challenging. In this chapter, the blind identification of MIMO FIR systems will be studied in detail, which can be considered to be an extension of the blind SIMO system identification. In addition, the blind identification of a multivariable state-space model will be investigated, which can be regarded as the extension from the FIR systems to autoregressive systems.

For the blind identification problem, the concerned system model is usually represented as a transfer function vector/matrix, and the identification task aims to recover the transfer function vector/matrix as well as the unknown input signal using only the output observations. So far, there are rarely any research on the blind identification of state-space models, since a state-space model will introduce unknown system states and pose identification challenges. Although the blind identification of multi-channel state-space models has been investigated in Chap. 8, it relies on the special SIMO structure of the system model. As an extension, the blind identification of structured state-space model will be investigated in this chapter.

The blind identification requires to recover both the source signal and the system model using only the system output. For complex systems or high-dimensional LTI systems, it is computationally prohibitive to fulfill the whole blind identification process on a single computational unit. To deal with this problem, distributed blind identification approaches will be developed based on interconnected computational platforms (also called network nodes), where a complex identification task is performed by local information exchange among neighboring nodes. In other words, a computationally demanding blind identification problem shall be handled by the cooperation of a number of “cheap” computational platforms.

For a large-scale networked system, it is computationally prohibitive to conduct the global network identification on a single computational platform. To deal with this problem, the global network is split into a number of local subnetworks and the global identification is to be accomplished by local identifications of subnetworks in parallel. However, due to the couplings or unmeasurable interconnections among the systems operating in a large-scale network, the local identification is inherently a blind identification problem, which is similar to that investigated in Chap. 9. However, due to specific properties of the unmeasurable interconnection signals, a numerically reliable subspace identification approach will be developed by subsequently estimating the unknown inputs and the local state-space models.

To study the blind system identification with unknown inputs, it is essential to know the basic identification approaches in the system identification community. This chapter introduces three different methods for the identification of multi-variable system models using input and output data.