State-space based modeling for imaging system identification

State-space (SS) based modeling for imaging electro-optical (EO) systems representing various states facilitates a method for system estimation. Traditionally linear shift-invariant (LSI) systems are modeled using Fourier analysis (FA). However, models based on FA may not have a clear insight too the instability reasons, whereas SS based models with system poles and zeros have a clear insight to the system stability information. In this paper, we introduce three methods to estimate system parameters for LSI EO imaging systems using SS based modeling. These methods include batch processing version of least squares (LS) estimation, recursive version of LS estimation, and sliding window LS estimation. The accuracy of the developed methods was tested using input and output signals of simulated LSI systems. First, LSI systems with various system parameters (poles and zeros) were simulated, which were then used to generate output signals for a set of random input signals, with each input signal value representing the average of an image. Then, these input and output signals were used to estimate systems employing SS and FA based modeling. Further, the estimated systems were used to generate output signals for a new set of input signals. For any given input signal, output signals generated by both systems were compared for similarities and signal-to-noise ratio (SNR). Results show that SS based models generate output signals that have higher SNR values. In addition, developed methods were tested against the simulated data and results show promise for development of models for estimating more complicated systems (e.g., non-linear system).