Identification of physiological systems: estimation of linear time-varying dynamics with non-white inputs and noisy outputs.

A new technique to identify linear time-varying systems from ensembles of input-output realisations is presented. First, a correlation-based least-squares method is derived. This method consists of solving, for each sampling time, a matrix equation involving estimates of the input autocorrelation and input-output cross-correlation functions computed from data across the ensemble. Then, the matrix inverse needed to solve this matrix equation is replaced with a pseudo-inverse. The model is thus constrained to describe only those components of the dynamics that can be reliably identified. Ignoring 'unidentifiable' components has virtually no adverse effect on the predicted outputs. Simulation results demonstrate that the pseudoinverse technique yields more reliable estimates of the dynamics than a previously proposed least-squares technique when the inputs are coloured and the output signal-to-noise ratio (SNR) is low. With the input spectrum flat up to approximately 10% of the sampling rate and an output SNR of 5dB, the mean variance accounted for (VAF) between the true instantaneous impulse response functions (IRFs) and the instantaneous IRFs estimated with the least-squares technique was 0.2%. In contrast, the mean VAF between the true instantaneous IRFs and the instantaneous IRFs estimated with the pseudoinverse technique was 89.0%.