zation or dye-swap normalization. Although measurement errors on gene expression are assumed to be uncorrelated, thus Σ~*ϵ*~ is a diagonal matrix, this does not mean, nor imply, that the observed gene expression values themselves are uncorrelated. In fact, the observed gene expression values are modeled as linear combinations of regulators which are themselves correlated. The system matrix *F* describes the temporal development of the regulators, and the gene regulation matrix *G* is identifiable only if the dimension *m* of the state space is smaller than the number of observed time points *T*. Typically, in biological experiments the number of relevant regulators is small, and therefore this issue is not anticipated as problematic. Something that is dealt with later, but worth noting now, is that the gene regulation matrix *G* and the system matrix *F* are not unique, and any renumbering of the hidden regulators will most likely lead to different gene regulation and system matrices. We chose this model because it provides a large degree of flexibility in the hidden regulators which could be cell internal or external components. On the other hand, the simplifying assumptions of time independent regulation matrices *G* and *F* and a linear relationship between regulating elements and gene expressions are biologically reasonable.

2.2. KM-Algorithm {#sec2.2}
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A modified EM-algorithm is employed to estimate the parameters of the state space model. The parameters that are of interest, and that need to be estimated in the state space model ([1](#EEq1){ref-type="disp-formula"}), consist of the gene regulation matrix *G*, the system matrix *F*, the covariance matrices of the biological error Σ~*δ*~, the measurement error Σ~*ϵ*~, and the mean and covariance matrix for the Gaussian distribution of the initial regulator state *Y* ~0~ ∼ *N*(*μ*, Σ).

The KM-algorithm starts with random initial values for the model parameters and then alternates between the Kalman smoothing (KS) estimates of the 