  The problem of estimating parameters of a deterministic jump or piecewise
linear model is considered. A subspace technique referred to as spectral
clustering on subspace (SCS) algorithm is proposed to estimate a set of linear
model parameters, the model input, and the set of switching epochs. The SCS
algorithm exploits a block diagonal structure of the system input subspace,
which partitions the observation space into separate subspaces, each
corresponding to one and only one linear submodel. A spectral clustering
technique is used to label the noisy observations for each submodel, which
generates estimates of switching time epoches. A total least squares technique
is used to estimate model parameters and the model input. It is shown that, in
the absence of observation noise, the SCS algorithm provides exact parameter
identification. At high signal to noise ratios, SCS attains a clairvoyant
Cram\'{e}r-Rao bound computed by assuming the labeling of observation samples
is perfect.
