This chapter examines the estimation of multivariable linear models for which the parameters vary in a time-varying manner that depends in an affine fashion on a known or otherwise measured signal. These locally linear models which depend on a measurable operating point are known as linear parameter varying (LPV) models. The contribution here relative to previous work on the topic is that in the Gaussian case, an expectation-maximisation (EM) algorithm-based solution is derived and profiled.