The multiple-model recursive least-squares algorithm constitutes a very flexible technique for handling many models simultaneously. It is based on a single matrix factorization and directly yields all lower-order models, including parameter estimates and loss functions. The employed factorization structure improves numerical performance and, as a result, problems associated with overparametrization are avoided. In this paper, it is combined with an operator transformation, termed the \(\lambda\)-transform, that is known to allow for keeping a continuous-time parametrization while offering use of the discrete-time maximum likelihood approach to parameter estimation. The purpose of the resulting combination is the simultaneous identification of multiple-model continuous transfer functions from non-uniformly sampled input-output data which appear, e.g., in sensor and actuator networks. The authors demonstrate that the \(\lambda\)-transformation is equivalent to a canonical transformation between the discrete \(\mathcal{Z}\)-domain and the \(\delta\)-domain using the negative value of the \(\lambda\)-transform filter time-constant instead of the sampling interval parameter. The resulting algorithm handles oversampling, sampling jitter or non-uniform sample intervals without any need for extra digital anti-aliasing pre-filtering, downsampling or interpolation algorithms, simultaneously producing multiple models with a cost function that facilitates automatic selection of best-fitted models. Apart from that, measurement noise is indicated here as beneficial, bringing up an inherent bias toward low-order models.
The paper is accompanied by simulated examples, among which the one regarding a thermoelectric drum-boiler level loop exhibiting a non-minimum phase behaviour illustrates well the efficiency of the proposed method. It is complemented with a Matlab code implementing the proposed technique. Among prospective applications, identification of dominant dynamics of a drum-boiler level control loop using data collected from an industrial supervisory system or from archived compressed data is to be highlighted. Fault detection algorithms that rely on tracking the estimated physical parameters associated with continuous model transfer functions are also relevant applications that can benefit from the proposed approach.