Abstract
An indirect downsampling approach for continuous-time input/output system identification is proposed. This modus operandi was introduced to system identification through a sub-space algorithm, where the input/output data set is partitioned into lower rate m subsets. Then, a state-space discrete-time model is identified by fusing the data subsets into a single one. In the present work the identification of the input/output downsampled model is performed by a least squares and a simplified refined instrumental variables (IV) procedures. In this approach, the inter-sample behaviour is preserved by the addition of fictitious inputs, leading to an increase of excitation requirements of the input signal. This over requirement is removed by directly estimating from the data the parameters of the transfer function numerator. The performance of the method is illustrated using the Rao-Garnier test system.

Abstract
A kernel regressor to estimate a six-degree-of-fredoom non linear model of an autonomous underwater vehicle is proposed. Although this estimator assumes that the model coefficients are linear combinations of basis functions, it circumvents the problem of specifying the basis functions by using the kernel trick. The Gaussian radial basis function is the chosen kernel, with the Kernel matrix being regularized by its principal components. The variance of the Gaussian radial basis function and the number of principal components are hyper-parameters to be determined by the minimisation of a final prediction error criterion and using the training data. A simulated autonomous underwater vehicle is proposed was used as case study.

Abstract
Knowledge of the Kalman filter is very important in machine learning since is the basis for understanding more advanced concepts. Towards this end, control and estimation courses should assure the understanding of the concept and its correct application. A tutorial on the design, implementation and test of the KF to denoise the discharge current of a Li-ion cell is presented in this article. The students are also meant to acquire the discharge data used in the case study - Discharge of a Li-ion cell. The Battery Discharger Board is a low cost device to discharge Li-ion cells with a user programmable current discharge profile. The discharge is controlled and monitored by an external microcontroller connected to a host computer that stores and processes the discharge data. This board has been constructed to help students to gain insight into batteries. The current is measured by ACS712 Hall sensors, which are low cost but also very noisy. To de-noise the current measurements two different KF are used with the current being modelled as the state of a first order integrator. In the first approach, the KF assumes that the system is disturbed by process and measurement noises while in the second it only assumes measurement noise, The operation of the discharge board is illustrated in two experiments: (i) one with a constant discharge current and (ii) the other with a pulsed current. In both experiments, the filters performance was very good. Copyright (c) 2023 The Authors.

Abstract
In this work, the prediction of a time series is formulated as a gaussian process regression, for different levels of noise. The gaussian regressor is translated into lower rank Dynamic Mode Decomposition methods that use kernels (K-DMD) - Kernel regression and Least Squares Support Vector Machines. The presented unified approach delivers an algorithm where the optimisation of the marginal likelihood function can be used to find the parameters of the kernel regression. The viability of the procedure is demonstrated on a chaotic series, with quite good adjustment results being obtained. Copyright (c) 2023 The Authors.

Abstract
Forecasting is a task with many concerns, such as the size, quality, and behavior of the data, the computing power to do it, etc. This letter proposes the dynamic mode decomposition (DMD) as a tool to predict the annual air temperature and the sales of a stores' chain. The DMD decomposes the data into its principal modes, which are estimated from a training data set. It is assumed that the data is generated by a linear time-invariant high order autonomous system. These modes are useful to find the way the system behaves and to predict its future states, without using all the available data, even in a noisy environment. The Hankel block allows the estimation of hidden oscillatory modes, by increasing the order of the underlying dynamical system. The proposed method was tested in a case study consisting of the long term prediction of the weekly sales of a chain of stores. The performance assessment was based on the best fit percentage index. The proposed method is compared with three neural networkbased predictors.

Abstract