Abstract

Abstract

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
The successive approximation Linear Parameter Varying systems subspace identification algorithm for discrete-time systems is based on a convergent sequence of linear time invariant deterministic-stochastic state-space approximations. In this chapter, this method is modified to cope with continuous-time LPV state-space models. To do this, the LPV system is discretised, the discrete-time model is identified by the successive approximations algorithm and then converted to a continuous-time model. Since affine dependence is preserved only for fast sampling, a subspace downsampling approach is used to estimate the linear time invariant deterministic-stochastic state-space approximations. A second order simulation example, with complex poles, illustrates the effectiveness of the new algorithm. © 2012 by World Scientific Publishing Co. Pte. Ltd.

Abstract

Abstract
The fitting of a causal dynamic model to an image is a fundamental problem in image processing, pattern recognition, and computer vision. There are numerous other applications that require a causal dynamic model, such as in scene analysis, machined parts inspection, and biometric analysis, to name only a few. There are many types of causal dynamic models that have been proposed in the literature, among which the autoregressive moving average (ARMA) and state-space models are the most widely known. In this paper we introduce a 2-D stochastic state-space system identification algorithm for obtaining stochastic 2-D, causal, recursive, and separable-in-denominator (CRSD) models in the Roesser state-space form. The algorithm is tested with a real image and the reconstructed image is shown to be almost indistinguishable to the true image.