Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

http://ieeexplore.ieee.org/iel5/5/31307/01456462.pdf

Linear systems

Identification methods for Hammerstein nonlinear systems

Combined state and least squares parameter estimation algorithms for dynamic systems

Gradient based and least squares based iterative algorithms for matrix equations AXB + CXTD = F ☆

The output-error model structure is often used in practice and its identification is important for analysis of output-error type systems. This paper considers the parameter identification of linear and nonlinear output-error models. A particle filter which approximates the posterior probability density function with a weighted set of discrete random sampling points is utilized to estimate the unmeasurable true process outputs. To improve the convergence rate of the proposed algorithm, the scalar innovations are grouped into an innovation vector, thus more past information can be utilized. The convergence analysis shows that the parameter estimates can converge to their true values. Finally, both linear and nonlinear results are verified by numerical simulation and engineering.

Particle filtering based parameter estimation for systems with output-error type model structures

Hierarchical least-squares based iterative identification for multivariable systems with moving average noises

This paper deals with the parameter identification for dual-rate sampled-data systems, aiming to identify the systems directly from the dual-rate sampled data. The main idea is carried out by two steps. Firstly, a polynomial transformation technique is employed to change the output-error model for single-rate systems to the one that can directly use the dual-rate sampled data. Secondly, a bias compensation based identification is demonstrated to get the unbiased parameter estimates of the transferred dual-rate model. Simulation examples are given to illustrate the proposed algorithm.

Heqiang Han

Papers

Hierarchical least-squares based iterative identification for multivariable systems with moving average noises

Bias compensation based parameter estimation for dual-rate sampled-data systems