Towards Efficient Maximum Likelihood Estimation of LPV-SS Models

How to efficiently identify multiple-input multiple-output (MIMO) linear parameter-varying (LPV) discrete-time state-space (SS) models with affine dependence on the scheduling variable still remains an open question, as identification methods proposed in the literature suffer heavily from the curse of dimensionality and/or depend on over-restrictive approximations of the measured signal behaviors. However, obtaining an SS model of the targeted system is crucial for many LPV control synthesis methods, as these synthesis tools are almost exclusively formulated for the aforementioned representation of the system dynamics. Therefore, in this paper, we tackle the problem by combining state-of-the-art LPV input-output (IO) identification methods with an LPV-IO to LPV-SS realization scheme and a maximum likelihood refinement step. The resulting modular LPV-SS identification approach achieves statical efficiency with a relatively low computational load. The method contains the following three steps: 1) estimation of the Markov coefficient sequence of the underlying system using correlation analysis or Bayesian impulse response estimation, then 2) LPV-SS realization of the estimated coefficients by using a basis reduced Ho-Kalman method, and 3) refinement of the LPV-SS model estimate from a maximum-likelihood point of view by a gradient-based or an expectation-maximization optimization methodology. The effectiveness of the full identification scheme is demonstrated by a Monte Carlo study where our proposed method is compared to existing schemes for identifying a MIMO LPV system

Low Complexity Blind Equalization for OFDM Systems with General Constellations

This paper proposes a low-complexity algorithm for blind equalization of data in OFDM-based wireless systems with general constellations. The proposed algorithm is able to recover data even when the channel changes on a symbol-by-symbol basis, making it suitable for fast fading channels. The proposed algorithm does not require any statistical information of the channel and thus does not suffer from latency normally associated with blind methods. We also demonstrate how to reduce the complexity of the algorithm, which becomes especially low at high SNR. Specifically, we show that in the high SNR regime, the number of operations is of the order O(LN), where L is the cyclic prefix length and N is the total number of subcarriers. Simulation results confirm the favorable performance of our algorithm

Maximum-likelihood estimation of delta-domain model parameters from noisy output signals

Fast sampling is desirable to describe signal transmission through wide-bandwidth systems. The delta-operator provides an ideal discrete-time modeling description for such fast-sampled systems. However, the estimation of delta-domain model parameters is usually biased by directly applying the delta-transformations to a sampled signal corrupted by additive measurement noise. This problem is solved here by expectation-maximization, where the delta-transformations of the true signal are estimated and then used to obtain the model parameters. The method is demonstrated on a numerical example to improve on the accuracy of using a shift operator approach when the sample rate is fast

An empirical Bayes approach to identification of modules in dynamic networks

We present a new method of identifying a specific module in a dynamic network, possibly with feedback loops. Assuming known topology, we express the dynamics by an acyclic network composed of two blocks where the first block accounts for the relation between the known reference signals and the input to the target module, while the second block contains the target module. Using an empirical Bayes approach, we model the first block as a Gaussian vector with covariance matrix (kernel) given by the recently introduced stable spline kernel. The parameters of the target module are estimated by solving a marginal likelihood problem with a novel iterative scheme based on the Expectation-Maximization algorithm. Additionally, we extend the method to include additional measurements downstream of the target module. Using Markov Chain Monte Carlo techniques, it is shown that the same iterative scheme can solve also this formulation. Numerical experiments illustrate the effectiveness of the proposed methods

Least Squares Based and Two-Stage Least Squares Based Iterative Estimation Algorithms for H-FIR-MA Systems

This paper studies the identification of Hammerstein finite impulse response moving average (H-FIR-MA for short) systems. A new two-stage least squares iterative algorithm is developed to identify the parameters of the H-FIR-MA systems. The simulation cases indicate the efficiency of the proposed algorithms

Membership-set estimation using random scanning and principal component analysis

A set-theoretic approach to parameter estimation based on the bounded-error concept is an appropriate choice when incomplete knowledge of observation error statistics and unavoidable structural model error invalidate the presuppositions of stochastic methods. Within this class the estimation of non-linear-in-the-parameters models is examined. This situation frequently occurs in modelling natural systems. The output error method proposed is based on overall random scanning with iterative reduction of the size of the scanned region. In order to overcome the problem of computational inefficiency, which is particularly serious when there is interaction between the parameter estimates, two modifications to the basic method are introduced. The first involves the use of principal component transformations to provide a rotated parameter space in the random scanning because large areas of the initial parameter space are thus excluded from further examination. The second improvement involves the standardization of the parameters so as to obtain an initial space with equal size extension in all directions. This proves to largely increase the computational robustness of the method. The modified algorithm is demonstrated by application to a simple three-parameter model of diurnal dissolved oxygen patterns in a lake

A new kernel-based approach to system identification with quantized output data

In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. This serves as a starting point to cast our system identification problem into a Bayesian framework. We employ Markov Chain Monte Carlo methods to provide an estimate of the system. In particular, we design two methods based on the so-called Gibbs sampler that allow also to estimate the kernel hyperparameters by marginal likelihood maximization via the expectation-maximization method. Numerical simulations show the effectiveness of the proposed scheme, as compared to the state-of-the-art kernel-based methods when these are employed in system identification with quantized data.Comment: 10 pages, 4 figure