Finite Impulse Response Systems Research Articles

Iterative parameter and order identification for fractional‐order nonlinear finite impulse response systems using the key term separation

SummaryThis article considers the parameter estimation for a fractional‐order nonlinear finite impulse response system with colored noise. For the fractional‐order systems, the challenge and difficulty are to identify the order and parameters of the systems simultaneously under colored noise disturbances. In order to reduce the problem of redundant parameter estimation, the output form of the system can be expressed by a linear combination of unknown parameters through the separation of the key term separation. A key term separation auxiliary model gradient‐based iterative algorithm is derived by using the negative gradient search. Meanwhile, to achieve the higher estimation accuracy, we propose a key term separation auxiliary model multiinnovation gradient‐based iterative algorithm by utilizing the multiinnovation theory. Finally, the simulation results test the effectiveness of the proposed algorithms.

Parameter identification for Wiener‐finite impulse response system with output data of missing completely at random mechanism and time delay

SummaryIn this paper, the parameter estimation issue of Wiener system with random time delay and missing output data is studied. The linear part of Wiener system is described by Finite Impulse Response (FIR) model. The mathematical formula of the Expectation Maximum algorithm to identify Wiener‐FIR system that contains the random time delay and the nonlinear output data in missing completely at random mechanism is derived, which is never considered before. To obtain the unmeasurable intermediate variable in Wiener‐FIR system, the idea of auxiliary model is adopted. The time delay and system parameters can be estimated simultaneously by this method. Numerical example and the identification of water tank system example are carried out, the effectiveness of the algorithm is proved.

Bayesian positive system identification: Truncated Gaussian prior and hyperparameter estimation

Bayesian methods have been extended for the linear system identification problem in the past ten years. The traditional Bayesian identification selects a Gaussian prior and considers the tuning of kernels, i.e., the covariance matrix of a Gaussian prior. However, Gaussian priors cannot express the system information appropriately for identifying a positive finite impulse response (FIR) model. This paper exploits the truncated Gaussian prior and develops Bayesian identification procedures for positive FIR models. The proposed parameterizations in the truncated Gaussian prior can reflect the decay rate and the correlation of the impulse response of the system to be identified. The expectation–maximization (EM) algorithm is tailored to the hyperparameter estimation problem of positive system identification with the truncated Gaussian prior. Numerical experiments compare the truncated Gaussian prior to the traditional Gaussian prior for positive FIR system identification. The simulation results demonstrate that the truncated Gaussian prior outperforms the Gaussian prior.

Column shifting algorithm to compute iteration bound of finite impulse response systems having inline delays

Column shifting algorithm to compute iteration bound of finite impulse response systems having inline delays

Power-Optimal Distributed Beamforming for Multi-Carrier Asynchronous Bidirectional Relay Networks

We consider the problem of joint power allocation and distributed beamforming design for asynchronous two-way multi-relay networks, where two transceivers rely on an orthogonal frequency division multiplexing (OFDM) scheme to exchange information through multiple amplify-and-forward relay nodes. The network is assumed to be asynchronous in the sense that different relaying paths are subject to different propagation delays. This assumption renders the end-to-end channel between the two transceivers frequency-selective. The impulse response of such a channel can be modeled as a finite impulse response (FIR) system with multiple taps. We present a simple semi-closed-form solution for the problem of minimization of the total transmission power consumed in such networks subject to two quality of service constraints on the transceivers rates. We show that at the optimum, the end-to-end channel must be frequency-flat, which means only one tap of the end-to-end channel impulse response is non-zero. As a result, our semi-closed-form solution leads to a relay selection scheme, in which only those relays associated with the non-zero tap of the end-to-end channel impulse response are switched on, and the rest of the relays are kept off. The simulation results demonstrate that using the proposed semi-closed-form algorithm significantly outperforms the traditional best relay selection method.

Three‐stage forgetting factor stochastic gradient parameter estimation methods for a class of nonlinear systems

AbstractThis article focuses on the parameter estimation for a class of nonlinear systems, that is, multi‐input single‐output or two‐input single‐output Hammerstein finite impulse response systems with autoregressive moving average noise. The key is to investigate new estimation methods for on‐line parameter estimation of the considered system. By using the gradient search and introducing the forgetting factor, the forgetting factor stochastic gradient estimation method is developed. For the purpose of improving the parameter estimation accuracy, the system is decomposed into three subsystems with fewer variables applying the key term separation technique: the first two subsystems contain the unknown parameters related to the input and the third subsystem contains the unknown parameters related to the noise. Then a three‐stage forgetting factor stochastic gradient algorithm is proposed based on the hierarchical identification principle for interactively identifying each subsystem. The simulation results show the effectiveness of the presented algorithm.

Identification of switched FIR systems with random missing outputs: A variational Bayesian approach

Identification of switched finite impulse response (FIR) systems in the presence of random missing outputs is investigated in this paper and the practical problems of unknown number of local models and unknown switching mechanism are handled. From a Bayesian perspective, the probabilistic model for describing the identification problem is constructed and the algorithm to estimate all of the unknown parameters is derived by using the variational Bayesian (VB) approach. In addition, the number of local models can be selected based on the probability of each local component, and the predicted output can be obtained as the output of the local model that takes effect. A simulated example and the mass-spring-damper system are explored to illustrate the efficacy of the developed algorithm.

Impulse response identification from input/output binary measurements

In this paper, we study the identification of Finite Impulse Response systems in a particular context: data on the input and the output are obtained with one-bit quantizers, the thresholds of quantizers can be different from zero. A three-step identification algorithm is proposed from these binary-valued measurements. This algorithm is based on the normal distribution of the input and noises. The algorithm is appropriately analyzed: it is shown to be asymptotically unbiased, its asymptotic variance is also expressed. Numerical simulations are provided to demonstrate the effectiveness of the proposed algorithm even in presence of noise and to validate the analysis.

Asymptotic efficiency and probabilistic error bound for maximum likelihood‐based identification of finite impulse response systems with binary‐valued observations and unreliable communications

SummaryThis article addresses the identification of finite impulse response systems with binary‐valued observations under packet losses and transmission errors. First, the maximum likelihood function of the available data sequence is derived, based on which the estimation algorithm for the unknown parameter vector is given. Then, by making full use of the statistical properties of communication uncertainty and system noise, the algorithm performance is established, including the strong convergence, the mean‐square convergence rate, and the asymptotic efficiency in terms of Cramér‐Rao low bound. Also the probabilistic upper bound and lower bound of the estimation error are presented. Finally, the validity and rationality of the results are verified by numerical simulation.

Hierarchical least squares parameter estimation algorithm for two-input Hammerstein finite impulse response systems

This paper considers the parameter estimation problems of two-input single-output Hammerstein finite impulse response systems. A hierarchical least squares algorithm is proposed for improving the computational efficiency through combining the hierarchical identification principle and the identification model decomposition, and a multi-innovation least squares algorithm is proposed for enhancing the parameter estimation accuracy based on the multi-innovation identification theory. The key is to derive two sub-identification models, each of which contains a set of merged parameter vectors. The proposed algorithm is effective and can generate highly accurate parameter estimates compared with the over-parametrization identification method, and can be easily extended to multi-input multi-output systems. Finally, an illustrative example is provided to verify the effectiveness of the proposed algorithm.

A New Variable Forgetting Factor-Based Bias-Compensated RLS Algorithm for Identification of FIR Systems With Input Noise and Its Hardware Implementation

This paper proposes a new variable forgetting factor QRD-based recursive least squares algorithm with bias compensation (VFF-QRRLS-BC) for system identification under input noise. A new variable forgetting factor scheme is proposed to improve its convergence speed and steady-state mean squares error. A new method for recursive estimation of the additive noise variance is also proposed for reliable bias compensation. The mean and mean-square asymptotic behaviors of the algorithm are analyzed and a self-calibration scheme is further proposed to improve the steady-state mean squares error (MSE) due to finite sample effect. Simulations show that the proposed VFF approach offers improved tracking and steady-state MSE performance over the conventional recursive least squares method and its fixed FF counterpart. A linear array architecture is proposed for the realization of this algorithm and several hardware efficient techniques are introduced to avoid the expensive cubic root and division operations required. The proposed algorithm is validated on Xilinx Zynq®-7000 AP SoC ZC702 Field Programmable Gate Array (FPGA). For a 10-tap finite impulse response (FIR) system, the implementation requires only about 11.5k slice look-up table (LUT)s, 4.5k slice registers and 50 DSP48s and it can work up to about 0.58 MHz sample rate with a 200 MHz system clock. The hardware resources are considerably lower than traditional techniques using divider and cubic root realization. The linear array architecture also serves as an attractive alternative to the systolic array in medium to low rate applications due to its reduced hardware usages.

Prediction-based event-triggered identification of quantized input FIR systems with quantized output observations

This paper addresses the identification of finite impulse response (FIR) systems withboth quantized and event-triggered observations.An event-triggered communication scheme for the binary-valued output quantization is introducedto save communication resources.Combining the empirical-measure-based identification techniqueand the weighted least-squares optimization,an algorithm is proposed to estimate the unknown parameterby full use of the received data and thenot-triggered condition.Under quantized inputs,it is shown that the estimate can strongly converge to the real valuesand the estimator is asymptotically efficient in terms of the Cramer-Rao lowerbound.Further, the limit of the average communication rate is derived and the tradeoff between this limitand the estimation performance is discussed.Moreover, the case of multi-threshold quantized observations is considered.Numerical examples are included to illustrate the obtained main results.

Adaptive Tracking Control of FIR Systems Under Binary-Valued Observations and Recursive Projection Identification

In this article, adaptive tracking control of finite impulse response (FIR) systems is studied with binary-valued measurements. An adaptive control strategy is proposed based on an online identification algorithm. First, the designed control inputs are proved to be bounded and satisfy a persistent excitation (PE) condition under the assumption of periodic and PE target signals, which ensures the convergence of the identification algorithm. Second, the convergence rate of the identification algorithm is proved to be O(1/t) and it depends on the true parameter instead of a priori information of the parameter, which is more intuitive. Due to the convergence and the convergence rate of the identification algorithm, we finally prove that the adaptive tracking control is asymptotically optimal and the tracking speed is faster than the previous control algorithm. The simulations are given to validate the developed results in this article.

Type II, III, and IV Linear-Phase FIR Structures Based on Cardinal Filters

Novel structures of type II, III, and IV linear-phase finite impulse response (FIR) systems are proposed. It is constituted of a linear combination of basic sub-filters, called cardinal filters , with weighting coefficients equal to the derivatives of the system amplitude response at a prescribed frequency. Since the cardinal filters can be synthesized via recursive closed-form expressions, regardless of the desired system amplitude response, the proposed structure provides a universal design for arbitrary derivative-constrained linear-phase FIR filters. Design examples of maximally flat filters show that further improvement by combining derivative constraints with the least squared error optimization technique can be obtained.

Generalized Savitzky–Golay filters for identification of nonstationary systems

The problem of identification of nonstationary systems using noncausal estimation schemes is considered and a new class of identification algorithms, combining the basis functions approach with local estimation technique, is described. Unlike the classical basis function estimation schemes, the proposed local basis function estimators are not used to obtain interval approximations of the parameter trajectory, but provide a sequence of point estimates corresponding to consecutive instants of time. Based on the results of theoretical analysis conducted for nonstationary finite impulse response systems the paper proposes two mechanisms for adaptive selection of the number of basis functions and the size of the local analysis window.

A nonparametric Bayesian model for system identification based on a super‐Gaussian distribution

AbstractIn the acoustic signal processing applications of finite impulse response (FIR) system identification, it is important to develop the identification method that is robust to super‐Gaussian noises. Moreover, the identification method that estimates the FIR coefficients and the order of the unknown system is required, because the order of the unknown system is unavailable in advance. Therefore, in this paper, we propose a nonparametric Bayesian (NPB) model for FIR system identification using a super‐Gaussian likelihood and the beta‐Bernoulli process. In the proposed NPB model, we employ the hyperbolic secant distribution for the likelihood function. Then, we derive the inference algorithm to simultaneously estimate the FIR coefficients and the order of the unknown system. Our inference algorithm based on a hybrid inference approach combining the majorization‐minimization (MM) algorithm and the Gibbs sampler. The simulation results suggest that the proposed method outperforms the conventional identification algorithms in a super‐Gaussian noise environment.

Nonlinear system identification via data augmentation

This paper presents a novel nonparametric approach to the identification of nonlinear dynamical systems. The proposed methodology exploits the potential of manifold learning on an artificially augmented dataset, obtained without running new experiments on the plant. The additional data are employed for approximating the manifold where input regressors lie. The knowledge of the manifold acts as a prior information on the system, that induces a proper regularization term on the identification cost. The new regularization term, as opposite to the standard Tikhonov one, enforces local smoothness of the function along the manifold. A graph-based algorithm tailored to dynamical systems is proposed to generate the augmented dataset. The hyperparameters of the method, along with the order of the system, are estimated from the available data. Numerical results on a benchmark Nonlinear Finite Impulse Response (NFIR) system show that the proposed approach may outperform the state of the art nonparametric methods.

FIR system identification with set-valued and precise observations from multiple sensors

This paper considers the system identification problem for FIR (finite impulse response) systems with set-valued and precise observations received from multiple sensors. A fusion estimation algorithm based on some suitable identification algorithms for different types of observations is proposed. In particular, least square method is chosen for FIR systems with precise observations, while empirical measure method and EM algorithm are chosen for FIR systems with set-valued observations in the cases of periodic and general system inputs, respectively. Then, the quasi-convex combination estimator (QCCE) fusing the two different estimators by a linear combination with appropriate weights is constructed. Furthermore, the convergence properties are theoretically analyzed in terms of strong consistency and asymptotic efficiency. The fused estimator QCCE is proved to achieve the Cramer-Rao (CR) lower bound asymptotically under periodic inputs. Extensive numerical simulations validate the superiority of the fusion estimation algorithm under both periodic and general inputs.

FIR system identification under either–or communication with quantised inputs and quantised output observations

This study investigates the quantised-input FIR (finite impulse response) system identification under quantised and event-triggered output observations. For the binary-valued quantisation, they introduce a so-called either-or communication scheme to save communication resources. Based on the received data and the triggered indicator, an identification algorithm is proposed to estimate the unknown parameter by use of the empirical measure and weighted least squares. The convergence performance is established and the communication rate is derived. For the multi-threshold quantisation, it can be seen as a vector-valued observation in which each component represents a binary-valued output, and the corresponding identification problem is discussed. A numerical example is included to illustrate the main results obtained.

A Proportionate Normalized Maximum Correntropy Criterion Algorithm with Correntropy Induced Metric Constraint for Identifying Sparse Systems

A proportionate-type normalized maximum correntropy criterion (PNMCC) with a correntropy induced metric (CIM) zero attraction terms is presented, whose performance is also discussed for identifying sparse systems. The proposed sparse algorithms utilize the advantage of proportionate schemed adaptive filter, maximum correntropy criterion (MCC) algorithm, and zero attraction theory. The CIM scheme is incorporated into the basic MCC to further utilize the sparsity of inherent sparse systems, resulting in the name of the CIM-PNMCC algorithm. The derivation of the CIM-PNMCC is given. The proposed algorithms are used for evaluating the sparse systems in a non-Gaussian environment and the simulation results show that the expanded normalized maximum correntropy criterion (NMCC) adaptive filter algorithms achieve better performance than those of the squared proportionate algorithms such as proportionate normalized least mean square (PNLMS) algorithm. The proposed algorithm can be used for estimating finite impulse response (FIR) systems with symmetric impulse response to prevent the phase distortion in communication system.