Finite Impulse Response Systems Research Articles

Event-triggered identification of FIR systems with binary-valued output observations

This paper investigates the identification of FIR (finite impulse response) systems whose output observations are subject to both the binary-valued quantization and the event-triggered scheme. Based on the a priori information of the unknown parameters and the statistical property of the system noise, a recursive stochastic-approximation-type identification algorithm is proposed. Under a class of persistently exciting inputs, the algorithm is proved to be strongly convergent and the convergence rate of the estimation error is also established, where the corresponding event-triggering conditions are provided. Moreover, the communication rate is discussed. A numerical example is included to verify the effectiveness of the results obtained.

Identification for FIR Systems With Scheduled Binary-Valued Observations

This paper studies the identification of finite impulse response (FIR) systems whose output observations are subject to both the binary-valued quantization and the scheduling scheme. By utilizing the statistical property of the system noise and the scheduling policy, an empirical-measure-based identification algorithm is proposed. Under periodical inputs, it is proved that the estimation from the algorithm can converge to the real parameters. The mean-square convergence rate of the estimation error is established, based on which and the Cramer-Rao lower bound, the asymptotic efficiency of algorithm is proved. Moreover, the communication rate is derived and the input design problem is discussed. A numerical example is given to illustrate the main results obtained.

A recursive estimation approach to distributed identification of large-scale multi-input-single-output FIR systems

The problem of identifying single modules in multiple-input-single-output (MISO) systems is considered. A novel approach to distributed identification of MISO finite impulse response systems is presented. The distributed identification is discerned by the local estimation of local parameters, which correspond to a module in the MISO system. The local estimators are derived from the standard recursive least squares estimator and require limited information exchange. By Lyapunov’s second method, sufficient conditions are derived for asymptotic convergence of the estimators to the true parameters in the absence of disturbances, which lead to asymptotic unbiasedness in the presence of additive output disturbances.

Distributed parameter estimation of IIR system using diffusion particle swarm optimization algorithm

In wireless sensor networks (WSNs), distributed algorithms are used to estimate desired parameters for minimizing the communication overheads and make the network energy efficient. In literature, distributed estimation of finite impulse response (FIR) systems has been studied, because it is stable. In fact in many sensor network-based applications such as target tracking and fast rerouting, infinite impulse response (IIR) systems are required to be modeled. Thus, each sensor node uses the adaptive IIR filter and interact with each other under diffusion mode of cooperation to estimate the parameters. But the IIR filter inherently produces non-quadratic and multimodal error surfaces. Therefore gradient search algorithms that work well for FIR filters is not suitable for IIR system because they are likely to be trapped in the local minima. Keeping this in view, population based derivative free diffusion particle swarm optimization (DPSO) algorithms are proposed here to estimate the parameters of IIR systems. The algorithms are simulated for benchmark IIR systems and the steady state and transient performances are analyzed. The simulation results demonstrate that the proposed diffusion algorithms provide admirable improvement by resulting in faster convergence and low steady state value compared to that of conventional least mean squared algorithms.

Tensor-Based Large-Scale Blind System Identification Using Segmentation

Many real-life signals can be described in terms of much fewer parameters than the actual number of samples. Such compressible signals can often be represented very compactly with low-rank matrix and tensor models. The authors have adopted this strategy to enable large-scale instantaneous blind source separation. In this paper, we generalize the approach to the blind identification of large-scale convolutive systems. In particular, we apply the same idea to the system coefficients of finite impulse response systems. This allows us to reformulate blind system identification as a structured tensor decomposition. The tensor is obtained by applying a deterministic tensorization technique called segmentation on the observed output data. Exploiting the low-rank structure of the system coefficients enables a unique identification of the system and estimation of the inputs. We obtain a new type of deterministic uniqueness conditions. Moreover, the compactness of the low-rank models allows one to solve large-scale problems. We illustrate our method for direction-of-arrival estimation in large-scale antenna arrays and neural spike sorting in high-density microelectrode arrays.

Contravariant Adaptation on the Manifold of Causal, FIR, Invertible Multivariable Matrix Systems

This letter extends previous work on contravariant adaptation by providing a formula for the contravariant (natural) gradient on the manifold of multivariable, causal, invertible, finite impulse response (FIR) systems. The right action on the manifold of multivariable causal Toeplitz systems is defined. Using this right action, a bilinear form defined on the tangent space at the identity is extended throughout the entire manifold by invariance. This results in a formula analogous to the natural gradient for matrices, but which preserves the causal, FIR nature of the system. The contravariant conversion factor is block Toeplitz structured, so that implementations may employ fast Fourier transform based convolutions to produce lower complexity than would a comparably-sized generic matrix natural gradient.

Structure-Based Subspace Method for Multichannel Blind System Identification

In this work, a novel subspace-based method for blind identification of multichannel finite impulse response (FIR) systems is presented. Here, we exploit directly the impeded Toeplitz channel structure in the signal linear model to build a quadratic form whose minimization leads to the desired channel estimation up to a scalar factor. This method can be extended to estimate any predefined linear structure, e.g. Hankel, that is usually encountered in linear systems. Simulation findings are provided to highlight the appealing advantages of the new structure-based subspace (SSS) method over the standard subspace (SS) method in certain adverse identification scenarii.

Preserving Privacy of Finite Impulse Response Systems

Adding input and output noises for increasing model identification error of finite impulse response (FIR) systems is considered. This is motivated by the desire to protect the model of the system as a trade secret by rendering model identification techniques ineffective. Optimal filters for constructing additive noises that maximizes the identification error subject to maintaining the closed-loop performance degradation below a limit are constructed. Furthermore, differential privacy is used for designing output noises that preserve the privacy of the model.

A parameter estimation approach based on binary measurements using Maximum Likelihood analysis - Application to MEMS

This paper presents an attitude towards the parameter estimation problems, based on binary output observations, dedicated to the context of micro-electronic devices such as Micro-Electro-Mechanical Systems (MEMS) self-testing. This approach is based on Maximum Likelihood (ML) estimation of a logistic regression model of a Finite Impulse Response (FIR) system with binary output data. The results of the proposed method are compared with an appropriate approach in the micro-electronic field under various scenarios, where it is competitive with the compared one. This competition becomes bold in the case of a powerful signal-to-noise ratio (SNR) in the system.

Design of fractional order differentiator using type-III and type-IV discrete cosine transform

In this paper, an interpolation method based on discrete cosine transform (DCT) is employed for digital finite impulse response-fractional order differentiator (FIR-FOD) design. Here, a fractional order digital differentiator is modeled as finite impulse response (FIR) system to get an optimized frequency response that approximates the ideal response of a fractional order differentiator. Next, DCT-III and DCT-IV are utilized to determine the filter coefficients of FIR filter that compute the Fractional derivative of a given signal. To improve the frequency response of the proposed FIR-FOD, the filter coefficients are further modified using windows. Several design examples are presented to demonstrate the superiority of the proposed method. The simulation results have also been compared with the existing FIR-FOD design methods such as DFT interpolation, radial basis function (RBF) interpolation, DCT-II interpolation and DST interpolation methods. The result reveals that the proposed FIR-FOD design technique using DCT-III and DCT-IV outperforms DFT interpolation, RBF interpolation, DCT-II interpolation and DST interpolation methods in terms of magnitude error.

FIR system identification based on a nonparametric Bayesian model using the Indian buffet process

In this paper, we propose a nonparametric Bayesian model combined with the Indian buffet process (IBP) for a finite impulse response (FIR) system. We develop an FIR system identification method that can simultaneously estimate the number of FIR taps and coefficients. In the proposed model, each FIR tap consists of a coefficient and a gain, and the gain is a binary value. An infinite-dimensional binary vector is composed of binary values, and we assume that this binary vector is generated by the IBP. To identify the FIR system, we specify the likelihood function and prior distributions of the parameters and derive their posterior distributions. We can simultaneously estimate the number of FIR taps and coefficients by sampling from posterior distributions using the Gibbs sampler. Our simulations demonstrate that although the number of FIR taps is unknown, the identification performance of the proposed method in a high signal-to-noise ratio environment is similar to or better than that of the conventional least square solution.

Fractional Order Digital Differentiator Design Based on Power Function and Least squares

ABSTRACTIn this article, we propose the use of power function and least squares method for designing of a fractional order digital differentiator. The input signal is transformed into a power function by using Taylor series expansion, and its fractional derivative is computed using the Grunwald–Letnikov (G–L) definition. Next, the fractional order digital differentiator is modelled as a finite impulse response (FIR) system that yields fractional order derivative of the G–L type for a power function. The FIR system coefficients are obtained by using the least squares method. Two examples are used to demonstrate that the fractional derivative of the digital signals is computed by using the proposed technique. The results of the third and fourth examples reveal that the proposed technique gives superior performance in comparison with the existing techniques.

FIR system identification for correlated noise using the convolution matrix, an investigation

A novel approach to finite-impulse response system identification is given. The method is formulated differently from ordinary least mean squares (LMS) or block LMS, which are traditional approaches and has a significant advantage of speed improvement when the correlation matrix has a large condition number. Unlike other approaches which are numerically complex, this method has a similar computational burden as LMS and gives the same optimal solution after convergence. It avoids transformation matrices by writing the system description in terms of a convolution matrix which has a special lower-triangular format. In this way the correlation matrix is different from conventional least-squares approaches and maintains a modest condition number as the correlation matrix in ordinary least-squares climbs high. The method has as wide a range of applications as ordinary LMS-based solutions but can also work on deterministic inputs.

A CS Recovery Algorithm for Model and Time Delay Identification of MISO-FIR Systems

This paper considers identifying the multiple input single output finite impulse response (MISO-FIR) systems with unknown time delays and orders. Generally, parameters, orders and time delays of an MISO system are separately identified from different algorithms. In this paper, we aim to perform the model identification and time delay estimation simultaneously from a limited number of observations. For an MISO-FIR system with many inputs and unknown input time delays, the corresponding identification model contains a large number of parameters, requiring a great number of observations for identification and leading to a heavy computational burden. Inspired by the compressed sensing (CS) recovery theory, a threshold orthogonal matching pursuit algorithm (TH-OMP) is presented to simultaneously identify the parameters, the orders and the time delays of the MISO-FIR systems. The proposed algorithm requires only a small number of sampled data compared to the conventional identification methods, such as the least squares method. The effectiveness of the proposed algorithm is verified by simulation results.

Recursive identification of FIR systems with binary-valued outputs and communication channels

This paper investigates the recursive identification of the finite impulse response systems whose outputs are subject to both the binary-valued quantization and the communication unreliability. The discrete memoryless channel with packet losses and the additive white Gaussian noise channel with time-delay are considered, a stochastic gradient type algorithm and a stochastic approximation type algorithm are respectively proposed to estimate the unknown system parameters. Under some mild conditions, the algorithms can be proved to be convergent in the almost sure and mean square senses. Also, the convergence rates are given. Numerical examples are included to illustrate the performance of the algorithms.

Asymptotically efficient identification of FIR systems with quantized observations and general quantized inputs

This paper introduces identification algorithms for finite impulse response systems under quantized output observations and general quantized inputs. While asymptotically efficient algorithms for quantized identification under periodic inputs are available, their counterpart under general inputs has encountered technical difficulties and evaded satisfactory resolutions. Under quantized inputs, this paper resolves this issue with constructive solutions. A two-step algorithm is developed, which demonstrates desired convergence properties including strong convergence, mean-square convergence, convergence rates, asymptotic normality, and asymptotical efficiency in terms of the Cramér–Rao lower bound. Some essential conditions on input excitation are derived that ensure identifiability and convergence. It is shown that by a suitable selection of the algorithm’s weighting matrix, the estimates become asymptotically efficient. The strong and mean-square convergence rates are obtained. Optimal input design is given. Also the joint identification of noise distribution functions and system parameters is investigated. Numerical examples are included to illustrate the main results of this paper.

Dual MPC for FIR Systems: Information Anticipation

Dual model predictive control (dmpo) optimally combines plant excitation and control based on current and predicted parameter estimation errors. Exact solution of dual control problems with constraints is in general computationally prohibitive. Our deterministic equivalent of the stochastic optimal control problem enables convergence toward optimality for a specific class of finite-horizon problems. The cost function shows that the optimal controls are functions of the current and future parameter-estimate error covariances. Our proposed objective-function reformulation provides the optimal combination of caution, probing, and nominal control. We show that the nonconvex optimization problem can be solved as a quadratic program with bilinear constraints. This type of problem can be efficiently solved with existing algorithms based on branch and bound with McCormick-type estimators. We demonstrate the application of DMPC to a singe-input single-output (siso) finite impulse response (fir) system. In the simulation example the parameter estimates converge quickly, and accurate and precise estimates are obtained even though the excitation vanishes.

Identification of FIR Systems with Quantized Inputs and Observations

This paper introduces identification algorithms for finite impulse response systems under quantized output observations and general quantized inputs. While asymptotically efficient algorithms for quantized identification under periodic inputs are available, their counterpart under general inputs has encountered technical difficulties and evaded satisfactory resolutions. Under quantized inputs, this paper resolves this issue with constructive solutions. A two-step algorithm is developed, which demonstrates desired convergence properties including strong convergence, mean-square convergence, convergence rates, asymptotic normality, and asymptotical efficiency in terms of the Cramér-Rao lower bound. Some essential conditions on input excitation are derived that ensure identifiability and convergence. It is shown that by a suitable selection of the algorithm’s weighting matrix, the estimates become asymptotically efficient. The strong and mean-square convergence rates are explicitly obtained. Optimal input design is discussed. Numerical examples are included to illustrate the main results of this paper

Identification of Stochastic Wiener Systems using Indirect Inference

We study identification of stochastic Wiener dynamic systems using so-called indirectinference. The main idea is to first fit an auxiliary model to the observed data and then in a second step, often by simulation, fit a more structured model to the estimated auxiliary model. This two-step procedure can be used when the direct maximum-likelihood estimate is dificult or intractable to compute. One such example is the identification of stochastic Wiener systems, i.e., linear dynamic systems with process noise where the output is measured using a nonlinear sensor with additive measurement noise. It is in principle possible to evaluate the loglikelihood cost function using numerical integration, but the corresponding optimization problem can be quite intricate. This motivates studying consistent, but sub-optimal, identification methods for stochastic Wiener systems. We will consider indirect inference using the best linear approximation as an auxiliary model.We show that the key to obtain a reliable estimate is to use uncertainty weighting when fitting the stochastic Wiener model to the auxiliary model estimate. The main technical contribution of this paper is the corresponding asymptotic variance analysis. A numerical evaluation is presented based on a first-order finite impulse response system with a cubic non-linearity, for which certain illustrative analytic properties are derived.

Identification of FIR Systems Based on Quantized Output Measurements: A Quadratic Programming-Based Method

This technical note proposes a quadratic programming (QP)-based method for identification of finite impulse response (FIR) dynamic systems from quantized or binary data. The main idea of the proposed method is to reformulate this identification problem, usually viewed as a nonlinear estimation problem with discontinuous nonlinearities, in the form of a standard QP problem, which is a convex optimization problem and can be solved efficiently. The so-called complete input conditions to ensure the unique solution of the QP problem are developed, and the consistency of the estimated parameters is established under the complete input conditions. Numerical examples demonstrate the effectiveness of the proposed method.