Finite Impulse Response Estimator Research Articles

Multipath Canceled RF Fingerprinting for Wireless OFDM Devices Based on Hammerstein System Parameter Separation

Radio frequency fingerprint (RFF) based authentication of wireless devices can be used in the fields of the access security at the physical-layer of wireless networks and radio spectrum management. However, the stability of RFF is easily damaged by the wireless multipath fading channel in mobile communications. An RFF fingerprinting method with the nonlinearity and in-phase and quadrature (IQ) imbalance of the transmitter is proposed for chunk-based wireless orthogonal frequency division multiplexing (OFDM) devices based on a Hammerstein system parameter separation technique, which cancels the adverse influence of the time-varying multipath channel. First, the parameters of the nonlinear model of the transmitter and finite impulse response (FIR) of the wireless multipath channel are estimated with the Hammerstein system parameter separation technique. Second, the best IQ imbalance parameter combination is obtained with the FIR estimation of the channel. Finally, the estimated parameters of the nonlinear model and IQ imbalance are used as RFFs to classify the transmitters. Theoretical analyses and numerical experiments demonstrate that the obtained RFFs are stable and the fusion authentication of transmitters with subtle differences from the same model and same series is feasible using the novel method.

A unified identification algorithm of FIR systems based on binary observations with time-varying thresholds

This paper is concerned with parameter estimation of finite impulse response (FIR) systems with binary observations. Combining a suitable design of the time-varying thresholds, a kind of sign-error type unified algorithm with projection is investigated for either deterministic systems or stochastic systems. The convergence properties of the studied algorithm are established under bounded persistent excitations. Specifically, for the case without noise, the square convergence rate is proved to be close to O1k2 with respect to the time step k. For the case with bounded noises, the upper bound of the estimation error is obtained, which depends on the bound of the noises and the lower bound of the input persistent excitation condition. For the case with independent and identically distributed (i.i.d.) stochastic noises, the estimate is shown to converge to the true parameter in the sense of mean square and almost surely. Besides, the mean square convergence rate of the estimation error is of the order O1k. Numerical examples are supplied to demonstrate the theoretical results.

Forward–Backward Smoothers With Finite Impulse Response Structure

State estimation is an important component for advance control and fault detection. This paper addresses the problem of smoother design for state estimation based on a finite number of measurements collected in a finite estimation horizon. Three different finite impulse response (FIR) smoothing algorithms are proposed using the maximum likelihood FIR estimation, which is robust against uncertain noise statistics and model parameters, and also independent of the initial states of each finite horizon. Moreover, we provide equivalent but iterative Kalman-like structures of these algorithms for practical implementation. The applications of the proposed smoothing algorithms to an object tracking and image processing examples are demonstrated, and it shows that they have better robustness against model uncertainties than traditional smoothing approaches.

Least-squares finite impulse response fixed-lag smoother and filter in linear discrete-time stochastic systems

This paper proposes the least-squares (LS) finite impulse response (FIR) fixed-lag smoother and filter in linear discrete-time wide-sense stationary stochastic systems. The FIR fixed-lag smoothing estimate is given as a linear convolution sum of the impulse response function and the observed values. It is assumed that the signal is observed with additional white noise, which is uncorrelated with the signal process. By solving the simultaneous linear equations transformed from the Wiener–Hopf equation, the optimal impulse response function is obtained. The necessary information of the LS FIR fixed-lag smoothing algorithm is the auto-covariance function of the signal process and the variance of the observation noise process. In particular, this paper proposes the Levinson–Durbin algorithm, which needs less amount of arithmetic operations than the Gauss–Jordan elimination method in the inverse of the Toeplitz matrix, for the optimal impulse response function. From the numerical simulation example, the proposed LS FIR fixed-lag smoother and filter are superior in estimation accuracy to the RLS Wiener FIR estimators.

New Receding Horizon FIR Estimator for Blind Smart Sensing of Velocity via Position Measurements

Smart sensors often require that embedded estimators are robust and blind for given averaging horizons. This brief proposes a new receding horizon (RH) finite impulse response (FIR) velocity estimator that fits these needs by utilizing data from ${N}$ recent discrete position measurements with fading weights. The conventional Kalman estimator typically exhibits poor performance and may even diverge under imprecisely defined noise statistics and/or numerical errors. In contrast, the proposed weighted RH FIR estimator does not require any information about noise, which makes it more robust and blind for a given ${N}$ . The weighted RH FIR estimator minimizes the effects of uncertainties caused by imprecisely defined noise statistics and/or numerical errors and demonstrates better robustness than the existing FIR estimators. We also discuss how to choose the optimal horizon size for the weighted RH FIR estimator. The better performance of the proposed weighted RH FIR estimator against the Kalman and FIR estimators is shown through simulations under diverse operation conditions.

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.

Optimal finite impulse response estimation of linear models in receiver channels with imbedded digital signal processing units

Two finite impulse response (FIR) estimators (optimal and unbiased) are addressed for filtering, smoothing and predicting linear time-invariant state-space signal models perturbed by white Gaussian noise in receiver channels with imbedded digital signal processing units. The FIR estimators are efficient in estimating oversampled and highly oversampled signals, respectively. Special attention is paid to the unbiased FIR (UFIR), owing to its ability of becoming optimal when the processing memory is large. An iterative UFIR algorithm is discussed in detail and compared with the Kalman filter. The optimal memory and errors are also discussed for such kind of estimators. Examples of applications are given for one-dimensional tracking of a two-state polynomial model and state estimation in a harmonic one. Based on this study, the authors show that the UFIR estimator is more efficient than the Kalman filter in blindly estimating receiver channels under the model temporary uncertainties.

GPS-Based FIR Estimation and Steering of Clock Errors: A Review

This paper refers to recent patents in GPS-based clock estimation and synchronization and observes advances in estimation and steering of clock errors with the finite impulse response (FIR) technique. The problem one meets here is caused by the GPS time temporary uncertainty and non-Gaussian sawtooth noise induces in the commercially available GPS timing receivers. It is complicated with the clock colored noise (flicker and random walks) often making the Kalman filter low efficient and requiring weighted averaging. We examine applications of optimal FIR filtering, prediction, and smoothing for polynomial and state space clock models. Optimal and unbiased FIR estimators are observed in line with the ladder, thinning, and Kalman-like algorithms. It is noticed that, for large averaging horizons featured to highly oversampled and slowly changing with time clock models, simple unbiased FIR solutions become virtually optimal. The trade-off with the Kalman filter is also discussed and we show that the unbiased FIR estimator ignoring noise and initial conditions is a better choice in terms of accuracy, stability, and robustness in solving many of the clock problems.

Time‐variant linear optimal finite impulse response estimator for discrete state‐space models

SUMMARYA general p‐shift linear optimal finite impulse response (FIR) estimator is proposed for filtering (p = 0), p‐lag smoothing (p < 0), and p‐step prediction (p > 0) of discrete time‐varying state‐space models. An optimal solution is found in the batch form with the mean square initial state function self‐determined by solving the discrete algebraic Riccati equation. An unbiased batch solution is shown to be independent on noise and initial conditions. The mean square errors in both the optimal and unbiased estimates have been determined along with the noise power gain and estimate error bound. The following important inferences have been made on the basis of numerical simulation. Unlike the time‐invariant Kalman filter, the relevant optimal FIR one is very less sensitive to noise, especially when N ≫ 1. Both time varying, the optimal FIR and Kalman estimates trace along almost the same trajectories with similar errors and sensitivities to noise. Overall, the optimal FIR estimator demonstrates better robustness than the Kalman one against faults in the noise description. Copyright © 2011 John Wiley & Sons, Ltd.

FIR modeling of voltage instrument transformers with iron core for the study of fast transients

Modern electronics found in various measuring equipment is sensitive to the effect of transient over-voltages. This paper treats the measurement procedure for the estimation of Finite Impulse Response (FIR) models of voltage instrument transformers, dedicated for the study of fast electromagnetic transients, with the special concern to its influence on the equipment connected to the secondary. A black-box approach is applied, and the model identification is based solely on a single measurement with the impulse excitation. The paper proposes two different procedures for the estimation of the analytical expression of the excitation, based on the parameters of the impulse generator or its estimation using a least-squares procedure. The frequency response of the transformer is used for the design of an initial FIR model, which was further reduced using corrected Akaike information criterion. This way the duration of the transient response calculation is further decreased, and the computation complexity reduced. Once determined, the FIR model allows, through the digital filtering operation (closely related to the concept of recursive convolution), a very easy time-domain calculation of the system’s response at any excitation.

Full horizon optimal FIR estimator of clock state employing measurement of time errors

This paper addresses a p-shift full horizon optimal finite impulse response (FIR) estimator of clock state employing all the measurement data available of the time interval error (TIE). A solution proposed is general for filtering ( p=0), prediction ( p > 0 ) , and smoothing ( p < 0 ) of discrete time clock models in state space. The optimal estimator self-determines the clock initial mean square state by solving the discrete algebraic Riccati equation on a measurement interval of N points. Noise is allowed to be zero-mean with arbitrary distribution and covariance functions. The unbiased FIR estimator is proposed in the batch form producing near optimal estimates when N ⪢ 1 or the clock initial mean square state dominates noise in the order of magnitudes. An application is given to a master clock.

Optimal Gains of FIR Estimators for a Class of Discrete-Time State-Space Models

The gain of an optimal finite impulse response (FIR) filter of the system k-state is derived and analyzed for discrete real-time state-space models with jointly independent zero-mean noises of arbitrary distributions and covariances. Several special cases are considered, and the gain is modified accordingly. It is stated that if the model is deterministic or slowly changing with time and such that an averaging horizon is large, N Gt 1, then a relatively simple unbiased FIR filter produced by the deadbeat constraint yields virtually an optimal estimate. An application is given to the crystal clock time error estimation via GPS-based measurements with temporary uncertainty in the presence of sawtooth noise.

A thinning algorithm for GPS-based unbiased FIR estimation of a clock TIE model

A thinning algorithm is proposed for real-time unbiased finite impulse response (FIR) estimation of the local clock time interval error (TIE) model (time error, fractional frequency offset, linear frequency drift rate, etc.) employing GPS-based sawtooth measurements. We show that the approach allows obtaining practically optimal estimates of the clock states, by large horizons (number of the points in the average). The algorithm is applied to the TIE measurements allowing for different time steps and averaging horizons for each of the clock states and compared to the three state Kalman filter. It is demonstrated that, in the presence of the sawtooth noise induced by the GPS receiver, the unbiased FIR estimates with thinning out fit the clock states better than the Kalman filter, in terms of the Allan deviation and precision time protocol deviation.

NONPARAMETRIC METHOD FOR IDENTIFICATION OF MIMO HAMMERSTEIN MODELS

A new nonparametric approach to identify multivariable Hammerstein models is presented in this paper. The linear dynamic subsystem is identified and represented by its finite impulse response (FIR) model, and, the static nonlinearity is identified and represented as an MIMO input-output mapping. By specially designed test signals, the estimation of FIRs for multivariable linear subsystems can be conducted under a SISO framework and can be decoupled from the identification of the static nonlinearity. Due to the nonparametric nature, the representation of MIMO Hammerstein model may not be unique. By making uses of this fact, several parameters can be adjusted to shape the model for achieving engineer's requirement. These above-mentioned representations can be used to obtain an exact process model or an apparent model suitable for control design.

An unbiased FIR filter for TIE model of a local clock in applications to GPS-based timekeeping

An unbiased finite impulse response (FIR) filter is proposed to estimate the time-interval error (TIE) K-degree polynomial model of a local clock in global positioning system (GPS)-based timekeeping in the presence of noise that is not obligatory Gaussian. Generic coefficients for the unbiased FIRs are derived. The low-degree FIRs and noise power gains are given. An estimation algorithm is proposed and examined for the TIE measurements of a crystal clock in the presence of the uniformly distributed sawtooth noise induced by the multichannel GPS timing receiver. Based upon this algorithm, we show that the unbiased FIR estimates are consistent with the reference (rubidium) measurements and fit them better than the standard Kalman filter.

Dealing with Collinearity in Finite Impulse Response Models Using Bayesian Shrinkage

Finite impulse response (FIR) models are widely used in the chemical industry due to their simplicity and easily defined model structures. However, they usually require a large number of coefficients to capture the process dynamics. This large number of coefficients introduces collinearity or redundancy in the models, which usually increases the uncertainty of their estimation. This paper presents a Bayesian approach, called empirical Bayesian FIR (EBFIR) modeling, to deal with this collinearity problem. Unlike ridge regression (RR), which shrinks the FIR model parameters toward zero in order to reduce their variations, EBFIR makes better use of the data by estimating a prior density function for the FIR coefficients, which is then used within a Bayesian framework to shrink the FIR coefficients in a more rigorous fashion. The developed Bayesian approach is computationally inexpensive, as a closed form solution of the Bayesian estimate of the FIR coefficients is derived. The EBFIR approach is also more general than some of the existing methods, such as ordinary least squares regression (OLS) and RR, which are shown to be special cases of EBFIR. Finally, the developed EBFIR approach has been shown to outperform some of the commonly used existing FIR estimation methods over a wide range of noise levels.

Blind source estimation of FIR channels for binary sources: a grouping decision approach

This paper proposes a novel grouping decision approach for blind source estimation of FIR (finite impulse response) channels with binary sources. First, solvability is discussed for single-input systems and multi-input systems. Necessary and sufficient conditions for recoverability are derived. For single-input systems, a new deterministic algorithm based on grouping and decision is proposed to recover the source up to a delay. The algorithm is easy to implement and has several advantages. For instance, when the solvability conditions are satisfied, it can be applied to cases in which: (i) the channel has zeros on the unit circle or outside of the unit circle; (ii) there are fewer sensors than sources; (iii) the source is temporarily dependent. To improve noise tolerance and reduce computational cost, the algorithm is further elaborated for highly noisy channels and high-order FIR channels, respectively. For the channels with high unimodal noise, fewer peaks appear in the probability density function (pdf) of the outputs compared to the pdf of the outputs of channels with a higher SNR. After the peaks representing cluster centers are estimated using a maximum likelihood (ML) approach, the deterministic algorithm can be used. Similar to highly noisy channels, the algorithm is also effective for high-order, exponentially decaying channels after fewer cluster centers are estimated. Furthermore, blind source estimation for multi-input systems also can be carried out as with the case of single input systems. Two deflation algorithms are presented for temporarily dependent sources and i.i.d. sources. Based on the source estimation and deflation algorithms, the sources can be obtained one by one. Finally, the validity and performance of the algorithms are illustrated by several simulation examples.

Identifying regional activity associated with temporally separated components of working memory using event-related functional MRI

This study describes the neural circuitry underlying temporally separated components of working memory (WM) performance—stimulus encoding, maintenance of information during a delay, and the response to a probe. While other studies have applied event-related fMRI to separate epochs of WM tasks, this study differs in that it employs a methodology that does not make any a priori assumptions about the shape of the hemodynamic response (HDR). This is important because no one model of the HDR is valid across the range of activated brain regions and stimulus types. Systematic modeling inaccuracies may lead to the misattribution of activity to adjacent events. Twelve healthy subjects performed a numerical version of the Sternberg Item Recognition Paradigm adapted for rapid presentation event-related fMRI. This paradigm emphasized maintenance rather than manipulative WM processes and used a subcapacity WM load. WM trials with different delay lengths were compared to fixation. The HDR of the entire WM trial for each trial type was estimated using a finite impulse response (FIR). Regional activity associated with the Encode, Delay, and Probe epochs was identified using contrasts that were based on the FIR estimates and by examining the HDRs. Each epoch was associated with a distinct but overlapping pattern of regional activity. Activation of the dorsolateral prefrontal cortex, thalamus, and basal ganglia was exclusively associated with the probe. This suggests that frontostriatal neural circuitry participates in selecting an appropriate response based on the contents of WM.

Blind equalization and estimation of digital communication FIR channels using cumulant matching

We consider the problem of blind estimation and equalization of digital communication FIR (finite impulse response) channels. The channel parameters are estimated by nonlinear batch optimization of a quadratic cumulant matching criterion involving second and fourth order cumulants of the received data. A new algorithm is proposed for (asymptotically) globally convergent, linear estimation of the FIR channel parameters where the FIR model order is not necessarily known. The nonlinear cumulant matching algorithm is initialized by the linear parameter estimator. The estimated channel impulse response is then used to construct a linear equalizer. Two illustrative simulation examples using 4, 16 and 64-QAM signals are presented. >

Fast Newton transversal filters-a new class of adaptive estimation algorithms

A class of adaptive algorithms for the estimation of FIR (finite impulse response) transversal filters is presented. The main characteristic of this class is the fast computation of the gain vector needed for the adaptation of the transversal filters. The method for deriving these algorithms is based on the assumption that the input signal is autoregressive of order M, where M can be much smaller than the order of the filter to be estimated. Under this assumption the covariance matrix of the input signal is estimated by extending in a min-max way the M order sample covariance matrix. This estimate can be regarded as a generalization of the diagonal covariance matrix used in LMS and leads to an efficient computation of the gain needed for the adaptation. The new class of algorithms contains the LMS and the fast versions of LS as special cases. The complexity changes linearly with M, starting from the complexity of the LMS (for M=0) and ending at the complexity of the fast versions of LS. >