Feedforward Estimation Research Articles

Imposing FIR Structure on $H^2$ Preview Tracking and Smoothing Solutions

This paper studies continuous-time $H^2$ feedforward tracking and estimation problems with FIR (finite impulse response) solutions. Both causal and noncausal solutions are considered. It is shown that these problems can be treated as special cases of static problems in the lifted domain, which, in turn, can be solved in terms of a two-point boundary value (Hamilton-Jacobi) system. This results in fixed-dimension closed-form solutions. A numerically stable form of these solutions, which uses matrix exponentials of Hurwitz matrices only, is also derived.

Cerebellum Predicts the Future Motor State

Feed forward control and estimates of the future state of the motor system are critical for fast and coordinated movements. One framework for generating these predictive signals is based on the central nervous system implementing internal models. Internal models provide for representations of the input-output properties of the motor apparatus or their inverses. It has been widely hypothesized that the cerebellum acquires and stores internal models of the motor apparatus. The results of psychophysical, functional imaging and transcranial magnetic stimulation studies in normal subjects support this hypothesis. Also, the deficits in patients with cerebellar dysfunction can be attributed to a failure of predictive feed forward control and/or to accurately estimate the consequences of motor commands. Furthermore, the computation performed by the cerebellar-like electrosensory lobes in several groups of fishes is to predict the sensory consequences of motor commands. However, only a few electrophysiological investigations have directly tested whether neurons in the cerebellar cortex have the requisite signals compatible with either an inverse or forward internal model. Our studies in the monkey performing manual pursuit tracking demonstrate that the simple spike discharge of Purkinje cells does not have the dynamics-related signals required to be the output of an inverse dynamics model. However, Purkinje cell firing has several of the characteristics of a forward internal model of the arm. A synthesis of the evidence suggests that the cerebellum is involved in integrating the current state of the motor system with internally generated motor commands to predict the future state.

Iterative ML-based estimation of carrier frequency offset, channel impulse response and data in OFDM transmissions

This paper provides an approximate closed form solution to the problem of data-aided joint maximum likelihood estimation of the carrier frequency offset and of the channel impulse response in an Orthogonal Frequency Division Multiplexing transmission over a multipath fading channel. This results in a novel pilot-aided feedforward estimator, that can be employed for pilot-based receiver training. It is also shown how the novel joint estimation strategy can be exploited in an iterative (turbo) receiver structure to track the fast channel and frequency offset changes occurring during the transmission of information symbols. The performance of this structure is assessed by computer simulations and is compared with that provided by other estimation/detection strategies.

Feedforward Delay Estimators in Adverse Multipath Propagation for Galileo and Modernized GPS Signals

The estimation with high accuracy of the line-of-sight delay is a prerequisite for all global navigation satellite systems. The delay locked loops and their enhanced variants are the structures of choice for the commercial GNSS receivers, but their performance in severe multipath scenarios is still rather limited. The new satellite positioning system proposals specify higher code-epoch lengths compared to the traditional GPS signal and the use of a new modulation, the binary offset carrier (BOC) modulation, which triggers new challenges in the delay tracking stage. We propose and analyze here the use of feedforward delay estimation techniques in order to improve the accuracy of the delay estimation in severe multipath scenarios. First, we give an extensive review of feedforward delay estimation techniques for CDMA signals in fading channels, by taking into account the impact of BOC modulation. Second, we extend the techniques previously proposed by the authors in the context of wideband CDMA delay estimation (e.g., Teager-Kaiser and the projection onto convex sets) to the BOC-modulated signals. These techniques are presented as possible alternatives to the feedback tracking loops. A particular attention is on the scenarios with closely spaced paths. We also discuss how these feedforward techniques can be implemented via DSPs.

Acquisition performance for NDA symbol‐timing recovery with simple adaptive first‐order loops

AbstractPowerful feedforward estimators for symbol‐timing recovery are more or less mandatory for efficient acquisition in time‐division multiple access (TDMA) modems. However, in many cases, feedback solutions are much less complex from the computational point of view. The latter can be an attractive alternative for continuous transmission of data like DVB, where rapid acquisition is not so important as with TDMA. In order to describe analytically the acquisition performance of first‐order loops with Gardner detectors, it is shown that the related analog model can be successfully applied. In the sequel, this approach is used to demonstrate that the acquisition process may be accelerated significantly via simple adaptive loop filters. Copyright © 2006 AEIT

Generalised analysis of monomial-based Viterbi and Viterbi algorithms for NDA carrier phase estimation

For non-data-aided carrier phase recovery of M-PSK modulated signals, Viterbi and Viterbi suggested a feedforward estimator based on a modification of the Mth power nonlinearity. With respect to the jitter variance, they presented a closed-form solution for even integer values of the generic design parameter /spl mu/, 0/spl les//spl mu//spl les/M-2. It is shown that their analysis can be simplified considerably as well as extended to any real value of /spl mu/>-M-2. Furthermore, it is verified that the Cramer-Rao lower bound, as the theoretical limit, is solely approached for larger values of the signal-to-noise ratio and negligible carrier frequency offsets. Finally, to minimise the jitter performance, the closed-form solution is used for optimisation of the design parameter.

Adaptive regression estimation with multilayer feedforward neural networks

We prove a general bound on the expected L 2 error of adaptive least squares estimates. By applying it to multilayer feedforward neural network regression function estimates, we are able to obtain fast rates of convergence in special classes of regression functions such as additive functions.

Analysis of non-data-aided carrier frequency recovery with Luise–Reggiannini estimators applied to M-PSK schemes

Luise and Reggiannini introduced a data-aided feedforward estimator for carrier frequency recovery in an all-digital receiver. For M-PSK as a modulation scheme, the concept is easily extended to the non-data-aided case. In this context, a closed-form solution for computation of the jitter variance is provided, which agrees with the simulation results for medium-to-high SNR values and frequency offsets representing a smaller fraction of the operational range. In the sequel, the analytical result is used for comparison purposes and parameter optimisation.

Extended analysis of Viterbi-Viterbi synchronizers

For non-data-aided carrier phase recovery of M-ary phase-shift keying (MPSK) as modulation scheme, Viterbi and Viterbi (V&V) suggested a feedforward (FF) variant of the Mth-power non-linearity. With respect to the jitter variance, a closed-form solution has been presented for even integer values of the generic design parameter m, 0 ≤ m ≤ M. Basically, the V & V principle may be applied to feedback (FB) systems as well, where little is found in the open literature. To this end, the characteristic of the open loop (S-curve) is derived in closed form for any value of m. The jitter variance of the linearized FB synchronizer is then computed using the slope in the stable equilibrium point of the S-curve. Furthermore, in order to minimize the jitter variance, it is shown that the optimized value mopt 1 for increasing values of the signal-to-noise ratio (SNR), whereas in the opposite case mopt M. Finally, it is verified that the developed relationships are also valid for FF estimators if they are operated with negligible carrier frequency offsets. Copyright © 2004 AEI.

On the Design of a Digital Blind Feedforward, Nearly Jitter-Free Timing-Recovery Scheme for Linear Modulations

This letter deals with the compensation of the self-noise (jitter) in a nondata-aided (blind) feedforward symbol-timing estimator using two samples per symbol for linearly modulated waveforms transmitted through additive white Gaussian noise channels. The main contribution of this letter is the derivation of an appropriate prefilter to achieve nearly jitter-free digital blind feedforward timing recovery. Computer simulations illustrate that the proposed prefiltering scheme improves significantly the performance at mid and high signal-to-noise ratios.

Low-Complexity Feedforward Symbol Timing Estimator Using Conditional Maximum-Likelihood Principle

A low complexity feedforward symbol-timing estimator based on the conditional maximum-likelihood principle is proposed. An approximation is applied to the Fourier series expansion of the conditional maximum-likelihood function such that implementation complexity is greatly reduced. It is shown that the proposed estimator can be viewed as a generalization of the well-known square nonlinearity estimator proposed by Oerder and Meyr in 1988. Simulation results show that the performance of the proposed estimator is very close to the conditional Cramer-Rao bound and is better than that of the square nonlinearity estimator.

Timing and Frequency Synchronization for the Uplink of an OFDMA System

This paper deals with timing and frequency recovery for the uplink of an orthogonal frequency-division multiple access (OFDMA) system. The frequency estimator is derived from ad hoc reasoning, whereas the timing estimator is based on the maximum-likelihood criterion. Both schemes rely on the repetition of a fixed pilot symbol. Their main feature is that they provide feedforward estimates and allow synchronization in only two OFDM blocks. In contrast to other existing methods, they do not require that the subcarriers of a given user occupy adjacent positions in the signal bandwidth. This makes it possible to interleave subcarriers of different users so as to optimally exploit the frequency diversity of the channel. Theoretical analysis and computer simulations are used to assess the performance of the proposed synchronizers. It is found that the degradations due to residual frequency and timing errors are negligible at signal-to-noise ratios of practical interest.

A class of blind phase recovery techniques for higher order QAM modulations: estimators and bounds

This letter proposes a class of blind feedforward carrier-phase estimators for higher order quadrature amplitude-modulated transmissions. As an extension of the Viterbi and Viterbi (V&V) estimator, a constellation-dependent optimal matched nonlinear estimator is derived such that its asymptotic variance is minimized. The asymptotic variances of the optimal matched and V&V estimators are established in closed-form expressions and compared. Computer simulations are presented to corroborate the theoretical performance analysis.

A new narrowband interference suppression scheme for spread-spectrum CDMA communications

This paper presents a new nonlinear approach for narrowband interference (NBI) suppression in code-division multiple-access (CDMA) systems. The proposed scheme is an adaptive nonlinear predictor that consists of an (N+1)-level quantizer, four adders, and two adaptive linear filters, where N is the number of users in the CDMA system. Both adaptive filters have the same coefficients at each iteration: one for feedforward estimation of NBI and the other for feedback compensation for the estimated result. It could be regarded as an improved version of the nonlinear predictor with offset outputs presented recently by Wang et al. (1996). Computer simulation results support that the improved offset predictor performs much better than the original one under the same complexity. As compared with the nearly optimal approximate conditional mean filter, it achieves almost the same performance even at very low signal-to-noise ratio but involves much less complexity.

Process modeling and optimization using focused attention neural networks

Neural networks have been shown to be very useful for modeling and optimization of nonlinear and even chaotic processes. However, in using standard neural network approaches to modeling and optimization of processes in the presence of unmeasured disturbances, a dilemma arises between achieving the accurate predictions needed for modeling and computing the correct gains required for optimization. As shown in this paper, the Focused Attention Neural Network (FANN) provides a solution to this dilemma. Unmeasured disturbances are prevalent in process industry plants and frequently have significant effects on process outputs. In such cases, process outputs often cannot be accurately predicted from the independent process input variables alone. To enhance prediction accuracy, a common neural network modeling practice is to include other dependent process output variables as model inputs. The inclusion of such variables almost invariably benefits prediction accuracy, and is benign if the model is used for prediction alone. However, the process gains, necessary for optimization, sensitivity analysis and other process characterizations, are almost always incorrect in such models. We describe a neural network architecture, the FANN, which obtains accuracy in both predictions and gains in the presence of unmeasured disturbances. The FANN architecture uses dependent process variables to perform feed-forward estimation of unmeasured disturbances, and uses these estimates together with the independent variables as model inputs. Process gains are then calculated correctly as a function of the estimated disturbances and the independent variables. Steady-state optimization solutions thus include compensation for unmeasured disturbances. The effectiveness of the FANN architecture is illustrated using a model of a process with two unmeasured disturbances and using a model of the chaotic Belousov–Zhabotinski chemical reaction.

The addition of neural networks to the inner feedback path in order to improve on the use of pre-trained feed forward estimators

A learning control architecture which uses a multi-layer feed forward neural network with error back propagation is described. The architecture includes a feed forward estimator which is pre-trained and a feedback controller which continues to learn. The properties of the architectures are investigated through a series of experiments, and the application of the prototype adaptive controllers is described. To examine the performance of this controller, square wave demand signals are applied to the controller and the results are presented.

Global estimation of feedforward networks with a priori constraints

This paper presents a feedforward network estimation algorithm that addresses two issues, (i) avoiding local inferior minima to the performance criteria, and (ii) imposinga priori constraints to improve generalization and test economic hypotheses. The algorithm combines methods either previously developed or obviously beneficial but not yet combined. These involve combining linear least squares with simulated annealing, along with weight space reducing methods, to considerably improve its speed relative to pure simulated annealing. We present evidence on the algorithm's reliability at finding a global minimum. We also demonstrate how to constrain the estimation process to find networks that satisfy a givena priori condition. We provide examples of imposinga priori information to (i) prevent the trained network from making fundamental errors and (ii) to test economically interesting hypotheses.

Optimal parametric feedforward estimation of frequency-selective fading radio channels

Estimation of time-varying dispersive radio channels is one of the most important tasks of receiver synchronisation. State-of-the-art adaptive estimators employing decision feedback suffer from error propagation and limited robustness against faster fading. In this paper, the optimal feedforward channel estimator using only known training symbols is systematically derived. Statistical channel information is assumed to be available. For moderately rapid fading channels (snapshot assumption), the optimal estimator is shown to be divided into the two subtasks of maximum-likelihood acquisition and subsequent Wiener filtering of the acquired quantities. If perfect training sequences resulting in optimal performance are used, the Wiener filtering operation collapses into independent filtering of the individual acquired tap estimates, and the resulting channel estimator becomes efficient and flexible. The performance of the optimal estimator is evaluated for important cases. A design example of a near-optimal HF channel estimator/receiver is discussed. Linear interpolation is used to reduce the computational complexity of receiver coefficient adjustment. Simulation results confirm the superiority and robustness of feedforward synchronization having near-optimal performance at reduced complexity.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Design and Analysis of a Class of Optimal Discrete Control Systems

Abstract The paper describes a method for designing optimal discrete control systems with specified stability. The method is based on finding a state weighting matrix in the performance index so that specified eigenvalues are obtained. The result is a recursive procedure that allows the design to be started from scratch, or started with an existing optimal system that needs improved stability. The method is also extended to the design of optimal state estimators with specified stability. The paper further describes the design of different controller structures, incorporating feedback, feedforward, integral action and state estimation. The error reduction properties of the different structures are analyzed.