Unknown Delay Research Articles

Video-to-Audio Synchrony Monitoring and Correction

Contemporary practices in the transmission of network television programming have rendered traditional methods of restoring video-to-audio synchronization inadequate. Constantly changing transmission path lengths encountered in satellite transmissions make it impossible to predict accurately the amount of delay that will be introduced by video processing, and other kinds of processing may introduce further unknown delay times. A new method of using encoded audio to determine relative time differences between audio and video can fully automate and guarantee proper video-to-audio synchronization at the receiving station. This correction can be made at any point in the system and does not require any knowledge of the amount of delay that may have been accumulated along the way.

A Bayesian approach to gross error detection in chemical process data: Part I : Model development

Tamhane, A.C., Iordache, C. and Mah, R.S.H., 1988. A Bayesian approach to gross error detection in chemical process data. Part I: Model development. Chemometrics and Intelligent Laboratory Systems, 4: 33–45. A new statistical test based on the Bayesian approach for detecting gross errors in chemical process data is presented in this paper. Part I gives the theoretical development of the underlying model and the proposed test, while Part II gives the results of a simulation study for assessing the performance of the test. In Part I we first develop a one-time application of the Bayes test, and then embed it in a sequential setting. For this setting a probabilistic model is proposed for updating the prior probabilities of gross error occurrences in the light of accumulating data. Modifications in the basic model are suggested to take account of unknown magnitudes of gross errors and the aging of measuring instruments. Some practical difficulties in the application of the Bayes test, e.g., adjustments for unknown delay times in detecting gross errors in instruments, adjustments of instrument lifetimes when updating their failure probabilities, and computational complexity of the scheme, are discussed and heuristic methods for their amelioration are suggested.

Present and Future of Synchronization in the US Telephone Network

The need for phase (timing) control in a digital network is described. Because of unknown and unstable path delays, phase con- trol is done on a local basis, whereas only frequency control is feasible on a global basis. The means to provide frequency control is potentially built into the network as a hierarchical masterislave system. The char- acteristics of the four levels of quality of the frequency sources (clocks) in this system are described. Each clock must be phase-locked to a clock of equal or better quality (e.g., S-3 locked to S-2). The pull-in range of the phase-lock loop associated with a clock must allow for inaccuracies of the clock to which it locks-even under startup condi- tions. The pull-in range for an S-3 clock expressed on a fractional fre- quency basis is about 9 X The importance of this number is placed in perspective by realizing two things: 1) the goal for frequency accu- racy of a signal controlling an S-3 clock is a minimum of 3.5 X 2) it is the current intention to equip about 98 percent of the 10 000 digital switches with S-3 clocks. This means that almost all S-3 clocks will be directly connected to an S-3, not an S-2, clock. Furthermore, many other types of equipment, such as digital cross connects and dig- ital channel banks (based on S-3 or S-4 clocks), will intentionally or inadvertently become sources of timing signals. The magnitude of the potential problem therefore becomes apparent. Experience in the field indicates that the number of instances of synchronization problems to- day is troublesomely large. The three major causes of these problems- equipment and line failures, design errors, and operational errors- are discussed. Means of limiting these problems, including the greater use of high-quality equipment and better system monitoring, are also discussed.

Auto tuning of the time horizon

The paper discusses a direct adaptive control strategy applicable to open loop stable systems and systems that have been stabilized via constant output feedback. The algorithm uses a least squares estimator and an extended horizon control policy based on step input predictions. The algorithm does not require that the time horizon is fixed a priori. It is tuned on-line to satisfy a stability condition which can be related to the closed loop pole locations. Asymptotic stability of the algorithm is established. The analysis applies to systems that have unknown delays, non minimum phase behaviour and bounded output disturbances. Thus, a certain amount of model mismatch can be tolerated. Simulation examples demonstrate the performance of the proposed adaptive strategy.

Stability analysis of discrete-time adaptive controllers for systems with unknown delay

The stability of discrete-time adaptive controllers when the process delay is unknown is studied. Conditions for stability and instability are derived based on the analysis of the homogeneous part of the linear time-varying difference equation describing the behavior of the parameter estimates. First, using a Lyapunov approach, it is shown that for slow adaptation the inclusion of a leakage [1] and a new normalization factor in the estimation law (2), (8) allows us to preserve stability when the delay is overestimated. Second, we prove that, when the delay is underestimated and no leakage is used, the parameters obtained with a projection estimator grow unbounded for sufficiently high adaptation gains.

Time delay estimation by combining efficient algorithms and generalized cross-correlation methods

This paper analyzes the performance of the two efficient algorithms (presented by Stein and Cabot) for time delay of arrival estimation (TDE) between two signals. It is shown that these estimators are unbiased, and explicit expressions for the TDE mean-square error (MSE) are presented. It is also shown how to improve the performance of these algorithms by combining them with generalized cross-correlation (GCC) methods. In the analysis, we only assume stationary signals which are not necessarily Gaussian. The first algorithm (Stein) is indirect and uses the symmetry of the cross-correlation function between the two signals. It is shown here that the TDE-MSE depends on the unknown delay. The performance of this algorithm can be improved by combining it with the GCC method, and the pertinent TDE-MSE expressions are presented. The second algorithm (Cabot) is based on finding the zero of the cross-correlation function between one signal and the Hilbert transform of the other signal. Here, too, the pertinent TDE-MSE expressions are presented. This algorithm is also combined with the GCC method, and the optimal weight function for which the TDE-MSE expression coincides with the Cramer-Rao lower bound is found.

Optimal delay estimation in a multiple sensor array having spatially correlated noise

The maximal likelihood (ML) estimation of time-of-arrival differences for signals from a single source or target arriving at M \geq 2 sensors has been the subject of a large number of papers in recent years. These time differences or delays enable target location. Nearly all previous work has assumed noises which are independent among all sensors. Herein, noises are taken to have complex correlation between sensors. A set of nonlinear equations in the unknown delays is derived and the Fisher information matrix (FIM) for the estimates is also derived. The Cramer-Rao matrix bound (CRMB), which is the inverse of FIM, shows optimal estimator covariances. Computer evaluations are plotted for CRMB elements with varied SNR and noise covariance values typical of turbulent boundary layer noise in towed arrays and signal sources at infinite range (plane-wave fronts). Maximum changes in the bound are within ±3 dB for complex noise correlations with magnitudes up to 0.4, which we tested.

An auto-pole-placement self-tuning controller†

Abstract An explicit self-tuning controller is described that incorporates closed-loop pole location as the principal design criterion for the objective function of Clarke and Gawthrop. The algorithm includes several minor extensions to improve robustness : a variable dead-time compensator to deal with unknown or time-varying delay, and a method of treating steady-state offset that avoids retaining an integrator in the loop continuously. A new technique has been developed and included in the algorithm that enables the controller to be auto-tuning in the sense that the closed-loop pole(s) and sampling period can be determined on-line so as to optimize the system set-point step response, leaving the system designer to specify only internal model orders and noise characteristics on which to initiate retuning. The resulting controller is quite robust and can easily handle unstable, non-minimum phase systems in a single-loop configuration, as is demonstrated by several simulations including a non-linear model ...

Fundamental limitations in passive time-delay estimation--Part II: Wide-band systems

This is the second part of a study which deals with the problem of passive time delay estimation. The focus here is on systems employing wide-band signals and/or arrays of very widely separated receivers. A modified (improved) version of the Ziv-Zakai lower bound (ZZLB) is used to analyze the effect of additive noise and signal ambiguities on the attainable mean-square estimation errors. When the lower bound is plotted as a function of signal-to-noise ratio (SNR), one observes two distinct threshold phenomena dividing the SNR domain into three disjointed segments. At high SNR, the lower bound coincides with the Cramér-Rao lower bound (CRLB). This is the ambiguity-free mode of operation where differential delay estimation is subject only to local errors. At moderate SNR (between the two thresholds), the lower bound exceeds the CRLB by a factor of 12(ω <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> /w) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_{0}</tex> and w are, respectively, the center frequency and signal bandwidth. In this region, the ambiguities in the received signal phases cannot be resolved; however, a useful estimate of the differential delay can still be obtained using the received signal envelopes. At low SNR, the lower bound approaches a constant level depending only on the a priori search domain of the unknown delay parameter. In this region, signal observations are subject to envelope ambiguities as well, and are thus essentially useless for the delay estimation.

On positional simulation in dynamic systems

The problem of simulating delays and controls in a dynamic system described by ordinary differential-difference equations is examined. The simulation is carried out in real time by the feedback principle on the basis of information and the current phase states of the system, measurable with a certain error. The simulation algorithm proposed —an algorithm for reconstructing the unknown delays and controls —is a regularizing one in the sense that the simulation results become better the less the measurement errors in the system's phase positions. The ideological source of the proposed method of solving the problem is Krasovskii's extremal aiming principle /1, 2/. The paper extends the investigation in /3, 4/ and touches on /1–5/.

Improved algorithms for parameter identification in continuous systems via Walsh functions

The paper first reviews the status of the Walsh-functions (WF) approach to the problem of parameter identification in continuous dynamical systems. The WF method of analysis and parameter estimation relies on the use of the so-called operational matrix for integration. For higher-order systems, the existing operational matrix has so far been applied after being raised to the required power. This procedure results in an accumulation of error at each stage of integration. To improve this situation, the paper introduces one-shot operational matrices for repeated integration (OSOMRI) via Walsh functions. The superiority of OSOMRI is demonstrated in problems of analysis and identification of higher-order systems. The paper then presents a direct noniterative method of parameter estimation for lumped linear systems in the presence of small unknown delays employing Walsh delay matrices developed recently by the authors. When the delay terms are not small, the results of this noniterative method will be considerably in error. However, these results can be taken as good initial values for the inevitable refining iterative shift algorithm of Prasada Rao and Sivakumar. The paper also presents an efficient multistep algorithm for parameter estimation in systems with large unknown time delays.

Detection, estimation, and classification with spectrograms

A locally optimum detector correlates the data spectrogram with a reference spectrogram in order to detect (i) a known signal with unknown delay and Doppler parameters, (ii) a random signal with known covariance function, or (iii) the output of a random, time-varying channel with known scattering function. Spectrogram correlation can also be used for maximum likelihood parameter estimation, e.g., estimation of delay or center frequency of a signal. To estimate an analog input signal from its spectrogram, a modified deconvolution operation can be used together with a predictive noise canceler. If no noise is added to the spectrogram, the mean-square error of this signal estimate is independent of the window function that is used to construct the spectrogram. When estimates of specific signal parameters are obtained directly from the spectrogram, these estimates have mean-square errors that depend upon both signal and window waveforms. Spectrogram correlation can be used for classification as well as for estimation and detection. Parameter estimators and detectors are, in fact, specialized kinds of classifiers.

Optimal reception of digital data over the Gaussian channel with unknown delay and phase jitter

Asymptotically optimum (in the sense of minimum per-symbol error rate) receiver structures for data communication over the white Gaussian channel with unknown time delay and carrier phase jitter are developed. The receiver structures apply to the following suppressed-carrier modulation systems: double sideband (DSB), quadrature amplitude modulation (QAM) with an arbitrary constellation, vestigial sideband (VSB) and single sideband. The resulting minimum error probability receivers are asymptotically equivalent to maximum-likelihood digital {\em sequence}-estimating receivers. The optimum structures implicitly derive joint maximum-likelihood estimates of the unknown parameters and of the sequence of data symbols. It is shown that the parameter estimates can be obtained from two data-directed stochastic approximation algorithms. Unlike traditional theoretical treatments of this communication situation, which have separated the highly important carrier phase and timing recovery problem from the detection problem, a unified theory is presented from which the complete ideal receiver structure can be deduced.

Estimation of the relative delay of two similar signals of unknown phases in white Gaussian noise

In this paper we consider the estimation of the delay of a signal of unknown phase obscured by white noise and by another signal of unknown phase and known delay. We also consider the situation where both delays are unknown. Use is made of Shannon's sampling analysis ^{1} as developed by Woodward. ^{2} We conclude that the relative carrier phase of the two signals must be first estimated in order to maximize the {\em a posteriori} probability of the estimate, but that knowledge of the absolute phase is only of secondary value.