Passive Time Delay Estimation Research Articles

Passive Multipath Time Delay Estimation Using MCMC Methods

Passive time delay estimation in multipath environments is studied in this paper. A novel restrained maximum likelihood (ML) estimator is proposed to estimate the multiple time delays. Unlike traditional ML function which has P global maximum values, restraint conditions limit the ML function of P paths time delays signal with only one global maximum value. Markov chain Monte Carlo (MCMC) algorithm is used to find the global maximum of the restrained likelihood function to avoid traditional complex multidimensional grid search, initialization-dependent iterative methods or methods using interpolation to enhance performance. Indeed, MCMC sampling technique for ML function has a lower computational complexity than importance sampling (IS), which needs to compute the required realizations before sampling. Furthermore, Cramer---Rao lower bound of this model is derived. Finally, simulations results and theoretical analysis demonstrate that MCMC-based approach has the same performance as IS-based algorithm and the lower computational complexity than IS-based technique.

Estimation of parameters of a non-stationary random process due to a moving source based on the covariance-equivalent model

In this paper the problem of estimating source/channel characteristics from acoustic measurements in the sound field of a moving source, especially in multi-path and/or multi-sensor measurement environments, is discussed. The estimation problem is formulated using a novel technique called the ‘complex covariance-equivalent’ method which is an extension of the conventional covariance-equivalent method to the multi-component cases. The estimation technique developed in this paper is applied to the passive time delay estimation problem in the presence of source motion and simulation studies are also performed.

Signal generation model considerations for time varying delayed signals

In their paper Correlator Compensation Requirements for Passive Time Delay Estimation with Moving Source or Receivers, Adams et al. discuss the problem of estimating the time varying delay between two separately time varying delayed sensor signals. This correspondence gives a more exact derivation of the time varying delay at the input of the estimator. The investigations are given with the intention of facilitating the synthesis of signal generation models with several time varying delay elements.

A new generalized cross correlator

A new generalized cross correlator (GCC) for the passive time delay estimation problem is presented. The interpretation of this GCC is that of estimating the cross-correlation function by cross correlating the least mean-square estimates of the signal component in each of the observed waveforms. The implementation is simply a GCC with the weighting filter equal to the magnitude coherency squared. Numerical evaluation of the performance of this processor and a robust version indicate that they compare favorably to some of the well-known GCC procedures.

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.

Composite bound on the attainable mean square error in passive time-delay estimation from ambiguity prone signals (Corresp.)

The location of a radiating source can be determined by measuring the relative time-delay of its signal wavefront to several spatially separated receivers. A new technique is presented to investigate the performance of time-delay measurement schemes based on a modified version of the Ziv-Zakai lower bound. This technique is shown to yield a tight bound on the attainable mean-square measurement error for any prespecified signal-to-noise ratio conditions.

Correlator compensation requirements for passive time-delay estimation with moving source or receivers

An analysis is given of the effects of source or receiver motions on the output of a cross correlator used to estimate the source time-delay difference across a baseline. For both narrow-band and wide-band correlators, the need for time-varying correlator delay compensation is quantified for the case of a quadratic signal delay-difference variation. Two useful concepts which emerge are 1) the three-dimensional delay/delay-rate/delay-acceleration mean ambiguity function of the source signal, and 2) the equivalent τ-domain filter, which transforms the source autocorrelation function into the mean output of the mismatched correlator. The required correlator compensation is approximately a quadratic delay modulation matched to the input delay-difference function. For 3 dB peak output loss with a narrow-band signal, the maximum allowable delay-rate mismatch will produce 158° of phase rotation at the centroid frequency f <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> during the correlation integration time T, while the maximum allowable delay-acceleration mismatch will produce 156° of quadratic phase rotation at f <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> between the center (t = 0) and each edge (t = ± T/2) of the correlator integration window. For broad-band signals, the mismatch tolerances become about 11 percent tighter.

Estimation of time delay in the presence of source or receiver motion

Signals, received at two (or more) locations, and originating from a remote acoustic point source, exhibit time delay(s) that are useful for estimating source location or receiver geometries. Consequently, numerous procedures have been proposed for passive time-delay estimation in such cases. Past investigations apply, however, only when source and receiver motion is negligible. This paper extends previous results for maximum-likelihood (ML) estimation of time delay to the situation where the source, or the receivers, or both are in motion. It is shown that in the simplest case with two receivers, one of the signals must be appropriately time scaled prior to computing a generalized cross correlation of the received signals.