Fucheng Guo

Coherent summation of multiple short-time signals for direct positioning of a wideband source based on delay and Doppler

We consider identifying the source position directly from the received source signals. This direct position determination (DPD) approach has been shown to be superior in terms of better estimation accuracy and improved robustness to low signal-to-noise ratios (SNRs) to the conventional two-step localization technique, where signal measurements are extracted first and the source position is then estimated from them. The localization of a wideband source such as a communication transmitter or a radar whose signal should be considered deterministic is investigated in this paper. Both passive and active localization scenarios, which correspond to the source signal waveform being unknown and being known respectively, are studied. In both cases, the source signal received at each receiver is partitioned into multiple non-overlapping short-time signal segments for the DPD task. This paper proposes the use of coherent summation that takes into account the coherency among the short-time signals received at the same receiver. The study begins with deriving the Cramer-Rao lower bounds (CRLBs) of the source position under coherent summation-based and non-coherent summation-based DPDs. Interestingly, we show analytically that with coherent summation, the localization accuracy of the DPD improves as the time interval between two short-time signals increases. This paper also develops approximate maximum likelihood (ML) estimators for DPDs with coherent and non-coherent summations. The CRLB results and the performance of the proposed source position estimators are illustrated via simulations.

Localization of multiple disjoint sources with prior knowledge on source locations in the presence of sensor location errors

Sensor location errors are known to be able to degrade the source localization accuracy significantly. This paper considers the problem of localizing multiple disjoint sources where prior knowledge on the source locations is available to mitigate the effect of sensor location uncertainty. The error in the priorly known source location is assumed to follow a zero-mean Gaussian distribution. When a source location is completely unknown, the covariance matrix of its prior location would go to infinity. The localization of multiple disjoint sources is achieved through exploring the time difference of arrival (TDOA) and the frequency difference of arrival (FDOA) measurements. In this work, we derive the Cramer-Rao lower bound (CRLB) of the source location estimates. The CRLB is shown analytically to be able to unify several CRLBs introduced in literature. We next compare the localization performance when multiple source locations are determined jointly and individually. In the presence of sensor location errors, the superiority of joint localization of multiple sources in terms of greatly improved localization accuracy is established. Two methods for localizing multiple disjoint sources are proposed, one for the case where only some sources have prior location information and the other for the scenario where all sources have prior location information. Both algorithms can reach the CRLB accuracy when sensor location errors are small. Simulations corroborate the theoretical developments.

On the use of calibration sensors in source localization using TDOA and FDOA measurements

The accuracy of a source location estimate is very sensitive to the presence of the random noise in the known sensor positions. This paper investigates the use of calibration sensors, each of which is capable of broadcasting calibration signals to other sensors as well as receiving the signals from the source and other calibration sensors, to reduce the loss in the source localization accuracy due to uncertainties in sensor positions. We begin the study with deriving the Cramer-Rao lower bound (CRLB) for source localization using time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements when a single calibration sensor is available. The obtained CRLB result is then extended to the more general case with multiple calibration sensors. The performance improvement due to the use of calibration sensors is established analytically. We then propose a closed-form algorithm that can explore efficiently the calibration sensors to improve the source localization accuracy when the sensor positions are subject to random errors. We prove analytically that the newly developed localization method attains the CRLB accuracy under some mild approximations. Simulations verify the theoretical developments.

An Improved Algebraic Solution for TDOA Localization With Sensor Position Errors

This letter proposes an improved version of the popular two-stage weighted least squares (TSWLS) algorithm for source localization using time difference of arrival (TDOA) measurements in the presence of sensor position errors. The new technique remains to be closed-form and approximately efficient as TSWLS. But it exhibits lower estimation bias and better robustness to increased noise over TSWLS via using a new Stage-2 processing, where the localization error of its Stage-1 is estimated and subtracted from the Stage-1 output to generate the final source position estimate. Simulations corroborate the theoretical developments.

Source localization and calibration using TDOA and FDOA measurements in the presence of sensor location uncertainty

Source localization accuracy is very sensitive to sensor location error. This paper performs analysis and develops a solution for locating a moving source using time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements with the use of a calibration emitter. Using a Gaussian random signal model, we first derive the Cramér-Rao lower bound (CRLB) for source location estimate in this scenario. Then we analyze the differential calibration technique which is commonly used in Global Positioning System. It is indicated that the differential calibration cannot attain the CRLB accuracy in most cases. A closed-form solution is then proposed which takes a calibration emitter into account to reduce sensor location error. It is shown analytically that under some mild approximations, our approach is able to reach the CRLB accuracy. Numerical simulations are included to corroborate the theoretical developments.

Source localization using a moving receiver and noisy TOA measurements

This paper considers using a moving receiver to locate a stationary source that transmits periodically with an unknown period. The receiver records the time of arrivals (TOAs) of the intercepted signals for source localization. A new two-step localization algorithm is developed. Its first step ignores the signal propagation delay and identifies the signal period using existing period estimation techniques. Sufficient conditions for correctly relating the TOA measurements are established. The second step of the new algorithm jointly estimates the source position and the signal period using an iterative maximum likelihood estimator. Simulation results demonstrate the effectiveness of the newly proposed technique. HighlightsGive a new source position and period estimator using TOAs from a moving receiver.The new estimator considers the relative motion between the receiver and the source.The new method finds the signal period with higher accuracy than previous methods.The conditional CRLBs of the source position and signal period are derived.Sufficient conditions for the new method to reach the conditional CRLBs are provided.

Improving the projection method for TOA source localization in the presence of sensor position errors

This paper develops a closed-form solution that improves the projection matrix method for time of arrival (TOA) source localization in the presence of sensor position inaccuracy. The projection approach is attractive because it does not require the use of an extra variable as in the traditional closed-form solution. Compared with the previous projection method, the proposed algorithm offers a closed-form solution and at the same time attains the Cramer-Rao lower bound (CRLB) performance for Gaussian noise over the small noise region. The performance of the proposed method is validated by simulations.

Extraction of Pulse Repetition Interval Based on Incomplete, Noisy TOA Measurements by the Moving Passive Receiver

This paper investigates the problem of extracting the pulse repetition interval (PRI) of stationary pulsed radar emitter from noisy time of arrival(TOA) measurements with missing observations (incomplete) by the moving receiver. The relative motion between the receiver and emitter induces the large estimation bias to estimate PRI, we first discuss the conditions on which identifying the period integer numbers under the circumstance of relative movement, then propose two robust algorithms based on compensating delay of each observations on emitters status space grids. The proposed algorithms can efficiently reduce the estimation bias introduced by model mismatch without the requirement of specific emitter location information. Simulation studies indicates that the proposed solutions can improve the PRI estimation accuracy.

Multiple disjoint sources localization with the use of calibration emitters

Sensor location uncertainty is known to degrade significantly the source localization accuracy. This paper considers the problem of multiple disjoint sources localization with calibration emitters using time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements. The TDOAs and FDOAs are from unknown sources and calibration emitters. Using a Gaussian noise model, we first derive the Cramér-Rao lower bound (CRLB) for multiple disjoint sources localization with the use of calibration emitters whose locations are also not known exactly. By modeling the calibration location errors as additive Gaussian noise, the amount of reduction in localization accuracy due to calibration location errors is derived through CRLB analysis. The paper then proposes an algebraic closed-form solution for multiple disjoint sources localization using TDOA and FDOA measurements, which are both from unknown sources and calibration emitters. Finally, the algorithm is proved analytically to reach the CRLB accuracy when the sensor and calibration location errors are small. Simulations corroborate the theoretical results and the good performance of the proposed method.