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Minimizing False Peak Errors in Generalized Cross-Correlation and its Implementation on Water Leak Detection System

  • 최수환 (대학원 전자컴퓨터공학과 통신공학전공)

초록/요약

Multiple sensors are widely used for robust estimation, communication and target tracking. When several sensors of different physical characteristics and varying spatial locations sample a continuous time signal, they produce correlated time sequences. The cross correlation between any two of the sampled signals contains vital information about the original signal, and can play an important role in applications such as multi-sensor data fusion and tracking and sonar. The cross-correlation function (CCF) is a powerful tool for time delay estimation that registers different signals sampled by different sensors in time domain. An accurate time registration is crucial in processing of multi-sensor signals such as sonar, seismic data processing and tracking. Time delay estimation of two analog signals through cross-correlation has been studied by many authors. Estimation of time delay between deterministic signals received at two (or more) spatially separate sensors is a fundamental problem in tracking and localizing signal processing. For instance, target location and tracking may be determined directly from the time delay estimation (TDE). The classical time delay estimation algorithms search the maximum of cross-correlation function and have an accuracy limited by the sampling interval. For better accuracy less than one sampling period, the subsample time delay estimation can be applied by means of the phase displacement calculation for sinusoidal signals. Since the accuracy of the classical TDE time delay estimation is derived from cross-correlation function is limited by the sampling interval, false peak errors (FPEs) arise when there exists a second correlation peak with higher amplitude than the peak corresponding to the real displacement. Ambiguity (or false peak) errors result from the use of a finite bandwidth. It has been shown that, in the presence of false peak errors, the actual performance of a time-delay estimator may be worse than that predicted by the Cramér–Rao lower bound (CRLB). Previous research works, however, mostly regard it as a slight problem, and filter the false peak errors regarding series of detected peak which is not continuous with previous one or next one. Water leak detection and localization is one of the fields that time delay estimation is mostly required. A water leak detection system based on wireless sensor networks (WSNs) that detects leaks in a water supply, localizes the leak position, and then informs the water management center is presented in this paper. The traditional leak detection method uses experienced personnel who walk along a pipeline listening for the sound that is generated by leaks; its effectiveness obviously depends on the experience of the user. In addition, in order to make a more successful detection, it needs to be performed in the middle of the night when people do not use as much water causing users to have to operate the leak detection system overnight. Considering these challenging issues, this dissertation discusses the solutions to minimizing the false peak error for time delay estimation without changing sampling frequency and presents a water leak detection system using sensor networks. I introduce an algorithm that estimates two peaks for two cross-correlation functions using three types of signals such as a reference signal, a delayed signal, and a delayed signal with an additional time delay of half a sampling period. A peak selection algorithm is also proposed in order to identify which peak is closer to the true time delay using subsample TDE methods. The proposed algorithms can be seen to display better performance, in terms of the probability of the integer TDE errors, as well as the mean and standard deviation of absolute values of the time delay estimation errors. And, I present a new water leak detection system method based on WSNs and describe it in detail. Leak detection devices detect a leakage of water and then transmit and receive the results amongst each other through the configured WSNs in order to improve the reliability of the detection result. In addition, I analyzed the sound from the water flowing in a pipeline and developed the pre-signal processing used to separate a leak sound from the other noise. Finally, since it is especially important to synchronize the water leak detection devices that are installed on the pipeline, I use a 1PPS (1 pulse per second) signal generated by GPS (Global Positioning System), resulting in a precise time synchronization. The proposed system was deployed to a real pipe on small test bed and its performance was evaluated.

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목차

ABSTRACT i
Contents v
List of Figures viii
Abbreviations xi
Chapter 1 Introduction 1
1.1. Time Delay Estimation 1
1.1.1. Generalized Cross-Correlation (GCC) 2
1.1.2. False Peak Errors 6
1.2. Water Leak Detection and Localization 8
1.2.1. Water Leak Detection 9
1.2.2. Water Leak Localization 10
1.3. Dissertation Organization 12
Chapter 2 Minimizing False Peak Errors in Generalized Cross-Correlation 13
2.1. Introduction 13
2.2. Related Work 14
2.3. Conventional TDE Methods and Their Problems 16
2.3.1. Integer Part of the TDE 16
2.3.2. Fractional Part of the TDE 20
2.3.3. False Peak Error 22
2.3. The Proposed TDE Method 30
2.4. Simulation 37
2.4.1. Simulation Setup 37
2.4.2. Simulation results 39
2.5. Summary 46
Chapter 3 47
A Wireless Water Leak Detection System using Sensor Networks 47
3.1. Introduction 47
3.2. Related Works 49
3.3. The System 54
3.3.1. The Water Leak System Overview 54
3.3.2.The Leak Detecting Sensor 56
3.3.3. The DSP Board 57
3.3.4. The NCAP node 59
3.4. Water Leak Detection 60
3.5. Water Leak Localization 63
3.6. Evaluation 66
3.6.1. Evaluation Setup 66
3.6.2. Evaluation Results 68
3.7. Summary 71
Chapter 4 Conclusion 73
APPENDIX A Optimum Passive Bearing Estimation 75
A.1 Cramér–Rao Bound 75
Bibliography 85

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