Probability Of False Alarm Research Articles

A novel prognostics solution for accurate identification of degradation patterns in turbo machines with variable observation window

The degradation of a system is a time bound phenomenon, which leads to the deterioration of turbomachinery, in terms of performance and reliability. If undetected and not acted upon in time, this could also lead to sudden system failure, resulting in unplanned unit downtime and maintenance. Unplanned downtime of a turbomachine leads to severe production loss for the end customer and consequent economic damages. Early detection of a degradation pattern would provide the customer with the opportunity to timely carry out corrective actions, preventing an unscheduled down time. The paper evaluates degradation identification methodology currently known from literature and finds them not accurate enough for general purpose application required by the solution. The paper discusses a novel methodology which can accurately detect degradation patterns of timeseries data. Critical features of this methodology are novel time-based correlation enabled regression model with variable observation window, autonomous training, and automatic adjusting capability to incorporate operating behavior change or physical system replacement. This leads to high accuracy, high generalization, and domain agnostic application capability. Moreover, particular focus is given to achieving high probability of detection and a low probability of false alarm. The paper demonstrates the performance achieved by the methodology when applied to the field of prognostics and diagnostics of IoT connected turbomachines through 50+ real application cases.

Pedestrian detection using a MEMS acoustic array mounted on a moving vehicle

Automatic pedestrian detection in a vehicle is of vital importance in Advanced Driver Assistance Systems (ADAS). Sensors currently used are based on cameras, radars and lidars, whose performance is degraded in environments with reduced visibility: night, smoke, fog, etc. This paper has validated the use of an active array of 150 MEMS (Micro-Electro Mechanical Systems) microphones incorporated into a conventional car moving in real urban traffic conditions, with the system working in real time, at a rate of 8 detections per second. Together with beamforming, Constant False Alarm Rate (CFAR) detection and lane detection algorithms, a crucial algorithm has been incorporated for the proper performance of the system that discriminates the detections of objects or pedestrians generated by the system from the false alarms generated by road imperfections, such as bumps, cracks, etc. Based on 6000 captures, performed with the car moving at 30 km/h, which is the typical speed limit in urban environments, it has been possible to detect pedestrians positioned at a distance from the car varying between 5 and 20 m, with a detection probability of 0.91 and a false alarm probability of 0.01. The results obtained have validated the effectiveness of using active acoustic arrays in the field of pedestrian detection and position estimation from moving cars in urban environments. The fusion of the presented system with the systems currently used for this purpose, would significantly improve the performance of pedestrian detection systems interacting with AEB (Automatic Emergency Breaking) systems, extending their operability to environments with reduced visibility, and resulting in the reduction in the number of possible collisions with pedestrians, thus increasing their safety.

A novelty detection method for efficient data storage in smart grids

This work presents a new novelty detection method for efficiently storing electrical power system data. The proposed method makes innovative use of the Cycle-by-Cycle Difference (CCD) and the Mathematical Morphology (MM) techniques to identify novelties in the voltage of an electrical power system. Once the novelties are identified, the frames where they occur are extracted from the signal, and the other frames are discarded. Among the extracted frames, those containing power quality (PQ) disturbances are fully stored, while the frames that represent stationary states have only their main parameters stored, contributing to efficient storage. The proposed method exhibited low computational complexity in the operational phase, which was evaluated via a field-programmable gate array (FPGA) platform implementation using a customized embedded processor. The method was evaluated with real and simulated signals. The results indicate that the developed method attained high detection probabilities alongside low false alarm probabilities, resulting in a competitive Area Under the Curve (AUC) exceeding 0.976 (except for interharmonics). Comparison with other methods revealed that our approach yielded competitive results with the lowest computational cost. We concluded that the proposed method may be useful for monitoring PQ disturbances in smart grids, where the data volumes are too large.

Apparent non-variable stars from the Kepler mission

The analysis of non-variable stars is generally neglected in the literature. However, such objects are needed for many calibration processes and for testing pulsational models. The photometric time series of the Kepler satellite mission still stand as the most accurate data available today and are excellently suited to the search for non-variable stars. We analysed all long-cadence light curves for stars not reported as a variable so far from the Kepler satellite mission. Using the known characteristics and flaws of these data sets, we defined three different frequency ranges where we searched for non-variability. We used the Lomb-Scargle periodogram and the false-alarm probability (FAP) to analyse the cleaned data sets of light curves. We then used $ FAP -2$ to define a star as 'non-variable' in the ranges below 0.1\,c/d, 0.1 to 2.0\,c/d, and 2.0 to 25.0\,c/d, respectively. Furthermore, we also calculated the standard deviation of the mean light curve to obtain another parameter. In total, we found stars that fulfil the set criteria. These objects are mostly cooler than the K populating the whole main sequence (MS) to the red giant branch (RGB).

X-Band Radar Detection of Small Garbage Islands in Different Sea State Conditions

This paper presents an assessment of X-band radar’s detection capability to monitor Small Garbage Islands (SGIs), i.e., floating aggregations of marine litter consisting chiefly of plastic, under changing sea states. For this purpose, two radar measurement campaigns were carried out with controlled releases at sea of SGI modules assembled in the laboratory. One campaign was carried out with a calm sea and almost no wind in order to determine the X-band radar system’s detection capabilities in an ideal scenario, while the other campaign took place with rough seas and wind. An analysis of the data acquired during the campaigns confirmed that X-band radar can detect small aggregations of litter floating on the sea surface. To demonstrate the radar’s ability to detect SGIs, a statistical analysis was carried out to calculate the probability of false alarm and the probability of detection for two releases at two different distances from the radar. For greater readability of this work, all of the results obtained are presented both in terms of radar intensity and in terms of the radar cross-section relating to both the targets and the clutter. Another interesting study that is presented in this article concerns the measurement of the speed of movement (drift) of the SGIs compared with the measurement of the speed of the surface currents provided at the same time by the radar. The study also identified the radar detection limits depending on the sea state and the target distance from the antenna.

A novel geometric-based bistatic range grouping algorithm for multi-target localization in distributed MIMO radar systems

In this paper, a novel bistatic range grouping algorithm is proposed in order to localize multiple targets in distributed multiple-input multiple-output (MIMO) radar systems. In a distributed MIMO radar, target localization is performed based on bistatic ranges, the distances between antennas through a target, without directional information, and grouping bistatic ranges with respect to the target is a crucial step to estimate multiple targets efficiently. In contrast to the existing grouping schemes that use tentative target estimation or complicated joint bistatic range grouping and target estimation, the proposed algorithm uses only the geometric property of bistatic ranges, resulting in computationally efficient and robust grouping algorithm without noise enhancement, especially for realistic noisy environments where other existing grouping algorithms often fail. The performance of the proposed scheme is confirmed by evaluating the probability of miss detection and the probability of false alarm through numerical simulations for various environments including indirect paths and blocked paths. The root mean square error performance of the multi-target localization using the proposed bistatic grouping algorithm is also presented for realistic noisy environments.

Two-sided automatic censoring CFAR detector based on the interquartile range in a heterogeneous Weibull clutter

As it is well known, CFAR (Constant False Alarm Rate) detectors are intended to regulate the PFA (Probability of False Alarm) in the presence of a clutter background whose mean power is unknown and/or varying. In heterogeneous clutter backgrounds, CFAR detectors false alarm control and detection efficiency rely upon their ability of clutter edge resilience and/or interfering targets rejection. Aiming to improve radar signal detection in a heterogeneous Weibull clutter, the two-sided automatic censoring IQR-CFAR (InterQuartile Range-CFAR) detector is introduced in this paper. This new detector first resorts to a logarithmic amplifier to dynamically achieve a Weibull to Gumbel transformation of the reference samples. Then, working on a cell-by-cell basis, the CFCR (Constant False Censoring Rate) algorithm retains and rejects samples based on the IQR within the reference window. Upon removal of the unwanted samples, the remaining data set is utilized to estimate the unknown biparametric linear detection threshold through the BLU (Best Linear Unbiased) estimates of the Gumbel distribution’s location and scale parameters. Extensive MC (Monte Carlo) simulations with both simulated and real data show that the suggested detector outperforms its challenging automatic censoring CFAR detectors found in the literature.

Risk overbounding for ionospheric gradient monitor using geometry-free double differenced carrier phase measurements

Ionosphere anomaly can cause large spatial gradients in the double-differenced carrier phase (DDCP) measurements. Taking advantage of this characteristic, the ionospheric gradient monitor (IGM) is designed with multiple ground reference stations to detect threatening ionospheric gradients for safety of life applications. An optimal IGM should be most sensitive to ionospheric gradients and least sensitive to other errors. However, current IGM suffers from the influence of tropospheric error, which can degrade monitor performance under extreme weather conditions by causing risks of false alarms and missed detections. To address this issue, an alternative IGM is proposed using the geometry-free combination of DDCP as the test statistic. Ambiguity resolution procedure is designed for estimating the ambiguity term in the test statistic. The risk induced by the wrong ambiguity fix and tropospheric error are analyzed and bounded with required averaging period and minimum baseline length. The results show that the proposed theoretical IGM is capable of achieving probability of false alarm of 10–8 and probability of missed detection of 10–6 with a filtering period of 612 s and baseline length of 371.7 m or a filtering period of 544 s and baseline length of 384.4 m. The experimental results using data collected from Hong Kong Satellite Positioning Reference Station Network demonstrate that the performance of the proposed theoretical IGM is comparable to that of the existing detection algorithm.

Spectrum Sensing Using Cooperative Matched Filter Detector in Cognitive Radio

The vast rise in the number of internet-connected devices necessitates a more accessible spectrum. As a result, Cognitive Radio was already proposed as a solution to the problem of restricted spectrum resources by utilizing available spectrum which is assigned to primary users. This method allows the secondary user to utilize the spectrum whenever the primary user is not using it, and it does so without intruding with the primary user. Whenever the secondary user detects the spectrum, it faces many issues, such as complexity in sensing, leading to a lack of noise value, and the primary user is hidden to all secondary users. In order to tackle these challenges, many spectrum sensing frameworks were introduced in the literature. In this paper, an adaptive threshold matched filter detector and a cooperative matched filter detector frameworks are utilized to detect the spectrum and resolve the issues above. The probability of detection (Pd), probability of miss detection (Pm), and probability of false alarm (Pf) are the metrics used to assess sensing accuracy. To simulate suggested detectors results and proficiency, the MATLAB R2020a software was utilized. In comparison to earlier studies, the simulation conclusions reveal that the detection process starts with lower SNR values compared to previous work.

Spectrum sensing in uncalibrated MIMO-based cognitive radios

This paper addresses the problem of spectrum sensing (SS) in cognitive radio networks utilizing multiple-input multiple-output (MIMO) technology, even when the receivers are not calibrated. The study develops a framework by formulating various composite hypothesis testing SS problems based on different assumptions about the parameter space of the alternative hypothesis. To accomplish this, four new detectors are designed using the likelihood ratio test (LRT), Rao, and matrix information geometry (MIG) principles. We demonstrate analytically that three of the proposed detectors maintain a constant false alarm rate (CFAR) despite noise covariance matrix uncertainty. For the non-CFAR detectors, we introduce a novel analytical threshold-setting method to ensure that their false alarm probabilities remain below a predetermined level, thereby making them useful for practical situations. Finally, extensive simulations are conducted to verify the analytical results, assess false alarm regulation, and compare the proposed SS algorithms with existing approaches in terms of detection probability.

Forecasting High Wind Events in the HRRR Model over Wyoming and Colorado. Part I: Evaluation of Wind Speeds and Gusts

Abstract Strong wind events cause significant societal damage ranging from loss of property and disruption of commerce to loss of life. Over portions of the United States, the strongest winds occur in the cold season and may be driven by interactions with the terrain (downslope winds, gap flow, and mountain wave activity). In the first part of this two-part series, we evaluate the High-Resolution Rapid Refresh (HRRR) model wind speed and gust forecasts for the 2016–22 winter months over Wyoming and Colorado, an area prone to downslope windstorms and gap flows due to its complex topography. The HRRR model exhibits a positive bias for low wind speeds/gusts and a large negative bias for strong wind speeds/gusts. In general, the model misses many strong wind events, but when it does predict strong winds, there is a high false alarm probability. An analysis of proxies for surface winds is conducted. Specifically, 700- and 850-mb (1 mb = 1 hPa) geopotential height gradients are found to be good proxies for strong wind speeds and gusts at two wind-prone locations in Wyoming. Given the good agreement between low-level height gradients and surface wind speeds yet a strong negative bias for strong wind speeds and gusts, there is a potential shortcoming in the boundary layer physics in the HRRR model with regard to predicting strong winds over complex terrain, which is the focus of the second part of this two-part study. Last, the sites with the largest strong wind speed bias are found to mostly sit on the leeward side of high mountains, suggesting that the HRRR model performs poorly in the prediction of downslope windstorms. Significance Statement We investigate the performance of the High-Resolution Rapid Refresh (HRRR) model with respect to strong wintertime wind speeds and gusts over the complex terrain of Wyoming and Colorado. We show that the overall performance of the HRRR model is low with regard to strong wind speed and wind gust forecasts across the investigated winter seasons, with a large negative bias in predicted strong wind speeds and gusts and a small positive bias for weak wind speeds and gusts. The largest biases are found to be on the leeward side of high mountains, indicating poor prediction of downslope winds. This study also utilizes National Weather Service forecasting metrics to understand their performance with respect to strong wind forecasts, and we find that they provide skill in forecasting these events.

Adaptive coalition with Kullback‐Leibler divergence for cooperative spectrum sensing (KLDCSS) in cognitive radio networks

SummaryEffective, reliable, and rapid spectrum sensing in concordance with maximum throughput efficiency is necessary at the cognitive radio network to maximize the network's utilization. An adaptive coalition using Kullback–Leibler divergence (KLD)‐based cooperative spectrum sensing scheme (KLDCSS) with a nominal sensing time to optimize the spectral efficiency is presented in this paper. In a coalition‐based spectrum sensing scheme, cooperating secondary users (SUs) are allocated to different coalitions to sense different Primary User (PU) channels. The same cognitive users allocated to sense the primary user channels are allotted to detect in different sensing phases. In the proposed sensing scheme, the cooperating SUs are adaptively allocated to different coalitions to maximize the throughput efficiency. Collaborating cognitive users with a standard signal‐to‐noise ratio and distinct energy levels that are characterized by the localized probabilities of detection and false alarm is considered. An adaptive coalition and user allocation algorithm are proposed to optimize the average opportunistic throughput and diminish the sensing overhead. The expression for throughput efficiency in terms of average throughput and sensing accuracy is derived. In this scheme, the SU computes the log‐likelihood ratio (LLR) from the acquired sample and forwards the same to the fusion center. The fusion center then accumulates the LLR values computed by the SU to estimate the likelihood of spectrum availability. Simulation results highlighting the competitive edge of the proposed scheme, with higher throughput efficiency over various numbers of SUs, coalitions, and signal‐to‐noise ratios, are presented.

Adaptive radar pulse detection design based on difference of box filter

AbstractPrecise radar pulse detection is the premise of electronic support measures. A constant false alarm rate (CFAR) detection algorithm based on difference of box (DOB) filter is proposed to realise low‐complexity and environment‐adaptive radar pulse detection, and the principle behind the proposed algorithm is revealed. Specifically, the DOB filter is adopted to extract the rising edges and falling edges of radar pulses, and the signal variation law of probability density functions (PDFs) during the process of DOB filter are first theoretically analysed. Based on the derived PDFs, dynamic detection threshold and fixed threshold factor for the proposed CFAR algorithm based on DOB filter are deduced to detect the presence of radar pulses. Furthermore, the closed‐form expression of the detection probability is derived. Simulations and on‐board field programmable gate arrays implementation verify the superiority of the proposed CFAR algorithm based on DOB filter. Simulation results show that the proposed algorithm performs well in detecting various types of pulse signals, the detection probability ≥99% on condition that the signal‐to‐noise ratio ≥3 dB and false alarm probability = 10−8. Moreover, the proposed CFAR algorithm based on DOB filter can deal with both singular pulses and pulse on pulse signals.

Analysis of Wideband spectrum sensing using Anderson darling test statistics in underlay cognitive microcell

The most widely used sensing technique for detecting energy is due to its ease of use and lack of need for signal information beforehand. Traditional methods often employ a two-threshold strategy in low signal-to-noise ratio scenarios, which can lead to temporary detection outcomes when the signal's energy is between the low and high threshold values. This subsequently results in inadequate detection accuracy, characterized by a reduced probability of detection, which ultimately results in an extended duration of the spectrum sensing. The paper suggests enhancing the efficiency of spectrum sensing through the utilization of a modified version of the Anderson-Darling test statistic, as opposed to other test statistics.To detect the presence of licensed users in each subchannel from the base station, the cognitive user implements the Anderson Darling test statistics as a sensing technique. The proposed work involves the mathematical derivation of the Anderson-Darling test statistics under a bandwidth of 6MHz.The simulation outcomes show that the sensing technique presented in this research study achieved a detection probability of 0.963 at a false alarm probability of 1%, using a small sample size of 20 at a signal-to-noise ratio of -20dB. This performance outperformed the other three detection algorithms.

Dynamic Spectrum Sensing For 5G Cognitive Radio Networks Using Optimization Technique

With increasing development of 5G technology, the rapid growth of various technologies and the growth of various wireless devices, demand for wireless spectrum becomes more urgent. Wireless communication technologies have been advancing rapidly, leading to the emergence of 5G communication systems .Spectrum sensing is the key model utilized to access the spectrum dynamically in CRN. Various researchers are done in spectrum sensing scenario and different methods are designed to perform the task of spectrum resource sharing. Most of the methods design a decision statistics for identifying the signal by analyzing the features of noise and signals. One promising approach to address the challenges of spectrum sensing in cognitive radio networks for 5G communication is the integration of deep learning with hybrid optimization techniques. By combining the power of deep learning algorithms with optimization methods, it becomes possible to improve the efficiency and accuracy of spectrum sensing in dynamic and diverse communication scenarios. One of the key advantages of MIMO-based spectrum sensing is its ability to exploit the spatial diversity inherent in the environment. By using multiple antennas at both the transmitter and receiver, MIMO systems can distinguish between signals arriving from different directions, thereby improving the accuracy of spectrum sensing. Moreover, MIMO technology also enables the cognitive radio network to utilize the available spectrum more efficiently. With the ability to establish multiple parallel communication links, MIMO-based cognitive radio networks can achieve higher data rates and improved spectral efficiency, especially in dynamic and challenging radio environments. Research in this field is focused on further enhancing the performance of MIMO-based spectrum sensing in cognitive radio networks through advanced signal processing algorithms and machine learning technique Spectrum sensing detect existence of primary users (PUs) and it becomes a main research topic of CRN in industry and academic domain. This research developed a new framework based on algorithm to progress the mechanism of spectrum sensing in the CRN by detecting the availability of free channel. The signal components are extracted from the received signal and thereby spectrum availability of detected through fusion center using proposed Feedback Artificial Optimization Algorithm-based Deep Q network. However, Simulation results show that the proposed multiple-input-multiple-output(MIMO) spectrum sensing method achieves good performance Cognitive Radion Network attains maximum probability of detection and minimum probability of false alarm as 70%, and 38% for Rayleigh channel.

Prospects of Identifying Hierarchical Triple Mergers for the Third-generation Ground-based Detectors

A hierarchical triple merger (HTM) constitutes a type of event in which two successive black hole (BH) mergers occur sequentially within the observational window of gravitational-wave (GW) detectors, which has an important role in testing general relativity and studying BH population. In this work, we conduct an analysis to determine the feasibility of identifying HTMs from a large GW event catalog using third-generation ground-based GW detectors. By comparing the Bhattacharyya coefficient that measures the overlap between the posterior distributions of the remnant and progenitor BH parameters, we find that the overlap between the event pair can serve as a preliminary filter, which balances between computational demand and the probability of false alarms. Following this initial, time-efficient, yet less accurate screening, a subset of potential HTM candidates will be retained. These candidates will subsequently be subjected to a more precise, albeit time-intensive, method of joint parameter estimation for verification. Ultimately, this process will enable us to robustly identify HTMs.

Bayesian detection with feedback for cooperative spectrum sensing in cognitive UAV networks

AbstractUnmanned aerial vehicles (UAVs) are becoming a popular research topic in applications that do not require human intervention. A variety of applications and devices coexist in the environment where UAVs operate, resulting in a serious spectrum shortage. Therefore, cognitive radio (CR) is a promising solution for opportunistic access to underutilized spectrum bands by the primary user (PU) through cooperative spectrum sensing (CSS) technique. However, the flexible location of UAVs makes CSS inefficient and even difficult to be implemented. In view of this, a cognitive UAV network model consisting of a pair of UAVs which follows a circular flight trajectory to participate in CSS is proposed in a spectrum sensing frame structure. According to the local energy detection, we further propose an optimization problem about the stopping time in a quickest detection paradigm and conduct out Bayesian detection method with feedback to minimize the sensing delay and the false alarm probability by optimizing the stopping time. Moreover, we theoretically derive the optimal threshold pair and prove the optimal stopping time by means of Markov process. At last, a series of numerical simulations are shown to corroborate the proposed Bayesian detection method with feedback, in terms of the false alarm probability, the sensing delay, and achievable throughput. In contrast to the classic Neyman‐Pearson and Bayesian detection methods, the advantage of Bayesian detection method with feedback sensing is presented.

Sequential Detection under Correlated Observations using Recursive Method

Sequential analysis has been used in many cases when the decision is supposed to be taken quickly such as for signal detection in statistical signal processing, namely sequential detector. For identical error probabilities, a sequential detector needs a smaller average sample number (ASN) than its counterpart of a fixed sample number quadrature detector based on Neyman-Pearson criteria. The optimum sequential detector was derived based on the assumption that the observations are uncorrelated (independent). However, in realistic scenario, such as in radar, the assumption is commonly violated. Using a sequential detector under correlated observations is sub-optimal and it poses a problem. It demands a high computational complexity, since it needs to recalculate the inverse and the determinant of the signal covariance matrix for each new sample taken. This paper presents a technique for reducing the computational complexity, which involves using recursive matrix inverse to subsequently calculate conditional probability density functions (pdf). This eliminates the need to recalculate the inverse and determinant, leading to a more reasonable solution in real-world scenario. We evaluate the performance of the proposed (recursive) sequential detector by using Monte-Carlo simulations and we use the conventional and non-recursive sequential detectors for comparisons. The results show that the recursive sequential detector has equal probabilities of false alarm and miss-detection with the conventional sequential detector and performs better than the non-recursive sequential detector. In terms of ASN, it maintains comparable results to the two conventional detectors. The recursive approach has reduced the computational complexity for matrix multiplication to from and it also has rendered the calculation of matrix determinant to be unnecessary. Therefore, by having better probabilities of error and reduced computational complexities under correlated observations, the proposed recursive sequential detector may become a viable alternative to obtain a more agile detection system as required in future applications, such as in radar and cognitive radio.

Adaptive detection with tunable robustness via a linear combination of the test statistics and loss factor

In this paper, we propose an adaptive detection algorithm with tunable robustness to the mismatched target. We notice that the test statistic of existing algorithms is the function of the test statistic of the generalized likelihood ratio test (GLRT) and the loss factor, which motivates us to propose the tunable robustness test (TRT) via a linear combination of the above two variables. The probability of false alarm (Pfa) and the probability of detection (Pd) for the mismatched target are presented for the rank one target and the multidimensional subspace target, respectively. Through numerical simulations, we verify that the tuning parameter will influence the ability to distinguish between matched and mismatched targets, and therefore the TRT can achieve robustness that existing algorithms do not have.

Waveform reconstruction of core-collapse supernova gravitational waves with ensemble empirical mode decomposition

ABSTRACT Gravitational waves (GWs) from core-collapse supernovae (CCSNe) have been proposed as a probe to investigate the physical properties inside supernovae. However, how to search for and extract the GW signals from CCSNe remains an open question owing to their complicated time–frequency structure. In this paper, we apply the ensemble empirical mode decomposition (EEMD) method to decompose and reconstruct simulated GW data generated by the magnetorotational mechanism and the neutrino-driven mechanism within the Advanced LIGO, using the match score as the criterion for assessing the quality of the reconstruction. The results indicate that by decomposing the data, the sum of the first six intrinsic mode functions (IMFs) can be used as the reconstructed waveform. To determine the probability that our reconstructed waveform corresponds to a real GW waveform, we calculate the false alarm probability of reconstruction (FAPR). By setting the threshold of the match score to be 0.75, we obtain the FAPRs of GW sources at distances of 5 and 10 kpc to be 6 × 10−3 and 1 × 10−2, respectively. If we normalize the maximum amplitude of the GW signal to 5 × 10−21, the FAPR at this threshold is 4 × 10−3. Furthermore, in our study, the reconstruction distance is not equivalent to the detection distance. When the strain of GWs reaches 7 × 10−21, and the match score threshold is set at 0.75, we can reconstruct GW waveforms up to approximately 36 kpc.