Frequency Difference Of Arrival Research Articles

Joint source localisation and sensor refinement using time differences of arrival and frequency differences of arrival

The accuracy of sources locations and velocities estimate is very sensitive to the accurate knowledge of sensor locations and velocities. In the presence of sensor position and velocity errors, this study considers the problem of simultaneously locating multiple disjoint sources and refining erroneous sensor positions and velocities using time differences of arrival and frequency differences of arrival. The previous work by Sun and Ho to solve this problem provided an efficient estimator for multiple disjoint sources, but it cannot provide optimum accuracy for the sensor positions and sensor velocities. In many practical applications, it is necessary and helpful to refine sensor locations and velocities while localising multiple sources. The proposed method improves the previous method so that both the source and the sensor position and velocity estimates can achieve the Cramér–Rao lower bound accuracy very well over small noise region. The theoretical derivation is corroborated by simulations.

Modified CRLB for Cooperative Geolocation of Two Devices Using Signals of Opportunity

We consider the problem of localizing two devices using signals of opportunity from beacons with known positions. Beacons and devices have asynchronous local clocks or oscillators with unknown clock skews and offsets. We model clock skews as random, and analyze the biases introduced by clock asynchronism in the received signals. By deriving the equivalent Fisher information matrix for the modified Bayesian Cramér-Rao lower bound (CRLB) of device position and velocity estimation, we quantify the errors caused by clock asynchronism. We propose an algorithm based on differential time-difference-of-arrival (DTDOA) and frequency-difference-of-arrival (FDOA) that mitigates the effects of clock asynchronism to estimate the device positions and velocities. Simulation results suggest that our proposed algorithm is robust and approaches the CRLB when clock skews have small standard deviations.

Velocity Measurement using the Fdoa Method in Ground-Based Radio Navigation System

Abstract Velocity is one of the main navigation parameters of moving objects. However some systems of position estimation using radio wave measurements cannot provide velocity data due to limitation of their performance. In this paper a velocity measurement method for the DS-CDMA radio navigation system is proposed, which does not require full synchronization of reference stations carrier frequencies. The article presents basics of FDOA (frequency difference of arrival) velocity measurements together with application of this method to an experimental radio navigation system called AEGIR and with some suggestions about the possibility to implement such FDOA measurements in other kinds of asynchronous DS-CDMA radio networks. The main part of this paper present results of performance evaluation of the proposed method, based on laboratory measurements

Centralized Passive MIMO Radar Detection Without Direct-Path Reference Signals

This work addresses the problem of target detection in passive multiple-input multiple-output (MIMO) radar networks without utilization of direct-path reference signals. A generalized likelihood ratio test for this problem is derived, and the distribution of the test statistic is identified under both hypotheses. Equivalence is established between passive MIMO radar networks without references and passive source localization networks. Numerical examples demonstrate important characteristics of the detector, namely, the asymmetric contributions to detection performance from transmitters and receivers, and non-coherent integration gain as a function of signal length. The ambiguity properties of this detector are also investigated, and it is shown that the salient ambiguities can be explained in terms of the time-difference of arrival, frequency-difference of arrival, and angle-of-arrival of the target signals.

Novel method for radial velocity difference estimation of moving targets with wideband signals

For the frequency difference of arrival (FDOA) estimation in passive location, this paper transforms the frequency difference estimation into the radial velocity difference estimation, which is difficult to achieve a high accuracy due to the mismatch between the sampling period and the pulse repetition interval. The proposed algorithm firstly estimates the point-in-time that each pulse arrives at two receivers accurately. Secondly two time of arrival (TOA) sequences are subtracted. And finally the radial velocity difference of a target relative to two stations with the least square method is estimated. This algorithm only needs accurate estimation of the time delay between pulses and is not influenced by parameters such as frequency and modulation mode. It avoids transmitting a large amount of data between two stations in real time. Simulation results corroborate that the performance is better than the arithmetic average of the Cramer-Rao lower bound (CRLB) for monopulse under suitable conditions.

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 Cramer-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.

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.

Performance Analysis of TDOA and FDOA Location by Differential Calibration with Calibration Sources

This paper derives the performance equation of the differential calibration algorithm using the time differences of arrival (TDOA) and the frequency differences of arrival (FDOA) with calibration sources when the positions and velocities of the receivers have random errors. By comparing the performance with the Crame r-Rao lower bound (CRLB), it proves that the ability of the differential calibration algorithm to restrain these errors depends heavily on the parameters of the calibration sources. Then the influences of their amount, positions and measurement accuracy to the location accuracy are discussed. Simulations corroborate the theoretical results in this paper.

TDOA/FDOA 융합 기반 신호원의 위치추정 및 성능 분석

TDOA (time difference of arrival)와 FDOA (frequency difference of arrival) 정보를 동시에 이용하는 신호원 위치추정 기법은 단일 정보를 이용하는 경우에 비해 높은 정확도를 가지는 장점을 가지고 있다. 이러한 위치추정 기법의 추정성능은 수신단 쌍의 조합, 수신단의 기하학적 배치 특성 및 속도 등의 다양한 운용변수에 따라 크게 달라진다. 그러므로 전자전 시스템의 효율적인 운용을 위해서는 다양한 운용 조건에 따른 사전 성능 분석이 요구된다. 하지만 기존의 비 반복적인 위치추정 방법은 기준 수신단의 설정 및 수신단 배치 형태에 제약을 가진다. 따라서 본 논문에서는 임의의 다양한 수신단 조합과 배치 형태에서 적용이 가능한 Gauss-Newton 기법을 유도하고 이를 통해 위치추정을 수행한다. 또한 모의실험을 통해 TDOA/FDOA 융합 기반 위치추정 방법과 단일 TDOA 또는 FDOA를 독립적으로 사용했을 때의 성능을 비교 분석하고 CEP (circular error probability) 평면을 이용하여 융합 기반 위치추정 방법이 독립적 방법에 비해 상대적으로 높은 추정 성능을 가짐을 보인다. The emitter geolocation method using the time difference of arrival (TDOA) and the frequency difference of arrival (FDOA) has more accurate performance comparing to the single TDOA or FDOA based method. The estimation performance varies with the sensor paring strategies, the deployment and velocities of the sensors. Therefore, to establish effective strategy on the electronic warfare system, it is required to analyze the relation between the estimation accuracy and the operational condition of sensors. However, in the conventional non-iterative method, the restriction of the deployment of sensors and the reference sensor exists. Therefore, we derive the emitter geolocation method based on a Gauss-Newton method which is available to apply to any various sensor pairs and the deployment and velocities of the sensors. In addition, simulation results are included to compare the performance of geolocation method according to the used measurements: the combined TDOA/FDOA, TDOA, and FDOA. Also, we present that the combined TDOA/FDOA method outperforms over single TDOA or FDOA on the estimation accuracy with the CEP plane.

A Hybrid Distance Estimation for Wireless Body Sensor Networks

Wireless body area networks become a new research issue in recent years. In this paper, we propose hibernation and distance estimation schemes for wireless USB (WUSB) over wireless body area networks (WBAN) hierarchical protocol for body sensor networks (BSNs). The proposed middleware platform is composed of hibernation and optimal short distance estimation solution. Firstly, this paper provides WUSB private channel allocation scheme at the m-periodic allocation hibernation of a WBAN superframe. Secondly, three typical location estimation schemes of time difference of arrival (TDoA), frequency difference of arrival (FDoA), and angle of arrival (AoA) are analyzed through comparison of experiment results to propose optimal short distance estimation solution which is executed at each body sensor node on the basis of WUSB over WBAN protocol. And the WBAN host interprets status and motion of the body-sensor objects. The hybrid TDoA/FDoA/AoA algorithm based on UWB ranging shows best performances among the other hybrid schemes for wireless BSNs.

연속 측정된 TDOA와 FDOA를 이용한 Gauss-Newton 기법 기반의 신호원 위치추정 방법

순시(instantaneous) TDOA (time difference of arrival)와 FDOA (frequency difference of arrival)를 이용한 위치추정 방법은 추가적인 측정값 획득을 통해 정확도 향상을 도모할 수 있으며, 이를 위해서는 동시에 운용되는 수신단의 수를 증가하여야 한다. 하지만 전자전 환경에서 수신단 수의 증가는 아군의 피탐확률(probability of intercept) 상승으로 인한 전력 손실을 야기할 수 있고, 수신단 간의 데이터 링크 및 시각동기화와 같은 과정에 대한 추가적인 고려가 필요하다. 따라서 본 논문에서는 이격된 2개의 이동 수신단만을 운용하여 연속적으로 다수의 TDOA와 FDOA 정보를 측정하고, 이를 이용하여 고정 신호원의 위치를 추정하는 방법을 제안한다. 이 경우 매 측정 순간마다 독립된 수신단 쌍(pair)이 추가되므로 각 수신단 조합은 서로 다른 기준 수신단을 가지게 된다. 그러므로 모든 수신단 쌍이 동일한 기준 수신단을 공유해야하는 QCLS (quadratic correction least squares) 방법을 적용할 수 없다. 이러한 이유로 본 논문에서는 비선형 LS 최적해를 반복계산을 통해 얻어내는 Gauss-Newton 기법을 적용한다. 또한 모의실험을 통해 획득된 TDOA와 FDOA의 수가 증가함에 따른 위치추정 결과의 RMSE (root mean square error)값과 CRLB (Cramer-Rao lower bound)를 비교하고, CEP (circular error probable) 평면을 도시하여 2차원 공간상에서의 기대 추정 성능을 분석한다.

A Semidefinite Relaxation Method for Source Localization Using TDOA and FDOA Measurements

Localization by a sensor network has been extensively studied. In this paper, we address the source localization problem by using time-difference-of-arrival (TDOA) and frequency-difference-of-arrival (FDOA) measurements. Owing to the nonconvex nature of the maximum-likelihood (ML) estimation problem, it is difficult to obtain its globally optimal solution without a good initial estimate. Thus, we reformulate the localization problem as a weighted least squares (WLS) problem and perform semidefinite relaxation (SDR) to obtain a convex semidefinite programming (SDP) problem. Although SDP is a relaxation of the original WLS problem, it facilitates accurate estimate without postprocessing. Moreover, this method is extended to solve the localization problem when there are errors in sensor positions and velocities. Simulation results show that the proposed method achieves a significant performance improvement over existing methods.

A Robust Algorithm for Multiple Disjoint Moving Sources Localization with Erroneous Sensor Locations

This paper considers the problem of multiple disjoint sources localization using time difference of arrivals (TDOA) and frequency difference of arrival (FDOA) with sensor position and velocity errors. By exploiting the observation that the multiple disjoint sources exhibit the same sensor location errors, the influence of sensor location errors can be greatly alleviated. The CTLS technique, as a natural extension of LS when noise occurs in all coefficients and the noise components of the coefficients are algebraically related, is more appropriate for the above problem, and a localization algorithm based on constrained total least-squares (CTLS) for estimating the positions and velocities of multiple disjoint moving sources with sensor location errors is proposed. Simulation results show that the proposed estimator achieves remarkably better performance than the two-step weighted least squares (WLS) approach, which makes the Crame r-Rao lower bound (CRLB) at a sufficiently high noise level before the threshold effect occurs.  Index Terms—first term, second term, third term, fourth term, fifth term, sixth term

A Linear-correction Least-squares Approach for Geolocation Using FDOA Measurements Only

A linear-correction least-squares(LCLS) estimation procedure is proposed for geolocation using frequency difference of arrival (FDOA) measurements only. We first analyze the measurements of FDOA, and further derive the Cramér-Rao lower bound (CRLB) of geolocation using FDOA measurements. For the localization model is a nonlinear least squares(LS) estimator with a nonlinear constrained, a linearizing method is used to convert the model to a linear least squares estimator with a nonlinear constrained. The Gauss-Newton iteration method is developed to conquer the source localization problem. From the analysis of solving Lagrange multiplier, the algorithm is a generalization of linear-correction least squares estimation procedure under the condition of geolocation using FDOA measurements only. The algorithm is compared with common least squares estimation. Comparisons of their estimation accuracy and the CRLB are made, and the proposed method attains the CRLB. Simulation results are included to corroborate the theoretical development.

Approximate Maximum Likelihood Algorithm for Moving Source Localization Using TDOA and FDOA Measurements

A closed-form approximate maximum likelihood (AML) algorithm for estimating the position and velocity of a moving source is proposed by utilizing the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements of a signal received at a number of receivers. The maximum likelihood (ML) technique is a powerful tool to solve this problem. But a direct approach that uses the ML estimator to solve the localization problem is exhaustive search in the solution space, and it is very computationally expensive, and prohibits real-time processing. On the basis of ML function, a closed-form approximate solution to the ML equations can be obtained, which can allow real-time implementation as well as global convergence. Simulation results show that the proposed estimator achieves better performance than the two-step weighted least squares (WLS) approach, which makes it possible to attain the Cramér-Rao lower bound (CRLB) at a sufficiently high noise level before the threshold effect occurs.

Practical constrained least-square algorithm for moving source location using TDOA and FDOA measurements

By utilizing the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements of signals received at a number of receivers, a constrained least-square (CLS) algorithm for estimating the position and velocity of a moving source is proposed. By utilizing the Lagrange multipliers technique, the known relation between the intermediate variables and the source location coordinates could be exploited to constrain the solution. And without requiring apriori knowledge of TDOA and FDOA measurement noises, the proposed algorithm can satisfy the demand of practical applications. Additionally, on basis of convolute and polynomial rooting operations, the Lagrange multipliers can be obtained efficiently and robustly allowing real-time implementation and global convergence. Simulation results show that the proposed estimator achieves remarkably better performance than the two-step weighted least square (WLS) approach especially for higher measurement noise level.

Moving-Target Tracking Based on Particle Filter with TDOA/FDOA Measurements

In this letter, we propose a moving-target tracking algorithm based on a particle filter that uses the time difference of arrival (TDOA)/frequency difference of arrival (FDOA) measurements acquired by distributed sensors. It is shown that the performance of the proposed algorithm, based on the particle filter, outperforms the one based on the extended Kalman filter. The use of both the TDOA and FDOA measurements is shown to be effective in the moving-target tracking. It is proven that the particle filter deals with the nonlinear nature of the moving-target tracking problem successfully.

Moving-Target Tracking Based on Particle Filter with TDOA/FDOA Measurements

In this letter, we propose a moving-target tracking algorithm based on a particle filter that uses the time difference of arrival (TDOA)/frequency difference of arrival (FDOA) measurements acquired by distributed sensors. It is shown that the performance of the proposed algorithm, based on the particle filter, outperforms the one based on the extended Kalman filter. The use of both the TDOA and FDOA measurements is shown to be effective in the moving-target tracking. It is proven that the particle filter deals with the nonlinear nature of the movingtarget tracking problem successfully.

Location Estimation of Beacon in MEOSAR System

This paper describes the satellite aided search and rescue system that provides services to save the lives at the distress or emergency regions. COSPAS - SARSAT is a satellite-based system designed to provide distress alert and location data to facilitate SAR operations. The ground receiver named as Local User Terminals (LUTs) is in charge of processing the incoming signal and determining the beacon position via Frequency Difference of Arrival (FDOA) and Time Difference of Arrival (TDOA) technique. A common method of calculating TDOA and FDOA is the Cross Ambiguity Function (CAF). This paper proposes the implementation of CAF map method, which is a simple method that reduces the processing complexity over CAF method and also as the ability to locate several beacons that eliminates the false location of beacons.

An Efficient Constrained Weighted Least Squares Algorithm for Moving Source Location Using TDOA and FDOA Measurements

In this paper, by utilizing the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements of a signal received at a number of receivers, an efficient constrained weighted least-squares (CWLS) algorithm for estimating the position and velocity of a moving source is proposed, which exploits the known relation between the intermediate variable and the source location coordinates explicitly. On basis of Newton's method, a numerical iterative solution can be obtained allowing real-time implementation and ensuring global convergence. Simulation results show that the proposed estimator achieves remarkably better performance than the two-step weighted least squares (WLS) approach, which makes the Cramr-Rao lower bound (CRLB) at a sufficiently high noise level before the threshold effect occurs.