Time Of Arrival Measurements Research Articles

A Robust NLOS Bias Mitigation Technique for RSS-TOA-Based Target Localization

This letter proposes a novel robust mitigation technique to address the problem of target localization in adverse non-line-of-sight (NLOS) environments. The proposed scheme is based on combined received signal strength and time of arrival measurements. Influence of NLOS biases is mitigated by treating them as nuisance parameters through a robust approach. Due to a high degree of difficulty of the considered problem, it is converted into a generalized trust region sub-problem by applying certain approximations, and solved efficiently by merely a bisection procedure. Numerical results corroborate the effectiveness of the proposed approach, rendering it the most accurate one in all considered scenarios.

Neural Network Localization With TOA Measurements Based on Error Learning and Matching

Due to the widespread application of location information, the neural network localization method with the advantage of high localization accuracy has received significant interests in recent years. In this paper, we present two new neural network localization methods with time-of-arrival (TOA) measurements. In order to deal with three types of error about TOA measurements such as measurement error, non-line of sight (NLOS) error, and synchronization error, the proposed methods contain an offline training stage and an online localization stage. In the offline stage, the artificial neural network (ANN) or radial basis function (RBF) neural network is utilized to train the range measurements with the output of range errors rather than the position of the mobile terminal (MT). Moreover, due to the unknown signal propagation condition whether it is the line of sight or NLOS propagation, the $k$ -mean clustering algorithm is used to classifying the range errors into different clusters. In the online stage, the range errors are predicted and updated, and then, the linear least square algorithm with the adjusted range measurements is applied for the position estimate of MT. Comparing with the ANN or RBF neural network localization methods, the simulation results show that the proposed methods can effectively reduce the localization error, especially when the training sample is not adequate. In addition, they are insensitive to measurement error, synchronization error, and the distribution of NLOS error. Finally, the memory requirement and computational complexity about different algorithms are analyzed and compared.

Joint Multiple Sources Localization Using TOA Measurements Based on Lagrange Programming Neural Network

Multiple sources’ localization using the time-of-arrival (TOA) measurements in the presence of sensor position uncertainty is studied in this paper. The non-cooperative scenario where the clock between the source and sensors is not synchronized is also considered. First, we theoretically prove that the Cramer–Rao lower bound of multi-source joint localization is lower than that of the single source case when the TOA measurements from different sources possess the same sensor position errors. Moreover, different from the conventional numerical algorithms, we propose to employ a neural circuit named Lagrange programming neural network (LPNN) to fulfill this non-trivial task of jointly locating multiple sources. The maximum likelihood problem of multi-source localization is reformulated by utilizing the LPNN framework, and then we build up a neural model, which is proved to be asymptotically stable through both mathematical analysis and numerical experiments. The simulation results show that the proposed method is superior to other positioning algorithms, and it has excellent localization performance and robustness even in the case of large measurement noise, synchronization error, and sensor position displacements.

Target Localization in NLOS Environments Using RSS and TOA Measurements

This letter addresses the problem of target localization in adverse non-line-of-sight environments. By utilizing integrated received signal strength and time of arrival measurements, a novel alternating algorithm is proposed. The new algorithm is derived by converting the original nonconvex problem into a generalized trust region sub-problem framework, which can be solved exactly by just a bisection procedure. Therefore, the proposed algorithm is very light in terms of computational cost, and its excellent estimation accuracy is validated through computer simulations.

A Novel Hybrid RSS and TOA Positioning Algorithm for Multi-Objective Cooperative Wireless Sensor Networks

Due to the significance of positioning in complicated electromagnetic environment of its variety of applications, wireless localization techniques have attracted significant research interests with the trends moving toward boosting the capabilities of multi-objective cooperative networks. This paper addresses the problem of locating multiple targets in 3-D cooperative wireless sensor network. A novel hybrid received signal strength (RSS) and time-of-arrival (TOA) positioning scheme is proposed. Employing RSS and TOA measurements, four valuable expressions are drawn. The TOA and RSS technologies are combined with path loss difference variable being introduced. Based on the weighted least squares criterion, the rough solutions of multiple targets positions are derived. Finally, the locations of obtained targets are optimized by cooperative wireless communication between the target and another target. The location accuracy of the proposed estimation algorithm is analyzed and compared with the conventional RSS and TOA estimation algorithms through simulation experiments. The simulation result demonstrates that the proposed hybrid RSS and TOA localization algorithm for multi-objective cooperative wireless networks outperforms traditional approaches.

Location estimation and detection in wireless sensor networks in the presence of fading

In this paper, localization using narrowband communication signals are considered in the presence of fading channels with time of arrival measurements. When narrowband signals are used for localization, due to existing hardware constraints, fading channels play a crucial role in localization accuracy. In a location estimation formulation, the Cramer–Rao lower bound for localization error is derived under different assumptions on fading coefficients. For the same level of localization accuracy, the loss in performance due to Rayleigh fading with known phase is shown to be about 5dB compared to the case with no fading. Unknown phase causes an additional 1dB loss. The maximum likelihood estimators are also derived.In an alternative distributed detection formulation, each anchor receives a noisy signal from a node with known location if the node is active. Each anchor makes a decision as to whether the node is active or not and transmits a bit to a fusion center once a decision is made. The fusion center combines all the decisions and uses a design parameter to make the final decision. We derive optimal thresholds and calculate the probabilities of false alarm and detection under different assumptions on the knowledge of channel information. Simulations corroborate our analytical results.

Position and Velocity Estimation of a Non-Cooperative Source From Asynchronous Packet Arrival Time Measurements

We tackle the problem of identifying the trajectory of a moving radio source from Time of Arrival (TOA) measurements collected by a set of cooperating receivers. The considered system is completely asynchronous: nodes clocks are affected by unknown time and frequency offsets, and no control is exerted over packet transmission times. In the proposed solution, the receiver clock offset terms are estimated from TOA measurements on packets originated by non-cooperative reference transmitters, possibly but not necessarily coincidental with reference receivers. Transmission time ambiguity is resolved by exploiting the redundancy associated to the reception of the same packet at multiple receivers. A distinguishing feature of the proposed solution is that it seeks to identify the parameters of the trajectory as a whole, rather than the individual points of transmission as done in traditional point-based approaches. This allows the effective exploitation of TOA measurements collected in lossy scenarios, where the generic packet is received by a smaller subset of the available receivers (at least two). For the problem at hand, we provide distinct estimators based on TOA and Time-Difference of Arrival (TDOA) and prove their equivalence. Numerical results from simulations and from a real WiFi testbed are provided to validate the effectiveness of the proposed method.

Mitigating VHF Lightning Source Retrieval Errors

AbstractThe problem of inferring the location and time of occurrence of a very high frequency (VHF) lightning source emission from Lightning Mapping Array (LMA) network time-of-arrival (TOA) measurements is closely examined in order to clarify the cause of retrieval errors and to determine how best to mitigate these errors. With regard to this inverse problem, the previous literature lacks a comprehensive discussion of the associated forward problem. Hence, the forward problem is analyzed in this study to better clarify why retrieval errors increase with increasing source horizontal range and/or decreasing source altitude. Further insight is obtained by performing carefully designed Monte Carlo inversion simulations that provide specific retrieval error plots, which in turn lead to clear recommendations for mitigating retrieval errors. Based on all of the numerical results, the following strategies are recommended for mitigating retrieval errors (when possible, and without obstructing the line of sight): expand the horizontal extent of the LMA network, maximize the vertical sensor baseline by using mountainous terrain if available, and improve TOA measurement timing accuracy. Adding sensors to the network is relatively ineffective, unless of course the addition of sensors expands the horizontal extent and/or vertical baseline of the network. It is also shown how the standard retrieval method can be generalized by considering, in addition to the regular (unpolarized) point VHF source, the polarized transient very low frequency/low frequency (VLF/LF) electric point dipole source. Multiple observations (i.e., VHF arrival time and power, and VLF/LF arrival time and electric field amplitude) are simultaneously implemented into the new generalized mathematical framework, and the potential benefits are indicated.

Autonomous orbit determination for formations of Cubesats beyond LEO

This paper investigates the use of the Time Of Arrival (TOA) and Doppler shift to allow a small formation of CubeSats to navigate beyond low Earth orbit (LEO). The idea is to use a one way communication, from one or more ground stations to two or more CubeSats, to reconstruct an estimation of the position and velocity of the formation with respect to Earth. The paper considers the use of the difference in TOA and Doppler measurements to mitigate the error introduced by the onboard clock. These measurements are combined with inter-satellite distance and velocity measurements based on a two-way communication between pairs of spacecraft. The paper will provide an estimation of the error in position and velocity that can be obtained by a combination of these measurements. The reference case for these analyses will be a transfer trajectory to the Moon.

Experimental validation of attitude and rate-sensor bias filter using range-difference measurements

This paper considers the problem of constructing a filter for estimating attitude and rate-sensor bias, that has both proven stability and close-to-optimal performance with respect to noise. The filter is based on measuring the difference in time of arrival for signals sent from three or more known, fixed positions to two or more receivers on the vehicle. An inertial measurement unit is also used, both rate-sensor and accelerometer measurements, and a position estimate is needed, generated from depth and time of arrival measurements. The vectors between receivers on the vehicle are assumed to be known in the body frame, and are calculated in the inertial frame through an algebraic transformation. These vectors are used as input for a non-linear observer along with rate-sensor and accelerometer data, estimating Euler angles and rate-sensor bias. These estimates are used as a linearization point for a Linearized Kalman Filter, taking the full non-linear system into account. Two experiments are run, and the filter is compared to an Extended Kalman Filter, and a non-implementable Linearized Kalman Filter using the true state as linearization point.

Time of arrival 3-D position estimation using minimum ADS-B receiver configuration

The location from which a signal is transmitted can be estimated using the time it takes to be detected at a receiver. The difference between transmission time and the detection time is known as time of arrival (TOA). In this work, an algorithm for 3-dimensional (3-D) position estimation (PE) of an emitter using the minimum receiving stations configuration was developed. The TOA measurements estimated from three automatic surveillance dependent broadcast (ADS-B) receivers are used to evaluate the performance of the PE algorithm. The result shows that the triangular ADS-B receiver configuration is capable of 3-D PE for emitter locations within 190 km coverage radius and that the altitude estimation error is 2 km higher than the horizontal coordinate estimation error. Within the 3-D PE coverage of the ADS-B receiver, the maximum horizontal and altitude error expected are 0.12 km and 2.2 km respectively. Keywords: TOA, ADS-B, position estimation, minimum configuration, surveillance

Motion Parameter Capturing of Multiple Mobile Targets in Robotic Sensor Networks

A motion parameter capturing method is proposed to jointly estimate the initial positions and velocities of multiple mobile targets in robotic sensor networks. By using the time of arrival (TOA) measurements between the sensor nodes, the proposed method does not require any motion sensors. Noncooperative unconstrained linear least square (ULLS), constrained linear least square (CLLS), semidefinite programming (SDP), and mixed second-order cone semidefinite programming (SOCSDP) algorithms are designed by only exploiting the TOA measurements between anchor nodes and mobile targets. Then, the SDP and SOCSDP algorithms are extended to the cooperative approach in which the measurements between the mobile targets are also employed into the optimization model, as well as the measurements in the noncooperative approach. The simulations and real experiments show that the cooperative SDP and SOCSDP algorithms provide better performance than the noncooperative ULLS, CLLS, SDP, and SOCSDP. Compared with the linear ULLS and CLLS, the computation complexity of the convex SDP and SOCSDP is higher for a large number of variables and equality constraints. The positioning error of the SOCSDP is approximately identical to the SDP, but the SOCSDP runs faster than the SDP.

UWB pulse detection and TOA estimation using GLRT

In this paper, a novel statistical approach is presented for time-of-arrival (TOA) estimation based on first path (FP) pulse detection using a sub-Nyquist sampling ultra-wide band (UWB) receiver. The TOA measurement accuracy, which cannot be improved by averaging of the received signal, can be enhanced by the statistical processing of a number of TOA measurements. The TOA statistics are modeled and analyzed for a UWB receiver using threshold crossing detection of a pulse signal with noise. The detection and estimation scheme based on the Generalized Likelihood Ratio Test (GLRT) detector, which captures the full statistical information of the measurement data, is shown to achieve accurate TOA estimation and allows for a trade-off between the threshold level, the noise level, the amplitude and the arrival time of the first path pulse, and the accuracy of the obtained final TOA.

Combination linear lines of position and neural network for mobile station location estimation

To enhance the effectiveness and accuracy of mobile station location estimation, author utilizes time of arrival measurements from three base stations and one angle of arrival information at the serving base station to locate mobile station in non-line-of-sight environments. This article makes use of linear lines of position, rather than circular lines of position, to give location estimation of the mobile station. It is much easier to solve two linear line equations rather than nonlinear circular ones. Artificial neural networks are widely used techniques in various areas due to overcoming the problem of exclusive and nonlinear relationships. The proposed algorithms employ the intersections of three linear lines of position and one angle of arrival line, based on Levenburg–Marquardt algorithm, to determine the mobile station location without requiring a priori information about the non-line-of-sight error. The simulation results show that the proposed algorithms can always provide much better location estimation than Taylor series algorithm, hybrid lines of position algorithm as well as the geometrical positioning methods for different levels of biased, unbiased, and distance-dependent non-line-of-sight errors.

Distributed Hybrid Particle/FIR Filtering for Mitigating NLOS Effects in TOA-Based Localization Using Wireless Sensor Networks

For indoor localization based on wireless sensor networks, the transmission of wireless signals can be disrupted by obstacles and walls. This situation, called non-line-of-sight (NLOS), degrades localization accuracy and may lead to localization failures. This paper proposes a new NLOS identification algorithm based on distributed filtering to mitigate NLOS effects, including localization failures. Rather than processing all measurements via a single filter, the proposed algorithm distributes the measurements among several local filters. Using distributed filtering and data association techniques, abnormal measurements due to NLOS are identified, and negative effects can be prevented. To address cases of localization failures due to NLOS, the hybrid particle finite impulse response filter (HPFF) was adopted. The resulting distributed HPFF can self-recover by detecting failures and resetting the algorithm. Extensive simulations of indoor localization using time of arrival measurements were performed for various NLOS situations to demonstrate the effectiveness of the proposed algorithm.

Loran phase code revisited for continuous wave interference cancellation

A new phase coding is proposed to eliminate the continuous wave interference (CWI) in Loran navigation systems. In fact, CWI is one of the most important noise sources that make errors in signal phase tracking. Consequently, undesirable errors are constructed in time of arrival (TOA) measurement and ultimately navigation precision is reduced dramatically. The performance of Loran navigation systems is improved by applying the proposed phase coding and also using the averaging and phase decoding method. Analyses results show that if the interference is synchronous, then the proposed phase coding, called as Bayat-Madani phase code interval, cancels interference effects on TOA measurement completely. This interference cancelation is independent from the received signal signal-to-interference ratio. For near-synchronous and asynchronous CWI, the TOA error originated from interference is improved considerably, in some frequencies about 100 times, compared to the standard Loran. Furthermore, almost all of the sky multi-hops are eliminated as well.

Fundamental Limits of TOA/DOA and Inertial Measurement Unit-Based Wireless Capsule Endoscopy Hybrid Localization

In this paper, performance analysis of hybrid localization based on radio-frequency (RF) and inertial measurement unit (IMU) measurements for a single wireless capsule endoscopy (WCE) traveling the gastrointestinal tract is studied. Specifically, the multiple body-mounted sensors are considered which are located on the front and back of a patient’s medical jacket and form the uniform rectangular arrays (URAs). With the aim of locating the WCE, two types of RF measurements, namely time-of-arrival (TOA) and direction-of-arrival (DOA), are estimated from the received signals at the URAs transmitted by the WCE, which are integrated with the IMU acceleration measurements via the standard extended Kalman filter. Here, a posterior Cramer–Rao Bound (PCRB) of the proposed TOA/DOA and IMU-based hybrid localization is derived as fundamental limits on squared position error, where the accuracies of TOA and DOA measurements are entailed by means of CRB to account for their dependency on the environmental parameters, while the accuracies of the IMU measurements are addressed with the acceleration measurement error standard deviation. Numerical results are provided, sustained by simulations which verify the millimeter accuracy of the TOA/DOA and IMU-based hybrid localization within the regulation of medical implant communication services and the exactness of the PCRB.

ToA Ranging and Layer Thickness Computation in Nonhomogeneous Media

This paper introduces a novel and effective ranging approach in nonhomogeneous (NH) media consisting of frequency dispersive submedia via time-of-arrival (ToA). Here, the NH environment consists of sublayers with a specific thickness that is estimated throughout the ranging process. First, a novel technique for ToA estimation in the presence of frequency dispersive submedia via orthogonal frequency division multiple access subcarriers is proposed. In the proposed technique, preallocated orthogonal subcarriers are utilized to construct a ranging waveform that enables high-performance ToA estimation in dispersive NH media in the frequency domain. The proposed ToA technique is exploited for multiple ToA measurements at different carrier frequencies, which leads to a system of linear equations that can be solved to compute the thickness of the available submedia and calculate the range. Simulation results for underwater-airborne media and underground channel confirm that the proposed technique offers high-resolution ranging at different signal to noise ratio regimes in the NH media.

Optimal source localization problem based on TOA measurements

Determining an optimal emitting source location based on the time of arrival (TOA) measurements is one of the important problems in Wireless Sensor Networks (WSNs). The nonlinear least-squares (NLS) estimation technique is employed to obtain the location of an emitting source. This optimization problem has been formulated by the minimization of the sum of squared residuals between estimated and measured data as the objective function. This paper presents a hybridization of Genetic Algorithm (GA) for the determination of the global optimum solution with the local search Newton-Raphson (NR) method. The corresponding Cramer-Rao lower bound (CRLB) on the localization errors is derived, which gives a lower bound on the variance of any unbiased estimator. Simulation results under different signal-to-noise-ratio (SNR) conditions show that the proposed hybrid Genetic Algorithm-Newton-Raphson (GA-NR) improves the accuracy and efficiency of the optimal solution compared to the regular GA.

Cooperative Processing of Measurements in Pseudorange Radio-technical Finding System

Background/Objectives: The relevance of the current research is determined by the intensive development of multilateration systems which are widely used in time-positioning support systems. The authors propose to use the cooperative processing of coordinate information. Methods: In the present article a procedure of obtaining the ranging position lines with regard to each station is studied using a theory of redundant measurements which enables to implement cooperative processing. It is shown that using the least squares method, one can obtain the estimation of the required range-measurement parameters containing a minimum value of mean-square error. Findings: In our opinion, the new results of the study show that a multilateration system with one query station which forms a range line of position and with cooperative processing of Time Difference Of Arrival (TDOA) and Time Of Arrival (TOA), in some cases it is characterized by the improved accuracy compared to hyperbolic and elliptic systems. Measurement processing method studied in the present article enables to expand a system work area with respect to the accuracy for multilateration systems with short length base (distances between receiver stations). The offered procedures of radar data processing allow for a formation of range position lines that are indirectly obtained based on hyperbolic and elliptic lines of position. Cooperative processing of measurements in TOA and TDOA finding systems enables to improve the accuracy of the indirect range measurement. TDOA and TOA measurements do not improve the accuracy of the indirect range estimation with the offered method of measurement processing since the accuracy remains constant regardless of the number of stations. Application/ Improvements: The study results obtained could be used to upgrade the existing systems of aircraft position estimation and to make reasonable technical demands on the systems under development.