TOA Measurements Research Articles

LITM: Localization With Insufficient TOA Measurements for Unsynchronized Mobile Nodes in Underwater Acoustic Networks

LITM: Localization With Insufficient TOA Measurements for Unsynchronized Mobile Nodes in Underwater Acoustic Networks

Genetic Algorithm With Opposition-Based Learning and Redirection for Secure Localization Using ToA Measurements in Wireless Networks

Genetic Algorithm With Opposition-Based Learning and Redirection for Secure Localization Using ToA Measurements in Wireless Networks

A Semidefinite Relaxation Approach for Mobile Target Localization Based on TOA and Doppler Frequency Shift Measurements

In this paper, we discuss mobile source localization using both time of arrival and Doppler frequency shift (TOA-DFS) measurements, where the source moves at a nonuniform velocity. To obtain the position of a mobile source, we first formulate the weighted least squares (WLS) problem by ignoring the second-order noise terms. Due to the non-convexity, we apply the convex relaxation technique to transform the problem into a semi-definite programming problem. However, ignoring the second-order noise terms is only reasonable in the case of small noise levels. In view of this, we then directly establish the maximum likelihood (ML) estimator based on the measurements model without ignoring the second-order noise terms. Since the ML estimator is a non-convex problem, we also propose implementable semidefinite relaxation (SDR) technique to tackle it. Finally, the Cramér-Rao lower bound (CRLB) analysis and results verify that the proposed methods based on the TOA-DFS measurements can significantly enhance localization accuracy.

An Analytical Method for 3-D Target Localization Based on a Four-Element Ultrasonic Sensor Array With TOA Measurement

A new analytical method for 3D target localization based on a four-element ultrasonic sensor array is proposed. In the sensor array, with the consideration of good real-time performance, one ultrasonic sensor (the reference ultrasonic sensor) works both as a transmitter and as a receiver, while the other three sensors work as receivers. A basic target localization model is developed. The necessary and sufficient condition of the proposed method to obtain the unique and analytical solution is analyzed. It is proved that if and only if the four ultrasonic sensors are not in the same plane, the four-element ultrasonic sensor array can obtain a unique and analytical solution. In addition, with the consideration of the stability and the complexity of the analytical solution, a practical four-element ultrasonic sensor array configuration is proposed, which is characterized in that the reference ultrasonic sensor is at the origin, the other three ultrasonic sensors are on the three coordinate axes respectively and the distances from the three ultrasonic sensors to the reference ultrasonic sensor are equal. 3D target localization experiments are carried out. The experimental results verify the effectiveness of the proposed method and the localization performance is satisfactory. The proposed sensor array can realize the 3D localization with the advantages of simple construction and less computation.

Moving Target at Constant Velocity Localization Using TOA Measurements from Single Moving Receiver with Unknown Signal Period

Moving Target at Constant Velocity Localization Using TOA Measurements from Single Moving Receiver with Unknown Signal Period

Performance Analysis and Sensor-Target Geometry Optimization for TOA and TDOA-Based Hybrid Source Localization Method

Currently, the performance analysis of positioning algorithms and optimization of ground station deployment schemes are predominantly based on pure TOA or TDOA measurement information, and the relevant theoretical analysis is primarily the geometric analysis of optimal station deployment for fixed point targets, with few placement ranges and amount of station constraints. In practice, however, there are typically several measurements from TOA and TDOA stations, with a focus on positioning precision within a certain region or line trajectory, as well as the necessity for constraints on the ground station placement range. This paper proposes an efficient method for hybrid source localization using TOA and TDOA measurement information, establishes a mathematical model for hybrid source localization based on TOA and TDOA measurement information, derives and simulates the Gauss–Newton iterative localization algorithm with the least squares criterion, and performs a theoretical analysis of the least squares error and CRLB boundary to improve the accuracy of target localization in the aforementioned scenarios. Taking the average CRLB value of target line trajectory positioning error as the objective function, the ground station placement scheme of TOA- and TDOA-receiving sensors is optimized by utilizing a Genetic Algorithm with strong global optimization capability under the constraints of station placement range and station quantities, and a station placement geometry with better performance than typical station placement is obtained. Meanwhile, we summarize the general placement principles for TOA and TDOA hybrid source localization of target line trajectories.

Closed-Form Two-Way TOA Localization and Synchronization for User Devices With Motion and Clock Drift

A two-way time-of-arrival (TOA system is composed of anchor nodes (ANs and user devices (UDs . Two-way TOA measurements between AN-UD pairs are obtained via round-trip communications to achieve localization and synchronization (LAS for a UD. Existing LAS method for a moving UD with clock drift adopts an iterative algorithm, which requires accurate initialization and has high computational complexity. In this paper, we propose a new closed-form two-way TOA LAS approach, namely CFTWLAS, which does not require initialization, has low complexity and empirically achieves optimal LAS accuracy. We first linearize the LAS problem by squaring and differencing the two-way TOA equations. We employ two auxiliary variables to simplify the problem to finding the analytical solution of quadratic equations. Due to the measurement noise, we can only obtain a raw LAS estimation from the solution of the auxiliary variables. Then, a weighted least squares step is applied to further refine the raw estimation. We analyze the theoretical error of the new CFTWLAS and show that it empirically reaches the Cramer-Rao lower bound (CRLB with sufficient ANs under the condition with proper geometry and small noise. Numerical results in a 3D scenario verify the theoretical analysis that the estimation accuracy of the new CFTWLAS method reaches CRLB in the presented experiments when the number of the ANs is large, the geometry is appropriate, and the noise is small. Unlike the iterative method whose complexity increases with the iteration count, the new CFTWLAS has constant low complexity.

Weighing the spacetime along the line of sight using times of arrival of electromagnetic signals

We present a new method of measuring the mass density along the line of sight, based on precise measurements of the variations of the times of arrival (TOA's) of electromagnetic signals propagating between two distant regions of spacetime. The TOA variations are measured between a number of slightly displaced pairs of points from the two regions. These variations are due to the nonrelativistic geometric effects (Roemer delays and finite distance effects) as well as the gravitational effects in the light propagation (gravitational ray bending and Shapiro delays). We show that from a sufficiently broad sample of TOA measurements we can determine two scalars quantifying the impact of the spacetime curvature on the light propagation, directly related to the first two moments of the mass density distribution along the line of sight. The values of the scalars are independent of the angular positions or the states of motion of the two clock ensembles we use for the measurement and free from any influence of masses off the line of sight. These properties can make the mass density measurements very robust. The downside of the method is the need for extremely precise signal timing.

TOA and TDTOA-based augmented state pulsar integrated navigation error suppression method

Pulsar navigation is a promising deep space autonomous navigation technology, which usually uses the time of arrival (time of arrival, TOA) as the measurement information. However, system errors such as pulsar ephemeris errors and space-borne atomic clock errors have a significant impact on navigation performance. To solve the above problems, an error suppression method for augmented state pulsar integrated navigation based on TOA and time difference TOA (TDTOA) is proposed. By adding the ephemeris error and clock error of each pulsar to the state vector, the TOA and TDTOA measurements are used to estimate and correct them. Simulation results show that this method improves the observability of the pulsar ephemeris and clock errors, eliminates the effect of these systematic errors, and improves navigation accuracy by 29% compared to traditional pulsar navigation.

Moving source localization using TOA and FOA measurements with imperfect synchronization

The clock bias and drift caused by imperfect time synchronization is a practical issue in localization problems. In this paper, we address the moving source localization problem using time-of-arrival and frequency-of-arrival measurements, where imperfect time synchronization is present. We transform the measurement models and formulate a nonlinear and non-convex weighted least squares (WLS) problem to jointly estimate the unknown source position, velocity, clock bias and drift. We then apply semidefinite relaxation (SDR) to the non-convex WLS problem to obtain a convex semidefinite program, which can be solved efficiently. We show through theoretical mean square error analysis that the WLS solution is able to attain the Cramer–Rao lower bound (CRLB) under small Gaussian noise condition. Simulation results show that the proposed SDR method has comparable performance with the maximum likelihood estimation method, and thus achieves the CRLB accuracy, when the noise is not too large.

Performance Analysis of Wireless Location and Velocity Tracking of Digital Broadcast Signals Based on Extended Kalman Filter Algorithm

In order to improve the accuracy and reliability of wireless location in NLOS environment, a wireless location algorithm based on artificial neural network (ANN) is proposed for NLOS positioning error caused by non-line-of-sight (NLOS) propagation, such as occlusion and signal reflection. The mapping relationship between TOA and TDOA measurement data and coordinates is established. The connection weights of neural network are estimated as the state variables of nonlinear dynamic system. The multilayer perceptron network is trained by the real-time neural network training algorithm based on extended Kalman (EKF). Combined with the statistical characteristics of NLOS error, the state component NLOS bias estimation is modified to realize TDOA data reconstruction. Simulation and experimental data analysis show that the algorithm can effectively weaken the influence of NLOS error. The localization method does not depend on the specific NLOS error distribution, nor does it need LOS and NLOS recognition. It can significantly improve the mobile positioning accuracy.

Multi-Slots Joint MLE Relative Navigation Algorithm Based on INS/JTIDS/BA for Datalink Network

High accuracy relative navigation (RELNAV) information is crucial for datalink network members in the situation of joint operations, especially the situations that some datalink network members may not be able to obtain their location with absolute navigation. In this paper, relative navigation algorithm based on JTIDS/INS/BA is proposed, in this system datalink joint units(JUs) are positioned in two-dimensional plane with multi-slots joint maximum likelihood estimation (MLE), and altitude is located by a height filter independently, which overcome the problem of poor positioning geometry of altitude. Multi-slots joint MLE convert TOA measurements in different slots to one moment with short-time inertial navigation system(INS) information, which lead to a higher localization accuracy in two-dimensional plane. We simulate a joint tactical information distribution system (JTIDS) network with multiple members, to verify the performance and analyze the influence factors of the proposed algorithm. The simulation results show that compared to EKF that process TOA measurements sequentially in each navigation slot and MLE without multi-slots joint processing, the multi-slots joint MLE relative navigation algorithm based on INS/JTIDS/BA performs better in two-dimensional plane location, and the height filter based on barometric altimeter (BA) improves the relative height positioning accuracy greatly.

Cramér-Rao Lower Bound of Target Localization Method Based on TOA Measurements

The Cramér-Rao bound of target localization method based on time-of-arrival measurements is analyzed. For the localization error analysis, the CRLB is derived under the assumptions that the measurement errors are independent and characterized by zero-mean Gaussian distributed process with identical variance, which is not satisfied in the situation of localizing noncooperative targets. Cramér-Rao bound is deduced by using the fact that the variances of TOA measurements of different sensors are affected by the signal-to-noise ratio of the echo signal and are different from each other. Simulations of Monte Carlo experiments are carried out so as to verify the analytical results.

Cooperative Localization Based on Efficient Covariance Intersection

This work proposes a geometric covariance intersection (CI)-based algorithm for efficiently solving the decentralized cooperative localization (CL) problem with multiple TOA measurements. Unlike existing algorithms that only process one measurement at a time, our proposed algorithm processes multiple measurements in a batch style, which improves the precision performance by considering the correlation among these measurements. An efficient way to get the optimal solution is given in our algorithm, which reduces the computational complexity to $\mathcal {O}(N \log N)$ . Furthermore, the sparsity of the optimal solution is proved, which enables a heuristic state buffering approach to reduce the usage of ranging link resources and improve measurement efficiency. The simulation results show that our algorithm outperforms the conventional methods.

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.

RETRIEVAL OF AEROSOL MICROPHYSICAL PROPERTIES BASED ON THE OPTIMAL ESTIMATION METHOD: INFORMATION CONTENT ANALYSIS FOR SATELLITE POLARIMETRIC REMOTE SENSING MEASUREMENTS

Abstract. This paper evaluates the information content for the retrieval of key aerosol microphysical and surface properties for multispectral single-viewing satellite polarimetric measurements cantered at 410, 443, 555, 670, 865, 1610 and 2250 nm over bright land. To conduct the information content analysis, the synthetic data are simulated by the Unified Linearized Vector Radiative Transfer Model (UNLVTM) with the intensity and polarization together over bare soil surface for various scenarios. Following the optimal estimation theory, a principal component analysis method is employed to reconstruct the multispectral surface reflectance from 410 nm to 2250 nm, and then integrated with a linear one-parametric BPDF model to represent the contribution of polarized surface reflectance, thus further to decouple the surface-atmosphere contribution from the TOA measurements. Focusing on two different aerosol models with the aerosol optical depth equal to 0.8 at 550 nm, the total DFS and DFS component of each retrieval aerosol and surface parameter are analysed. The DFS results show that the key aerosol microphysical properties, such as the fine- and coarse-mode columnar volume concentration, the effective radius and the real part of complex refractive index at 550 nm, could be well retrieved with the surface parameters simultaneously over bare soil surface type. The findings of this study can provide the guidance to the inversion algorithm development over bright surface land by taking full use of the single-viewing satellite polarimetric measurements.

반복적 연산을 이용하는 Distributed MIMO 레이다 시스템의 위치 추정 기법

This paper presents a target localization scheme for distributed Multi-input Multi-output(MIMO) radar system using ToA measurements obtained from multiple transmitter and receiver pairs. The proposed method can locate the target from an arbitrary initial point by iteratively finding the Taylor linear approximation equation. The simulation results show that proposed method achieves the better mean square error(MSE) performance than the existing target localization methods, and furthermore, attains Cramer-Rao Lower Bound(CRLB).

Passive source localization using importance sampling based on TOA and FOA measurements

Passive source localization via a maximum likelihood (ML) estimator can achieve a high accuracy but involves high calculation burdens, especially when based on time-of-arrival and frequency-of-arrival measurements for its internal nonlinearity and nonconvex nature. In this paper, we use the Pincus theorem and Monte Carlo importance sampling (MCIS) to achieve an approximate global solution to the ML problem in a computationally efficient manner. The main contribution is that we construct a probability density function (PDF) of Gaussian distribution, which is called an important function for efficient sampling, to approximate the ML estimation related to complicated distributions. The improved performance of the proposed method is attributed to the optimal selection of the important function and also the guaranteed convergence to a global maximum. This process greatly reduces the amount of calculation, but an initial solution estimation is required resulting from Taylor series expansion. However, the MCIS method is robust to this prior knowledge for point sampling and correction of importance weights. Simulation results show that the proposed method can achieve the Cramer-Rao lower bound at a moderate Gaussian noise level and outperforms the existing methods.

Tunnel personnel positioning method based on TOA and modified location-fingerprint positioning

To position personnel in mines, the study discussed in this paper built on the tunnel personnel positioning method on the basis of both TOA and location-finger print (LFP) positioning. Given non-line of sight (NLOS) time delay in signal transmission caused by facilities and equipment shielding in tunnels and TOA measurement errors in both LFP database data and real-time data, this paper puts forth a database data de-noising algorithm based on distance threshold limitation and modified mean filtering (MMF), as well as a real-time data suppression algorithm based on speed threshold limitation and MMF. On this basis, a nearest neighboring data matching algorithm based on historical location and the speed threshold limitation is used to estimate personnel location and realize accurate personnel positioning. The results from both simulation and the experiment suggest that: compared with the basic LFP positioning method and the method that only suppresses real-time data error, the tunnel personnel positioning methods based on TOA and modified LFP positioning permits effectively eliminating error in TOA measurement, making the measured data close to the true positional data, and dropping the positioning error: the maximal positioning error in measurements from experiment drops by 9 and 3m, respectively, and the positioning accuracy of 3m is achievable in the condition used in the experiment.

Localization scheme based on multistatic radar systems

A weighted least square (WLS) scheme to estimate the target location in the TRM multistatic radar system based on the modified TOA measurements is proposed. The performance of the location estimation scheme is evaluated according to the basis of the root mean square error (RMSE). In the proposed scheme, all the measured errors including the measured azimuth angle, the measured elevation angle, and the measured range from the sum of the distance for transmitter-to-target and the distance for target-to-receiver are considered. The performance of the proposed scheme is given under the cases of the bistatic radar system and the TR4 multistatic radar system, respectively. According to the simulation results, the performance could be improved with the increasing of the number of receivers in the system.