Hybrid TDOA/FDOA and track optimization of UAV swarm based on A-optimality

The source location based on the hybrid time difference of arrival(TDOA)/frequency difference of arrival(FDOA) is a basic problem in wireless sensor networks, and the layout of sensors in the hybrid TDOA/FDOA positioning will greatly affect the accuracy of positioning. Using unmanned aerial vehicle(UAV) as base stations, by optimizing the trajectory of the UAV swarm, an optimal positioning configuration is formed to improve the accuracy of the target position and velocity estimation. In this paper, a hybrid TDOA/FDOA positioning model is first established, and the positioning accuracy of the hybrid TDOA/FDOA under different positioning configurations and different measurement errors is simulated by the geometric dilution of precision(GDOP) factor. Second, the Cramer-Rao lower bound(CRLB) matrix of hybrid TDOA/FDOA location under different moving states of the target is derived theoretically, the objective function of the track optimization is obtained, and the track of the UAV swarm is optimized in real time. The simulation results show that the track optimization effectively improves the accuracy of the target position and velocity estimation.

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 con- volute and polynomial rooting operations, the Lagrange multipliers can be obtained efficiently and robustly allowing real-time imple- mentation 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.

Acoustic localization with multi-layer isogradient sound speed profile using TDOA and FDOA

In the underwater medium,the speed of sound varies with water depth,temperature,and salinity.The inhomogeneity of water leads to bending of sound rays,making the existing localization algorithms based on straightline propagation less precise.To realize high-precision node positioning in underwater acoustic sensor networks(UASNs),a multi-layer isogradient sound speed profile(SSP)model is developed using the linear segmentation approximation approach.Then,the sound ray tracking problem is converted into a polynomial root-searching problem.Based on the derived gradient of the signal’s Doppler shift at the sensor node,a novel underwater node localization algorithm is proposed using both the time difference of arrival(TDOA)and frequency difference of arrival(FDOA).Simulations are implemented to illustrate the effectiveness of the proposed algorithm.Compared with the traditional straight-line propagation method,the proposed algorithm can effectively handle the sound ray bending phenomenon.Estimation accuracy with different SSP modeling errors is also investigated.Overall,accurate and reliable node localization can be achieved.

Direct solution for fixed source location using well-posed TDOA and FDOA measurements

Based on the time differences of arrival(TDOA) and frequency differences of arrival(FDOA) measurements of the given planar stationary radiation source, the joint TDOA/FDOA location algorithm which solves the location of the target directly is proposed. Compared with weighted least squares(WLS) methods,the proposed algorithm is also suitable for well-posed conditions,and gets rid of the dependence on the constraints of Earth's surface. First of all, the solution formulas are expressed by the radial range. Then substitute it into the equation of the radial range to figure out the radial range between the target and the reference station. Finally use the solution expression of the target location to estimate the location of the target accurately. The proposed algorithm solves the problem that WLS methods have a large positioning error when the number of observation stations is not over-determined. Simulation results show the effectiveness of the proposed algorithm, including effectively increasing the positioning accuracy and reducing the number of observatories.

Joint TDOA, FDOA and differential Doppler rate estimation： Method and its performance analysis

Considering the estimation accuracy reduction of Frequency Difference of Arrival （FDOA） caused by relative Doppler companding, a joint Time Difference of Arrival （TDOA）, FDOA and differential Doppler rate estimation method is proposed and its Cramer-Rao low bound is derived in this paper. Firstly, second-order ambiguity function is utilized to reduce the dimensionality and estimate initial TDOA and differential Doppler rate. Secondly, the TDOA estimation is updated and FDOA is obtained using cross ambiguity function, in which relative Doppler com- panding is compensated by the existing differential Doppler rate. Thirdly, differential Doppler rate estimation is updated using cross estimator. Theoretical analysis on estimation variance and Cramer-Rao low bound shows that the final estimation of TDOA, FDOA and differential Doppler rate performs well at both low and high signal-noise ratio, although the initial estimation accuracy of TDOA and differential Doppler rate is relatively poor under low signal-noise ratio conditions. Simulation results finally verify the theoretical analysis and show that the proposed method can overcome relative Doppler companding problem and performs well for all TDOA, FDOA and differential Doppler rate estimation.

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 Cramer-Rao lower bound （CRLB） of geoloeation 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 con- strained. 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 re- sults are included to corroborate the theoretical development.

A direct position determination method with combined TDOA and FDOA based on particle filter

The localization of a stationary transmitter using moving receivers is considered. The original Direct Position Determination （DPD） methods, with combined Time Difference of Arrival （TDOA） and Frequency Difference of Arrival （FDOA）, do not perform well under low Signal-to-Noise Ratio （SNR）, and worse still, the computation cost is difficult to accept when the computational capabilities are limited. To get better positioning performance, we present a new DPD algorithm that proves to be more computationally efficient and more precise for weak signals than the conventional approach. The algorithm partitions the signal received with the same receiver into multiple non-overlapping short-time signal segments, and then uses the TDOA, the FDOA and the coherency among the short-time signals to locate the target. The fast maximum likelihood estimation, one iterative method based on particle filter, is designed to solve the problem of high computation load. A secondary but important result is a derivation of closed-form expressions of the Cramer-Rao Lower Bound （CRLB）. The simulation results show that the algorithm proposed in this paper outperforms the traditional DPD algorithms with more accurate results and higher computational efficiency, and especially at low SNR, it is more close to the CRLB.

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.