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

Abstract

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 Cramér-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. INDEX TERMS Multi-source localization, time-of-arrival (TOA), clock asynchronization, sensor position uncertainties, Lagrange programming neural network (LPNN).

Personalized Teaching Strategy of University Ideology Course Based on Lagrange Neural Network and Big Data Technology

“…In literature [ 20 ], a single-layer feedback neural network based on projection operation is proposed to solve the nonsmooth optimization problem with different objective functions. Literature [ 21 , 22 ] puts forward a new type of neural network to solve general nonlinear programming problems. Literature [ 23 ] proposed a new type of neural network, LNN (Lagrange neural network), to solve nonlinear programming problems.…”

A novel time difference of arrival source localization method based on constrained scoring algorithm with a calibration emitter

“…where F 1 ðϑÞ is the full row rank as stated in (31). Then based on ( 24), (30) and the analysis in [51], Δϑ is the optimal solution for the optimization problem as follows…”

“…The proof of Proposition 2 begins with reformulating the estimated covariance expression of θ in (38). We first define that Z s o ð Þ is the Jacobian matrix of ϑ with respect to s o , which is given by According to the definition of F 1 ðϑÞ in (31), it is easy to check that…”

“…Besides, this method relies on the particular calculation toolboxes, which is often computationally timeconsuming. More recently, applying neural networks to the optimization problem has attracted attentions [30,31]. This kind of method first transforms the ML problem into a constrained optimization problem, and then designs a neural network by utilising the Lagrangian neuro-dynamic model [32,33].…”