Abstract
This paper proposes a new geolocation technique to improve the accuracy of the position estimate of a single unknown (anonymous) radio wave emitter. We consider a factor graph (FG)-based geolocation technique, where the input are the samples of direction-of-arrival (DOA) measurement results sent from the sensors. It is shown that the accuracy of the DOA-based FG geolocation algorithm can be improved by introducing approximated expressions for the mean and variance of the tangent and cotangent functions based on the first-order Taylor series (TS) at the tangent factor nodes of the FG. This paper also derives a closed-form expression of the Cramer-Rao lower bound (CRLB) for DOA-based geolocation, where the number of samples is taken into account. The proposed technique does not require high computational complexity because only mean and variance are to be exchanged between the nodes in the FG. It is shown that the position estimation accuracy with the proposed technique outperforms the conventional DOA-based least square (LS) technique and that the achieved root mean square error (RMSE) is very close to the theoretical CRLB.
Highlights
Accurate wireless geolocation has received considerable attention in the past two decades [1] and is expected to play important roles in current and future wireless communications systems
The primary objectives of this paper are as follows: (A) We introduce a new set of formulas to be calculated at the tangent and cotangent factor nodes, to better approximate the mean and variance of the function values by utilizing the first-order Taylor series (TS) expansion of the functions, so that the Gaussianity assumption still holds. (B) We derive the Cramer-Rao lower bound (CRLB) of the DOA-based geolocation technique taking into account the number of samples; the accuracy of the new CRLB obtained by this paper is higher than that shown in [7]. (C) The results of a series of simulations are presented to evaluate the convergence property of the proposed technique, where the trajectory of the iterative estimation process is presented
We have derived a set of new approximated expression for the mean and variance of the tangent and cotangent functions based on the first-order TS to hold the Gaussianity assumption
Summary
Accurate wireless geolocation has received considerable attention in the past two decades [1] and is expected to play important roles in current and future wireless communications systems. A joint TOA-DOA-based FG geolocation algorithm was proposed in [6], where the measured samples are efficiently used in FG to estimate the position accurately. It should be noted here that it is impossible to calculate variance with only one sample It is shown in this paper that with the proposed technique, the accuracy of the target position estimation outperforms the conventional DOA-based LS geolocation technique and the results are very close to theoretical CRLB for the DOA-based geolocation. Each sensor in the proposed DOA-based TS FG geolocation technique first calculates the mean mDθ →Nθ and the variance σD2θ →Nθ from the K measured samples.
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