A Robustly Convergent Algorithm for Source LocalizationUsing Time Difference of Arrival and Frequency Difference of Arrival
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摘要: 為實(shí)現(xiàn)對目標(biāo)位置和速度的精確定位，該文提出一種基于正則化理論的時(shí)差頻差定位技術(shù)。該算法首先利用最大似然方法確定目標(biāo)函數(shù)，然后通過傳統(tǒng)牛頓法對目標(biāo)位置和速度進(jìn)行迭代求解。眾所周知傳統(tǒng)牛頓法對初始值要求較高，較差初始值會導(dǎo)致Hess矩陣趨于病態(tài)，從而致使迭代發(fā)散，該文引入正則化理論修正Hess矩陣，使其更加合理，保證算法穩(wěn)健收斂。實(shí)驗(yàn)結(jié)果表明：相對于傳統(tǒng)牛頓法，該文算法在初始值的選取上具有穩(wěn)健性，對誤差選取較大的初始值，仍能夠保證算法的收斂性；相對于現(xiàn)有閉合式定位方法，該文算法在噪聲較大時(shí)具有較好的定位精度，定位精度接近于Cramer-Rao界，具有廣泛的實(shí)用價(jià)值。
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關(guān)鍵詞:
- 無源定位 /
- 到達(dá)時(shí)差 /
- 到達(dá)頻差 /
- 傳統(tǒng)牛頓法 /
- Hess矩陣 /
- 正則化算法
Abstract: To pursue accurate source location and velocity, this paper proposes a method based on the Regularization theory to solve the source localization problem utilizing Time-Difference-Of-Arrival (TDOA) and Frequency-Difference-Of-Arrival (FDOA). The proposed algorithm determines the objective function using the maximum likelihood estimator, and then uses classical Newton method to estimate the source position and velocity in an iterative way. It is known that the Newton method requires a good initial value, and a bad initial value can cause an ill-posed Hess matrix which leads to the iteration divergence. This paper introduces the Regularization theory to modify the Hess matrix to make it more proper, which ensures the iteration convergence. The experiment results show that compared with the classical Newton method, the proposed algorithm is robust to the initial value, and is still able to ensure its convergence even with an inaccurate initial value of large error. Compared with some other closed-form source location methods, the proposed algorithm has better location accuracy in large noise levels which can achieve the Cramer-Rao bound. The proposed algorithm can be widely applied in practice. -
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