近場(chǎng)目標(biāo)方位和距離估計(jì)的克拉美-羅界研究
doi: 10.11999/JEIT150578 cstr: 32379.14.JEIT150578
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(西北工業(yè)大學(xué)電子信息學(xué)院 西安 710129) ②(西北工業(yè)大學(xué)無人機(jī)特種技術(shù)國家級(jí)重點(diǎn)實(shí)驗(yàn)室 西安 710065)
基金項(xiàng)目:
國家自然科學(xué)基金(61201320)，中央高?；究蒲袠I(yè)務(wù)費(fèi)專項(xiàng)資金(3102014JCQ01052)，中國博士后科學(xué)基金面上項(xiàng)目(2014M552489)，上海航天科技創(chuàng)新基金(SAST201455)
Cramr-Rao Bound for Near-field Source Localization
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1.
(School of Electronics and Information, Northwestern Polytechnical University, Xi&rsquo
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2.
(National Key Laboratory of Science and Technology on UAV, Northwestern Polytechnical University, Xi&rsquo
Funds:
The National Natural Science Foundation of China (61201320), The Fundamental Research Funds for the Central Universities (3102014JCQ01052), China Postdoctoral Science Foundation (2014M552489), Shanghai Aerospace Science and Technology Innovation Fund (SAST201455)
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摘要: 針對(duì)現(xiàn)有單源情況下近場(chǎng)目標(biāo)定位的窄帶克拉美-羅界(Cramr-Rao Bound, CRB)都是基于均勻直線陣模型，且沒能全面分析其CRB的特性和具體的影響因素。該文首先推導(dǎo)了基于窄帶模型的單源費(fèi)雪信息矩陣，進(jìn)而通過求舒爾補(bǔ)和雅克比變換，得到非均勻線陣條件下近場(chǎng)測(cè)距和測(cè)向的非矩陣形式的閉式CRB解析式。通過對(duì)該式從陣列相關(guān)因素(如陣列結(jié)構(gòu)、陣列孔徑等)和目標(biāo)信號(hào)相關(guān)因素(如目標(biāo)信號(hào)頻率和信噪比等)兩方面進(jìn)行分析，揭示了影響目標(biāo)角度和距離估計(jì)性能的物理因素，為后續(xù)陣列及信號(hào)的設(shè)計(jì)提供了理論指導(dǎo)。在最大孔徑給定的情況下，可通過設(shè)計(jì)合理的陣元配置方式，實(shí)現(xiàn)最優(yōu)的測(cè)距和測(cè)向效果。蒙特卡洛仿真結(jié)果驗(yàn)證了理論分析和上述結(jié)論的正確性。Abstract: In view of the existing CRB (Cramr-Rao Bound) for near-field single source is based on the uniform linear array, and analyzes less fully the CRB's characteristics and the influence factors of specific. In this paper, non-matrix, closed-form expression of the deterministic CRB for the near-field narrow band model is deduced based on Fisher information matrix, Schur complement and Jacobi transform with non-uniform linear array. The behavior of the performance with respect to some features of interest are discussed, namely, the array geometry, the array aperture, the thinned factor, the target signal frequency and the signal to noise ratio. Through the reasonable array design scheme, the direction and range of the target are both estimated. The Monte-Carlo simulation results validate the effectiveness of the theoretical analysis and the conclusion.
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