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 哈尔滨工程大学学报  2018, Vol. 39 Issue (6): 1087-1092  DOI: 10.11990/jheu.201612034 0

引用本文

WANG Jiao, JIANG Suyang, DI Shichao, et al. A low complexity carrier to noise ratio estimation algorithm in GNSS system[J]. Journal of Harbin Engineering University, 2018, 39(6), 1087-1092. DOI: 10.11990/jheu.201612034.

文章历史

GNSS系统中一种低复杂度的载噪比估计算法

1. 重庆邮电大学 光电信息感测与传输技术重庆市重点实验室, 重庆 400065;
2. 火箭军驻211厂军事代表室, 北京 100086;
3. 北京航天发射技术研究所, 北京 100076;
4. 中国科学院微电子研究所, 北京 100029

A low complexity carrier to noise ratio estimation algorithm in GNSS system
WANG Jiao1,4, JIANG Suyang2, DI Shichao3, LI Jinhai4, OU Songlin4
1. Chongqing Key Laboratory of Photoelectronic Information Sensing and Transmitting Technology, Chongqing University of Posts and Telecommunications, Chongqing 400065, China;
2. Military Representative Office, Rocket Army in 211 factory, Beijing 100086, China;
3. Beijing Institute of Space Launch of Technology, Beijing 100076, China;
4. Institute of Microelectronics of Chinese Academy of Sciences, Beijing 100029, China
Abstract: To provide a carrier-to-noise ratio estimation algorithm with low complexity and strong adaptability, this paper proposes a new algorithm after an analyses of the commonly used narrowband-wideband power ratio and variance summing methods. The distribution of the I-branch secondary moment and the I and Q fourth moment were used to deduce the accurate expression of the carrier-to-noise ratio estimation, and the consistency of the two different deduction methods was demonstrated. For the proposed algorithm, theoretical simulation and actual data demonstrations were carried out from the following four aspects:estimation bias, complexity of algorithm implementation, output delay time, and adaptability. The results show that, the estimation error of the proposed algorithm is less than 1 dB. In addition, this algorithm is a suitable alternative, since narrowband-wideband power ratio method is difficult to be directly applied to BD system and the variance summing method is highly complex. On the whole, the proposed method greatly reduces complexity, output delay, and improves adaptability. Therefore, it can be successfully used in global navigation satellite systems (GNSS) such as Beidou.
Key words: global navigation satellite system(GNSS)    carrier to noise ratio estimation    estimation bias    low complexity    output delay    adaptability

1 信号模型

 ${I_P}\left( n \right) = \frac{A}{2}D\left( n \right)R\left( {{\tau _P}} \right)\sin c\left( {{f_e}T} \right)\cos {\phi _e} + {n_I}$ (1)
 ${Q_P}\left( n \right) = \frac{A}{2}D\left( n \right)R\left( {{\tau _P}} \right)\sin c\left( {{f_e}T} \right)\sin {\phi _e} + {n_Q}$ (2)

 ${I_P}\left( n \right) = \frac{A}{2}\sin c\left( {{f_e}T} \right)\cos {\phi _e} + {n_I}$ (3)
 ${Q_P}\left( n \right) = \frac{A}{2}\sin c\left( {{f_e}T} \right)\sin {\phi _e} + {n_Q}$ (4)

 ${I_P}\left( n \right) = \sqrt {\left( {C/{N_0}} \right)\tau /M} \sigma \cos {\phi _e} + {n_I}$ (5)
 ${Q_P}\left( n \right) = \sqrt {\left( {C/{N_0}} \right)\tau /M} \sigma \sin {\phi _e} + {n_Q}$ (6)

 ${I_P}\left( n \right) = \sqrt {\left( {C/{N_0}} \right)\tau /M} \cos {\phi _e} + {n_I}$ (7)
 ${Q_P}\left( n \right) = \sqrt {\left( {C/{N_0}} \right)\tau /M} \sin {\phi _e} + {n_Q}$ (8)

 $\left\{ \begin{array}{l} {I_P}\left( n \right) = A/2 + {n_I}\\ {I_Q}\left( n \right) = {n_Q} \end{array} \right.$ (9)

2 典型载噪比估计算法 2.1 宽窄带功率比值法

 ${P_{WB}}\left( k \right) = \sum\limits_{n = kM + 1}^{kM + M} {\left( {I_P^2\left( n \right) + Q_P^2\left( n \right)} \right)}$ (10)

 ${P_{NB}}\left( k \right) = {\left( {\sum\limits_{n = kM + 1}^{kM + M} {{I_P}\left( n \right)} } \right)^2} + {\left( {\sum\limits_{n = kM + 1}^{kM + M} {{Q_P}\left( n \right)} } \right)^2}$ (11)

 ${{\bar P}_{NW}}\left( k \right) = \frac{1}{K}\sum\limits_{k = 1}^K {{P_{NW}}\left( k \right)} = \frac{1}{K}\sum\limits_{k = 1}^K {\frac{{{P_{NB}}\left( k \right)}}{{{P_{WB}}\left( k \right)}}}$ (12)

 $C/{N_0} = \frac{1}{T} \cdot \frac{{{{\bar P}_{NW}}\left( k \right) - 1}}{{M - {{\bar P}_{NW}}\left( k \right)}}$ (13)
2.2 方差求和法

 $Z\left( n \right) = I_P^2\left( n \right) + Q_P^2\left( n \right)$ (14)

 $\bar Z = \frac{1}{N}\sum\limits_{n = 1}^N {Z\left( n \right)}$ (15)
 $\sigma _Z^2 = \frac{1}{{N - 1}}\sum\limits_{n = 1}^N {\left( {Z\left( n \right) - \bar Z} \right)}$ (16)

 $C/{N_0} = \frac{1}{{2T}} \cdot \frac{{{P_s}}}{{\sigma _{IQ}^2}} = \frac{1}{T} \cdot \frac{{\sqrt {{Z^2} - \sigma _Z^2} }}{{\bar Z - \sqrt {{Z^2} - \sigma _Z^2} }}$ (17)
3 一种新型载噪比估计算法 3.1 算法的理论推导

 ${M_{I2}} = \frac{1}{N}\sum\limits_{n = 1}^N {I_p^2\left( n \right)}$ (18)

 $E\left( {{X^2}} \right) = {E^2}\left( X \right) + D\left( X \right)$ (19)

 $E\left( {{M_{I2}}} \right) = \frac{{{A^2}}}{4} + \frac{{{\sigma ^2}}}{2}$ (20)

 ${M_4} = \frac{1}{N}\sum\limits_{n = 1}^N {{{\left( {I_P^2\left( n \right) + Q_P^2\left( n \right)} \right)}^2}}$ (21)

 ${M_4} = \frac{1}{N}\sum\limits_{n = 1}^N {{{\left( {{{\left( {{n_I} + \frac{A}{2}} \right)}^2} + n_Q^2} \right)}^2}}$ (22)

 ${M_4} = \frac{1}{N}\sum\limits_{n = 1}^N {{{\left( {\frac{{{A^2}}}{4} + A{n_I} + n_I^2 + n_Q^2} \right)}^2}}$ (23)

M′=$\frac{{{A^2}}}{4}$+AnI+nI2+nQ2，则由式(9)、(19)可得

 $E\left( {M'} \right) = \frac{{{A^2}}}{4} + {\sigma ^2}$ (24)

χ2分布性质，可知

 $D\left( {{Y^2}} \right) = 2\;即\;D\left( {\frac{2}{{{\sigma ^2}}}n_I^2} \right) = 2$ (25)

 $D\left( {n_I^2} \right) = \frac{{{\sigma ^4}}}{2}$ (26)

 $D\left( {n_Q^2} \right) = \frac{{{\sigma ^4}}}{2}$ (27)

 $D\left( {M'} \right) = \frac{{{A^2}}}{2}{\sigma ^2} + {\sigma ^4}$ (28)

 $E\left( {{M_4}} \right) = \frac{{{A^4}}}{{16}} + {A^2}{\sigma ^2} + 2{\sigma ^4}$ (29)

MI2的均值的平方E(MI4)为

 $E\left( {{M_{I4}}} \right) = \frac{{{A^4}}}{{16}} + \frac{{{A^2}{\sigma ^2}}}{4} + \frac{{{\sigma ^4}}}{4}$ (30)

1) 方案一：

$M{P_1} = \frac{{{M_4}}}{{{M_{I4}}}}$, 得到

 $M{P_1} = \frac{{{A^4} + 16{A^2}{\sigma ^2} + 32{\sigma ^4}}}{{{A^4} + 4{A^2}{\sigma ^2} + 4{\sigma ^4}}}$ (31)

 $\frac{{{A^2}}}{{2\sigma _1^2}} = \frac{{M{P_1} - 4 - \sqrt {M{P_1} + 8} }}{{1 - M{P_1}}}$ (32)
 $\frac{{{A^2}}}{{2\sigma _2^2}} = \frac{{M{P_1} - 4 - \sqrt {M{P_1} + 8} }}{{1 - M{P_1}}}$ (33)

 $C/{N_0} = \frac{{{A^2}}}{{2{\sigma ^2}}} \cdot \frac{1}{{2T}} = \frac{1}{{2T}} \cdot \frac{{M{P_1} - 4 - \sqrt {M{P_1} + 8} }}{{1 - M{P_1}}}$ (34)

2) 方案二：

$M{P_2} = \frac{{{M_{I4}}}}{{{M_4}}}$, 得到

 $M{P_2} = \frac{{{A^4} + 4{A^2}{\sigma ^2} + 4{\sigma ^4}}}{{{A^4} + 16{A^2}{\sigma ^2} + 32{\sigma ^4}}}$ (35)

 $\frac{{{A^2}}}{{2\sigma _1^2}} = \frac{{4M{P_2} - 1 - \sqrt {8MP_2^2 + M{P_2}} }}{{1 - M{P_2}}}$ (36)
 $\frac{{{A^2}}}{{2\sigma _2^2}} = \frac{{4M{P_2} - 1 + \sqrt {8MP_2^2 + M{P_2}} }}{{1 - M{P_2}}}$ (37)

 $\begin{array}{*{20}{c}} {C/{N_0} = \frac{1}{{2T}} \cdot \frac{{{A^2}}}{{2{\sigma ^2}}} = }\\ {\frac{1}{{2T}} \cdot \frac{{4M{P_2} - 1 + \sqrt {8MP_2^2 + M{P_2}} }}{{1 - M{P_2}}}} \end{array}$ (38)
3.2 方案一致性验证

3.2.1 理论验证

 $C/{N_0} = \frac{1}{{2T}} \cdot \frac{{{M_4} - 4{M_{I4}} - \sqrt {{M_{I4}}{M_4} + 8M_{I4}^2} }}{{{M_{I4}} - {M_4}}}$ (39)

 $C/{N_0} = \frac{1}{{2T}} \cdot \frac{{4{M_{I4}} - {M_4} + \sqrt {8M_{I4}^2 + {M_{I4}}{M_4}} }}{{{M_4} - {M_{I4}}}}$ (40)

3.2.2 数据测试验证

4 性能分析

4.1 估计偏差比较 4.1.1 仿真数据测试分析

 Download: 图 1 仿真数据载噪比估计偏差 Fig. 1 The C/N0 estimation deviation of simulated data
4.1.2 实测数据测试分析

 Download: 图 2 实测数据载噪比估计偏差 Fig. 2 The C/N0 estimation deviation of measured data

4.2 算法实现复杂度比较 4.2.1 运算量比较

4.2.2 占用存储器资源比较

4.3 输出时延比较

4.4 适应性比较

5 结论

1) 仿真数据和实测数据都表明，本文提出的IBMM算法的估计偏差介于NWPRM和VSM之间，三种算法的估计偏差都维持在0.5 dB以内，总的来说，三种算法的估计性能相差不大。

2) 从实现复杂度方面来看，三种算法中，VSM的运算量最大且实现复杂度较高，存储数据过程中会对存储器资源造成极大的浪费；NWPRM和本文提出的IBMM运算量相当，且都能做到实时的运算，不会占用太大的存储器空间。

3) 输出时延和适应性比较结论：NWPRM和VSM存在20 ms的输出时延，而本文提出的算法则可以做到任意毫秒输出一个结果，而NWPRM不能应用于北斗系统，要能够准确估计GEO卫星的载噪比值时，VSM就不适用了，而本文提出的IBMM算法可广泛应用于北斗等GNSS系统，在这方面具有明显的优势。