CN103926603A

CN103926603A - Extremely-weak signal tracking method of GNSS receiver

Info

Publication number: CN103926603A
Application number: CN201410104010.XA
Authority: CN
Inventors: 杨峻巍
Original assignee: CETC 10 Research Institute
Current assignee: CETC 10 Research Institute
Priority date: 2014-03-19
Filing date: 2014-03-19
Publication date: 2014-07-16

Abstract

The invention proposes a method for tracking extremely weak signals of a GNSS receiver, aiming to provide a method for quickly and accurately tracking a GNSS receiver under the condition of extremely weak signals. The present invention is realized through the following technical solutions: first, the GNSS digital intermediate frequency signal and the carrier signal copied by the carrier ring are mixed and multiplied; The immediate and lag C/A codes are correlated, and the output six-way correlation results are respectively sent to the six-way integration-scavenger; then the six-way coherent integration values output by the six-way integration-scavenger are sent to the volumetric Kalman filter for correlation parameters Finally, the corresponding estimated values are sent to the code loop filter and the carrier loop filter for filtering. After filtering, they are respectively fed back to the carrier numerically controlled oscillator and the C/A code numerically controlled oscillator to realize the carrier phase and The real-time adjustment of carrier frequency, code phase and code frequency finally realizes fast and accurate tracking of GNSS signals.

Description

Tracking Method of Very Weak Signal of GNSS Receiver

技术领域technical field

本发明涉及一种GNSS接收机极弱信号的跟踪方法，该方法主要用于室内、隧道以及静止轨道和HEO卫星等所接收的导航信号较弱的环境下，GNSS接收机的实时、精确快速跟踪。The invention relates to a method for tracking extremely weak signals of a GNSS receiver. The method is mainly used for real-time, accurate and fast tracking of GNSS receivers in environments where navigation signals received by indoors, tunnels, geostationary orbits, HEO satellites, etc. are relatively weak .

背景技术Background technique

全球卫星导航系统GNSS已经在全世界范围内得到了广泛的应用，但是当GNSS接收机工作在室内,密集城区等各种信号条件恶劣的复杂信道环境中时,GNSS信号功率会受到严重衰减，信号幅度和相位也会受到多径衰落的影响变化剧烈，接收信噪比将会严重恶化，普通的GNSS接收机将难以正确的捕获和跟踪导航卫星信号。由于直接序列扩频信号具有高隐蔽性和抗截获、干扰能力强等优点,载噪比C/N0低于35dB/Hz微弱信号十分常见。GNSS接收机实现导航定位的基础是通过对接收到的卫星信号进行一系列的信号处理，进而提取出相应的导航参数。其信号处理过程一般包括以下几个阶段，即捕获、跟踪、位同步以及帧同步。在信号跟踪阶段，信号通道从捕获阶段获得的对当前卫星信号载波频率和码相位的粗略估计值出发，通过跟踪环路逐步精细对两个信号参量的估计，同时输出对信号各种GNSS测量值。The global satellite navigation system GNSS has been widely used all over the world, but when the GNSS receiver works in various complex channel environments with poor signal conditions such as indoors and dense urban areas, the power of the GNSS signal will be severely attenuated, and the signal The amplitude and phase will also be affected by multipath fading, and the signal-to-noise ratio will be severely deteriorated. It will be difficult for ordinary GNSS receivers to correctly capture and track navigation satellite signals. Due to the advantages of high concealment, anti-interception and strong interference ability of direct sequence spread spectrum signal, it is very common for weak signals with carrier-to-noise ratio C/N0 lower than 35dB/Hz. The basis for GNSS receivers to realize navigation and positioning is to perform a series of signal processing on the received satellite signals, and then extract the corresponding navigation parameters. Its signal processing generally includes the following stages, namely acquisition, tracking, bit synchronization and frame synchronization. In the signal tracking phase, the signal channel starts from the rough estimation of the carrier frequency and code phase of the current satellite signal obtained in the acquisition phase, gradually refines the estimation of the two signal parameters through the tracking loop, and outputs various GNSS measurement values of the signal at the same time .

GNSS跟踪环路包括两个基本环路，即码环与载波环。传统的载波环路采用标准延迟锁定环路（DLL）和锁相环（PLL）来实现，虽然其鲁棒性较好，但是其中的鉴别器存在非线性因素，以及信号相位的动态变化，使得锁定环路在信号极弱的情况下（即载噪比较低），极容易出现接收机的信号失锁。标准DDL与PLL跟踪环路在载噪比较低的情况下容易出现失锁甚至无法有效锁定的问题。为此一些学者提出了采用扩展卡尔曼滤波来实现弱信号的跟踪，但是该方法存在两方面的不足，其一，扩展卡尔曼滤波算法的线性化模型不准确,算法模型中系数计算复杂,参数估计累积误差大,且需计算较为复杂的雅克比矩阵；其二，通过对非线性系统的线性化来实现状态估计，因此其估计精度较低，甚至会出现发散。The GNSS tracking loop includes two basic loops, the code loop and the carrier loop. The traditional carrier loop is realized by standard delay-locked loop (DLL) and phase-locked loop (PLL). Although its robustness is good, there are nonlinear factors in the discriminator and the dynamic change of signal phase, which makes When the locked loop signal is extremely weak (that is, the carrier-to-noise ratio is low), it is very easy for the receiver to lose lock. Standard DDL and PLL tracking loops tend to lose lock or even fail to lock effectively when the carrier-to-noise ratio is low. For this reason, some scholars have proposed the use of extended Kalman filter to realize the tracking of weak signals, but this method has two shortcomings. First, the linearization model of the extended Kalman filter algorithm is not accurate, and the coefficient calculation in the algorithm model is complicated. The estimated cumulative error is large, and a more complex Jacobian matrix needs to be calculated; second, the state estimation is realized by linearizing the nonlinear system, so the estimation accuracy is low, and even divergence may occur.

发明内容Contents of the invention

本发明的目的是针对现有技术存在的不足之处，提供一种跟踪能力强，跟踪精度高，无需计算雅克比矩阵，在信号极弱的情况下，能够实时跟踪极弱信号小的快速精度跟踪方法，以解决传统（标准DDL与PLL）跟踪环路在载噪比较低的情况下容易出现失锁甚至无法有效锁定的问题。The purpose of the present invention is to address the deficiencies of the existing technology, to provide a tracking ability, high tracking accuracy, no need to calculate the Jacobian matrix, and in the case of extremely weak signals, it can track extremely weak signals in real time with small fast precision Tracking method to solve the problem that traditional (standard DDL and PLL) tracking loops tend to lose lock or even fail to lock effectively when the carrier-to-noise ratio is low.

本发明解决现有技术问题所采用的方案是：一种GNSS接收机极弱信号跟踪方法，其特征在于包括如下步骤：在GNSS接收机跟踪电路中，首先，将通过混频器的GNSS数字中频信号sIF(n)，在I支路上与正弦复制载波相乘，在Q支路上与余弦复制载波相乘；然后将I支路与Q支路的混频相乘结果分别与码环所复制的超前、即时和滞后C/A码进行相关运算，将相关运算输出的多路相关结果分别送入多路积分-清除器进行相干积分；再将多路积分-清除器输出的多路相干积分值送入容积卡尔曼滤波器进行相关参数的估计；最后，将相应的估计值分别送入码环滤波器和载波环滤波器进行滤波，经滤波后，分别反馈至载波数控振荡器和C/A码数控振荡器，进而实现载波相位和载波频率、码相位和码频率的实时调节，最终实现GNSS信号的跟踪。The solution adopted by the present invention to solve the problems of the prior art is: a GNSS receiver extremely weak signal tracking method, which is characterized in that it includes the following steps: in the GNSS receiver tracking circuit, at first, the GNSS digital intermediate frequency passed through the mixer The signal sIF(n) is multiplied by the sine replica carrier on the I branch, and multiplied by the cosine replica carrier on the Q branch; Lead, instant and lag C/A codes perform correlation operations, and send the multi-channel correlation results output by the correlation operations to the multi-channel integrator-scavenger for coherent integration; Send it to the volumetric Kalman filter to estimate the relevant parameters; finally, send the corresponding estimated values to the code loop filter and the carrier loop filter for filtering, and after filtering, feed back to the carrier numerically controlled oscillator and C/A Code numerical control oscillator, and then realize the real-time adjustment of carrier phase and carrier frequency, code phase and code frequency, and finally realize the tracking of GNSS signal.

本发明相比于现有技术具有如下有益效果：Compared with the prior art, the present invention has the following beneficial effects:

(1)跟踪能力强。本发明将六路相干积分值送入容积卡尔曼滤波器进行相关参数的估计，估计结果分别经过码环滤波器和载波环滤波器进行滤波，滤波后，分别作为C/A码数控振荡器与载波数控振荡器的输入，实现载波频率与相位、码频率与相位的快速精确跟踪。相比于传统的跟踪环路，该方法能够实现极弱信号小的实时跟踪。(1) Strong tracking ability. In the present invention, the coherent integral values of six channels are sent to the volumetric Kalman filter to estimate the relevant parameters, and the estimated results are respectively filtered through the code loop filter and the carrier loop filter. After filtering, they are used as the C/A code numerical control oscillator and carrier The input of the numerically controlled oscillator realizes fast and accurate tracking of carrier frequency and phase, code frequency and phase. Compared with the traditional tracking loop, this method can realize real-time tracking with extremely weak signals.

(2)跟踪精度高。本发明码环通过其内部的码发生器复制一个与接收信号中的C/A码相一致的C/A码序列，然后两者做相关运算，已实现剥离GNSS接收信号中的C/A码，同时也提高了原本淹没在噪声中的GNSS信号的信噪比。而载波环则是通过载波环路尽力地使其复制的载波信号与与接收到的卫星载波信号保持一致，从而通过混批机制彻底地剥离卫星信号中的载波。载波环与码环之间通过有机结合，相互支持，共同完成对信号的跟踪和测量。相比于基于扩展卡尔曼滤波的跟踪环路，其跟踪精度较高，且无需计算雅克比矩阵。提出的基于容积卡尔曼滤波的GNSS弱信号跟踪方法，相比于现有技术，本发明容积卡尔曼滤波不仅不需要计算雅克比矩阵，而且其滤波精度较高。(2) High tracking accuracy. The code loop of the present invention copies a C/A code sequence consistent with the C/A code in the received signal through its internal code generator, and then performs correlation operations between the two, and has realized the stripping of the C/A code in the GNSS received signal , while also improving the signal-to-noise ratio of the GNSS signal that was originally submerged in noise. The carrier loop is to try its best to make the copied carrier signal consistent with the received satellite carrier signal through the carrier loop, so that the carrier in the satellite signal is completely stripped through the mixed batch mechanism. The carrier ring and the code ring are organically combined to support each other and jointly complete the tracking and measurement of the signal. Compared with the tracking loop based on extended Kalman filter, its tracking accuracy is higher, and it does not need to calculate the Jacobian matrix. The proposed GNSS weak signal tracking method based on the volumetric Kalman filter, compared with the prior art, the volumetric Kalman filter of the present invention not only does not need to calculate the Jacobian matrix, but also has higher filtering accuracy.

附图说明Description of drawings

下面结合附图和实施例对本发明进一步说明。The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

图1为本发明基于容积卡尔曼滤波器的GNSS接收机跟踪原理框图。Fig. 1 is a functional block diagram of the GNSS receiver tracking based on the volumetric Kalman filter of the present invention.

图2为图1中容积卡尔曼滤波器工作原理框图。Fig. 2 is a block diagram of the working principle of the volumetric Kalman filter in Fig. 1 .

具体实施方式Detailed ways

参阅图1。本发明的跟踪环路如图1所示，其中的容积卡尔曼滤波器通过图2所示的工作流程来实现。首先，将通过混频器的GNSS数字中频信号与载波环所复制的载波信号进行混频相乘，其中s_IF(n)在I支路上与正弦复制载波相乘，在Q支路上与余弦复制载波相乘；然后将I支路与Q支路的混频相乘结果分别与码环所复制的超前、即时和滞后C/A码进行相关运算，将相关运算输出的多路相关结果分别送入多路积分-清除器进行相干积分值；再将多路相干积分值送入容积卡尔曼滤波器进行相关参数的估计；最后，将相应的估计值分别送入码环滤波器和载波环滤波器进行滤波，经滤波后，分别反馈至载波数控振荡器和C/A码数控振荡器，实现载波相位和载波频率、码相位和码频率的实时调节，跟踪GNSS信号。本实施例所述的多路可以是六路，六路积分-清除器是本发明的最佳实施例。See Figure 1. The tracking loop of the present invention is shown in FIG. 1 , and the volumetric Kalman filter is realized through the workflow shown in FIG. 2 . First, the GNSS digital intermediate frequency signal passed through the mixer is mixed and multiplied by the carrier signal copied by the carrier ring, where s _IF (n) is multiplied with the sine copy carrier on the I branch, and the cosine copy on the Q branch Carrier multiplication; then perform correlation operations on the mixed multiplication results of the I branch and the Q branch with the advanced, immediate and lagging C/A codes copied by the code ring, and send the multi-channel correlation results output by the correlation operations to the Then, the multi-channel coherent integral value is sent to the volumetric Kalman filter to estimate the relevant parameters; finally, the corresponding estimated value is sent to the code loop filter and the carrier loop filter respectively. After filtering, they are respectively fed back to the carrier numerically controlled oscillator and C/A code numerically controlled oscillator to realize real-time adjustment of carrier phase and carrier frequency, code phase and code frequency, and track GNSS signals. The multi-channel described in this embodiment may be six-channel, and the six-channel integrator-scavenger is the best embodiment of the present invention.

(1)GNSS数字中频信号s_IF(n)分别与两路相位差异90°的载波环复制载波信号进行混频处理，其中GNSS数字中频信号s_IF(n)表示为如下所示：(1) The GNSS digital intermediate frequency signal s _IF (n) is mixed with two carrier ring replica carrier signals with a phase difference of 90°, wherein the GNSS digital intermediate frequency signal s _IF (n) is expressed as follows:

y(t_n)＝A(t_n)C(t_n-τ(t_n))D(t_n-τ(t_n))sin(w_IFt_n-φ(t_n))+v_n y(t _n )＝A(t _n )C(t _n -τ(t _n ))D(t _n -τ(t _n ))sin(w _IF t _n -φ(t _n ))+v _n

式中：t_n表示离散采样时刻；y(t_n)表示数字中频信号s_IF(n)；A(t_n)表示载波的幅值；C(t_n)表示卫星所播发的C/A码，D(t_n)表示卫星所发送的数据码，且两者的电平值只可能是±1；τ(t_n)表示信号的传播时延；w_IF表示数字中频角频率；φ(t_n)表示信号的载波相位；v_n表示均值为零的高斯白噪声序列。In the formula: t _n represents the discrete sampling time; y(t _n ) represents the digital intermediate frequency signal s _IF (n); A(t _n ) represents the amplitude of the carrier; C(t _n ) represents the C/A code broadcast by the satellite , D(t _n ) represents the data code sent by the satellite, and the level value of the two can only be ±1; τ(t _n ) represents the propagation delay of the signal; w _IF represents the angular frequency of the digital intermediate frequency; φ(t _n ) represents the carrier phase of the signal; v _n represents a Gaussian white noise sequence with a mean value of zero.

(2)I支路与Q支路的混频结果分别与码环所复制的超前、即时和滞后C/A码进行相关运算，即：(2) The mixing results of the I branch and the Q branch are respectively correlated with the advanced, immediate and lagging C/A codes copied by the code ring, namely:

$\{\begin{matrix} \begin{matrix} {I I}_{k k} ((δ δ)) = = {Σ Σ}_{n no = = {n no}_{k k} + + 11}^{{n no}_{k k} + + {N N}_{k k}} y the y (({t t}_{n no})) \cdot \cdot (({C C}_{NCO NCO} (({t t}_{n no} + + δ δ - - {t t}_{NCOk NCO})) sin sin [[{w w}_{IF IF} {t t}_{n no} + + {φ φ}_{NCO NCO} (({t t}_{n no}))]])) \\ {Q Q}_{k k} ((δ δ)) = = {Σ Σ}_{n no = = {n no}_{k k} + + 11}^{{n no}_{k k} + + {N N}_{k k}} y the y (({t t}_{n no})) \cdot &Center Dot; (({C C}_{NCO NCO} (({t t}_{n no} + + δ δ - - {t t}_{NCOk NCO})) cos cos [[{w w}_{IF IF} {t t}_{n no} + + {φ φ}_{NCO NCO} (({t t}_{n no}))]])) \end{matrix} & δ δ = = - - \frac{{Δ Δ}_{e e__l l}}{22} \end{matrix}, ,, 00,, \frac{{Δ Δ}_{e e__l l}}{22}$

式中：k表示当前1ms时间间隔所处的位置；n表示1ms时间间隔的采样时刻；Nk表示每1ms时间间隔的采样个数；C_NCO(t_n)表示由接收机产生的被跟踪的卫星信号的PRN复制码；t_NCOk表示码NCO产生即时码的起始时间；φ_NCO(t_n)表示接收机复制的载波相位。Δ_{e_l}表示超前与滞后相关器之间的间距；δ表示所复制的三路C/A码与即时码之间的相位差异；I_k(δ)和Q_k(δ)分别表示I支路与Q支路的相关累加值；其中，当时，I_k(δ)、Q_k(δ)分别表示I支路和Q支路的混频结果与码环所复制的超前码进行相关运算；当δ＝0时，I_k(δ)、Q_k(δ)分别表示I支路和Q支路的混频结果与码环所复制的即时码进行相关运算；当时，I_k(δ)表示I支路和Q支路的混频结果与码环所复制的滞后码进行相关运算。In the formula: k represents the position of the current 1ms time interval; n represents the sampling moment of the 1ms time interval; Nk represents the number of samples per 1ms time interval; C _NCO (t _n ) represents the tracked satellite produced by the receiver The PRN copy code of the signal; t _NCOk represents the start time when the code NCO generates the real-time code; φ _NCO (t _n ) represents the carrier phase copied by the receiver. Δ _{e_l} represents the distance between the leading and lagging correlators; δ represents the phase difference between the copied three-way C/A code and the real-time code; I _k (δ) and Q _k (δ) represent the I branch and the The associated cumulative value of the Q branch; where, when When , I _k (δ), Q _k (δ) respectively represent the correlation operation between the mixing results of the I branch and the Q branch and the advanced code copied by the code ring; when δ=0, I _k (δ), Q _k (δ) respectively represent the correlation operation between the mixing results of the I branch and the Q branch and the real-time code copied by the code ring; when When , I _k (δ) means that the mixing result of the I branch and the Q branch is correlated with the lag code copied by the code loop.

相关运算后的相关结果可表示为：The correlation result after the correlation operation can be expressed as:

$\{\begin{matrix} \begin{matrix} {I I}_{k k} ((δ δ)) = = \frac{{N N}_{k k} {\overset{&OverBar; &OverBar;}{A A}}_{k k} {D D.}_{m m}}{22} cos cos (({Δφ Δφ}_{k k})) R R (({Δt Δt}_{k k} + + δ δ)) + + {v v}_{Ik Ik} \\ {Q Q}_{k k} ((δ δ)) = = \frac{{N N}_{k k} {\overset{&OverBar; &OverBar;}{A A}}_{k k} {D D.}_{m m}}{22} sin sin (({Δφ Δφ}_{k k})) R R (({Δt Δt}_{k k} + + δ δ)) + + {v v}_{Qk Q} \end{matrix} & δ δ = = - - \frac{{Δ Δ}_{e e__l l}}{22} \end{matrix}, 00,, \frac{{Δ Δ}_{e e__l l}}{22}$

式中：表示整个1ms累加时间段内载波幅值的平均值，D_m表示导航数据比特，Δφ_k表示1ms累加时间段内载波相位误差φ(t)-φ_NCO(t)的平均值，Δt_k＝τ(t_midk)-t_midk表示1ms累加时间段内中间点的码相位误差，且t_midk＝(t_NCOk+t_NCOk+1)2；v_Ik和v_Qk分别表示零均值互不相关的高斯白噪声序列，其方差均为；公式中没R(Δt_k+δ)表示PRN码的自相关函数。In the formula: Indicates the average value of the carrier amplitude in the entire 1ms accumulation time period, D _m represents the navigation data bit, Δφ _k represents the average value of the carrier phase error φ(t) _-φNCO (t) in the 1ms accumulation time period, Δt _k =τ (t _midk )-t _midk represents the code phase error at the middle point within the 1ms accumulation time period, and t _midk = (t _NCOk +t _NCOk+1 )2; v _Ik and v _Qk respectively represent the Gaussian white with zero mean and no correlation Noise sequence whose variance is ; No R (Δt _k + δ) in the formula represents the autocorrelation function of the PRN code.

则输出的六路相关结果i_E、i_P、i_L、q_E、q_P和q_L为：Then the output six-way correlation results i _E , i _P , i _L , q _E , q _P and q _L are:

$\{\begin{matrix} {i i}_{E E.} = = {I I}_{k k} ((- - \frac{{Δ Δ}_{e e__l l}}{22})) \\ {i i}_{P P} = = {I I}_{k k} ((00)) \\ {i i}_{L L} = = {I I}_{k k} ((\frac{{Δ Δ}_{e e__l l}}{22})) \\ {q q}_{E E.} = = {Q Q}_{k k} ((- - \frac{{Δ Δ}_{e e__l l}}{22})) \\ {q q}_{P P} = = {Q Q}_{k k} ((00)) \\ {q q}_{L L} = = {Q Q}_{k k} ((\frac{{Δ Δ}_{e e__l l}}{22})) \end{matrix}$

式中：i_E、i_P和i_L分别表示I支路上超前、即时与滞后支路的相关值；q_E、q_P和q_L分别表示Q支路上超前、即时与滞后支路的相关值。In the formula: i _E , i _P and i _L represent the correlation values of the leading, immediate and lagging branches on the I branch respectively; q _E , q _P and q _L represent the correlation values of the leading, immediate and lagging branches on the Q branch respectively .

(3)六路相关结果通过六路积分-清除器输出六路相干积分值。(3) The six-way correlation results output six-way coherent integral values through the six-way integrator-scavenger.

(4)将六路相干积分值送入容积卡尔曼滤波器，完成相关参数的估计，其中包括：容积卡尔曼滤波器系统状态方程x_m+1＝f_m(x_m,w_m)与量测方程的建立式中： $x_{m} = {[\begin{matrix} x_{φ_{m}} & x_{w_{m}} & x_{α_{m}} & A_{m} & t_{s_{m}} \end{matrix}]}^{T},$ 为系统的状态向量，m表示积分间隔开始时刻，这里选择积分时间为20ms,表示m时刻真实载波相位与接收机载波NCO复制的载波相位之差；表示m时刻真实载波多普勒漂移；表示m时刻载波多普勒漂移变化率；A_m表示m时刻载波幅值；表示m时刻码相位；x_m+1表示m+1时刻的系统状态向量；f_m表示非线性状态转移函数；w_m表示系统噪声向量。(4) Send the six-way coherent integral values into the volumetric Kalman filter to complete the estimation of related parameters, including: volumetric Kalman filter system state equation x _m+1 = f _m (x _m ,w _m ) and measurement In the establishment formula of the equation: $x_{m} = {[\begin{matrix} x_{φ_{m}} & x_{w_{m}} & x_{α_{m}} & A_{m} & t_{{the s}_{m}} \end{matrix}]}^{T},$ is the state vector of the system, m represents the start time of the integration interval, here the integration time is selected as 20ms, Indicates the difference between the real carrier phase at time m and the carrier phase copied by the receiver carrier NCO; Indicates the real carrier Doppler shift at time m; Indicates the change rate of carrier Doppler drift at time m; A _m indicates the carrier amplitude at time m; Represents the code phase at time m; x _m+1 represents the system state vector at time m+1; f _m represents the nonlinear state transfer function; w _m represents the system noise vector.

状态方程的具体表达式如下所示：The specific expression of the state equation is as follows:

${[\begin{matrix} {x x}_{φ φ} \\ {x x}_{w w} \\ {x x}_{α α} \end{matrix}]}_{m m + + 11} = = [\begin{matrix} 11 & {δt δt}_{m m} & {δt δt}_{m m}^{22} / / 22 \\ 00 & 11 & {δt δt}_{m m} \\ 00 & 00 & 11 \end{matrix}] {[\begin{matrix} {x x}_{φ φ} \\ {x x}_{w w} \\ {x x}_{α α} \end{matrix}]}_{m m} - - [\begin{matrix} {δt δt}_{m m} \\ 00 \\ 00 \end{matrix}] {W W}_{{NCO NCO}_{m m}} + + [\begin{matrix} 11 & 00 & 00 & 00 \\ 00 & 11 & 00 & 00 \\ 00 & 00 & 11 & 00 \end{matrix}] {w w}_{{φ φ}_{m m}}$

${t t}_{{s the s}_{m m + + 11}} = = {t t}_{{s the s}_{m m}} + + \frac{{w w}_{L L 11} {δt δt}_{nom nom} - - [\begin{matrix} 11 & 00 & 00 & 00 \end{matrix}] {w w}_{{φ φ}_{m m}}}{{w w}_{L L 11} + + {x x}_{{w w}_{m m}} + + 0.5 0.5 {δt δt}_{nom nom} {x x}_{{α α}_{m m}}} + + {w w}_{{ts ts}_{m m}}$

${A A}_{m m + + 11} = = {A A}_{m m} + + {w w}_{{A A}_{m m}}$

式中：表示累加时间段；表示载波NCO在累加时间段内产生的载波多普勒频移的值；wL1表示L1载波角频率；以及表示均值为零、互不相关的高斯白噪声序列。In the formula: Indicates the cumulative time period; Indicates the value of the carrier Doppler frequency shift generated by the carrier NCO within the accumulation time period; wL1 indicates the L1 carrier angular frequency; as well as Represents a zero-mean, uncorrelated white Gaussian noise sequence.

量测方程的建立。这里选取20ms即时相干积分值、20ms超前减滞后相干积分值作为量测量，建立量测方程，即：Establishment of measurement equations. Here, the 20ms instant coherent integral value and the 20ms lead minus lag coherent integral value are selected as the quantity measurement, and the measurement equation is established, namely:

$\begin{matrix} {z z}_{m m} = = \frac{11}{{σ σ}_{n no}} \sqrt{\frac{22}{{N N}_{m m}}} [\begin{matrix} {Σ Σ}_{k k = = {k k}_{m m}}^{{k k}_{m m} + + 1919} {I I}_{k k} ((00)) \\ {Σ Σ}_{k k = = {k k}_{m m}}^{{k k}_{m m} + + 1919} {Q Q}_{k k} ((00)) \\ \frac{11}{\sqrt{η η}} {Σ Σ}_{k k = = {k k}_{m m}}^{{k k}_{m m} + + 1919} [[{I I}_{k k} ((\frac{{Δ Δ}_{E E.__L L}}{22})) - - {I I}_{k k} ((- - \frac{{Δ Δ}_{E E.__L L}}{22}))]] \\ \frac{11}{\sqrt{η η}} {Σ Σ}_{k k = = {k k}_{m m}}^{{k k}_{m m} + + 1919} [[{Q Q}_{k k} ((\frac{{Δ Δ}_{E E.__L L}}{22})) - - {Q Q}_{k k} ((- - \frac{{Δ Δ}_{E E.__L L}}{22}))]] \end{matrix}] \\ = = {D D.}_{m m} {h h}_{m m} (({Δφ Δφ}_{m m},, {Δt Δt}_{m m},, {\overset{&OverBar; &OverBar;}{A A}}_{m m})) + + {v v}_{zm zm} \end{matrix} = = \frac{{\overset{&OverBar; &OverBar;}{A A}}_{m m} {D D.}_{m m}}{{σ σ}_{n no}} \sqrt{\frac{{N N}_{m m}}{22}} [\begin{matrix} cos cos (({Δφ Δφ}_{m m})) R R (({Δt Δt}_{m m})) \\ sin sin (({Δφ Δφ}_{m m})) R R (({Δt Δt}_{m m})) \\ \frac{11}{\sqrt{η η}} cos cos (({Δφ Δφ}_{m m})) {R R}_{E E.__L L} (({Δt Δt}_{m m})) \\ \frac{11}{\sqrt{η η}} sin sin (({Δφ Δφ}_{m m})) {R R}_{E E.__L L} (({Δt Δt}_{m m})) \end{matrix}] + + {v v}_{zm zm}$

式中：每隔20ms的采样个数η＝2[1-R(Δ_{E_L})]；表示20ms载波幅值的平均值；Δφ_m表示20ms载波相位差的平均值；表示中间点的码相位误差； $R_{E_L} (Δt) = R (Δt + \frac{Δ_{E_L}}{2}) - R (Δt - \frac{Δ_{E_L}}{2})$ 表示超前减滞后相关函数；表示超前码的相关函数；表示滞后码的相关函数；h_m表示量测函数；ν_zm表示零均值的高斯白噪声序列。In the formula: the number of samples every 20ms η=2[1-R( _{ΔE_L} )]; Indicates the average value of 20ms carrier amplitude; Δφ _m represents the average value of 20ms carrier phase difference; Indicates the code phase error at the middle point; $R_{E._L} (Δt) = R (Δt + \frac{Δ_{E._L}}{2}) - R (Δt - \frac{Δ_{E._L}}{2})$ Indicates the lead-minus-lag correlation function; Represents the correlation function of the advanced code; Represents the correlation function of the lag code; h _m represents the measurement function; ν _zm represents the zero-mean Gaussian white noise sequence.

其中量测方程中各项的具体表达式如下所示：The specific expressions of the items in the measurement equation are as follows:

${Δφ Δφ}_{m m} = = [\begin{matrix} 11 & {δt δt}_{m m} / / 22 & {δt δt}_{m m}^{22} / / 66 \end{matrix}] {[\begin{matrix} {x x}_{φ φ} \\ {x x}_{w w} \\ {x x}_{α α} \end{matrix}]}_{m m} - - \frac{{δt δt}_{m m}}{22} + + [\begin{matrix} 00 & 00 & 00 & 11 \end{matrix}] {w w}_{φm φm}$

${Δt Δt}_{m m} = = (({t t}_{{s the s}_{m m + + 11}} + + {t t}_{{s the s}_{m m}})) / / 22 - - {t t}_{{mid middle}_{m m}} = = {t t}_{{s the s}_{m m}} + + \frac{11}{22} \frac{{w w}_{L L 11} {δt δt}_{nom nom} - - [\begin{matrix} 11 & 00 & 00 & 00 \end{matrix}] {w w}_{{φ φ}_{m m}}}{{w w}_{L L 11} + + {x x}_{{w w}_{m m}} + + 0.5 0.5 {δt δt}_{nom nom} {x x}_{{α α}_{m m}}} + + \frac{11}{22} {w w}_{{ts ts}_{m m}} - - {t t}_{{mid middle}_{m m}}$

${\overset{&OverBar; &OverBar;}{A A}}_{m m} = = (({A A}_{m m + + 11} + + {A A}_{m m})) / / 22 = = {A A}_{m m} + + 0.5 0.5 {w w}_{{A A}_{m m}}$

根据上述建立的数学模型设计容积卡尔曼滤波器，完成相关参数的估计，其中包括时间更新与量测更新两个基本迭代过程。According to the mathematical model established above, the volumetric Kalman filter is designed to complete the estimation of relevant parameters, including two basic iterative processes of time update and measurement update.

参阅图2，容积卡尔曼滤波器的具体工作流程如下所示：Referring to Figure 2, the specific workflow of the volumetric Kalman filter is as follows:

①对系统状态及状态协方差矩阵进行初始化。① Initialize the system state and state covariance matrix.

②假设k-1时刻的状态估计值及状态协方差矩阵分别为和对状态协方差矩阵P_k-1|k-1进行因式分解，即：② Assume that the estimated state value and state covariance matrix at time k-1 are and Factorize the state covariance matrix P _k-1|k-1 , namely:

${P P}_{k k - - 11 | | k k - - 11} = = {S S}_{k k - - 11 | | k k - - 11} {S S}_{k k - - 11 | | k k - - 11}^{T T}$

③计算容积点③ Calculate the volume point

${X x}_{i i,, k k - - 11 | | k k - - 11} = = {S S}_{k k - - 11 | | k k - - 11} {ξ ξ}_{i i} + + {\overset{^^}{x x}}_{k k - - 11 | | k k - - 11}$

④传播容积点④Propagation volume point

${X x}_{i i,, k k - - 11 | | k k - - 11}^{* *} = = f f (({X x}_{i i,, k k - - 11 | | k k - - 11}))$

⑤计算系统状态一步预测及一步预测协方差矩阵⑤ Calculate the one-step prediction of the system state and the one-step prediction covariance matrix

${\overset{^^}{x x}}_{x x | | k k - - 11} = = \frac{11}{22 n no} {Σ Σ}_{i i = = 11}^{22 n no} {X x}_{i i,, k k | | k k - - 11}^{* *}$

${P P}_{k k | | k k - - 11} = = \frac{11}{22 n no} {Σ Σ}_{i i = = 11}^{22 n no} {X x}_{i i,, k k | | k k - - 11}^{* *} {X x}_{i i,, k k | | k k - - 11}^{* * T T} - - {\overset{^^}{x x}}_{k k | | k k - - 11} {\overset{^^}{x x}}_{k k | | k k - - 11}^{T T} + + {Q Q}_{k k - - 11}$

⑥对状态一步预测协方差矩阵P_k|k-1进行因式分解，即：⑥ Factorize the state one-step prediction covariance matrix P _k|k-1 , namely:

${P P}_{k k | | k k - - 11} = = {S S}_{k k | | k k - - 11} {S S}_{k k | | k k - - 11}^{T T}$

⑦计算容积点⑦ Calculate the volume point

${X x}_{i i,, k k | | k k - - 11} = = {S S}_{k k | | k k - - 11} {ξ ξ}_{i i} + + {\overset{^^}{x x}}_{k k | | k k - - 11}$

⑧传播容积点⑧Propagation volume point

Z_i,k|k-1＝h(X_i,k|k-1)Z _i,k|k-1 ＝h(X _i,k|k-1 )

⑨量测值预测⑨Measurement value prediction

${\overset{^^}{z z}}_{k k | | k k - - 11} = = \frac{11}{22} {Σ Σ}_{i i = = 11}^{22 n no} {Z Z}_{i i,, k k | | k k - - 11}$

⑩新息协方差矩阵估计⑩Innovation covariance matrix estimation

${P P}_{k k | | k k - - 11} = = \frac{11}{22 n no} {Σ Σ}_{i i = = 11}^{22 n no} {Z Z}_{i i,, k k | | k k - - 11} {Z Z}_{i i,, k k | | k k - - 11}^{T T} - - {\overset{^^}{z z}}_{k k | | k k - - 11} {\overset{^^}{z z}}_{k k | | k k - - 11}^{T T} + + {R R}_{k k}$

互协方差矩阵估计 cross-covariance matrix estimation

${P P}_{xz xz,, k k | | k k - - 11} = = \frac{11}{22 n no} {Σ Σ}_{i i = = 11}^{22 n no} {X x}_{i i,, k k | | k k - - 11} {Z Z}_{i i,, k k | | k k - - 11}^{T T} - - {\overset{^^}{x x}}_{k k | | k k - - 11} {\overset{^^}{z z}}_{k k | | k k - - 11}^{T T}$

滤波增益计算 Filter gain calculation

${K K}_{k k} = = {P P}_{xz xz . . k k | | k k - - 11} {P P}_{zz zz,, k k | | k k - - 11}^{- - 11}$

状态协方差距阵更新 State Covariance Gap Matrix Update

${P P}_{k k | | k k} = = {P P}_{k k | | k k - - 11} - - {K K}_{k k} {P P}_{zz zz,, k k | | k k - - 11} {K K}_{k k}^{T T}$

计算k时刻的状态估计值 Calculate the state estimate at time k

${\overset{^^}{x x}}_{k k | | k k} = = {\overset{^^}{x x}}_{k k | | k k - - 11} - - {K K}_{k k} (({z z}_{k k} - - {\overset{^^}{z z}}_{k k | | k k - - 11}))$

(5)六路相关结果的估计结果经分别经过码环滤波器和载波环滤波器进行滤波，滤波后，分别作为C/A码数控振荡器与载波环数控振荡器的输入，进而实现载波频率与相位、码相位与频率的快速精确跟踪。(5) The estimated results of the six correlation results are filtered by the code loop filter and the carrier loop filter respectively. Fast and accurate tracking of phase, code phase and frequency.

Claims

1. a kind of GNSS receiver very weak signal tracking method is characterized in that comprising the steps: in the GNSS receiver tracking circuit, at first, by the GNSS digital intermediate frequency signal s _IF (n) of the mixer, on the I branch Multiply with the sine replicated carrier, and multiply with the cosine replicated carrier on the Q branch; then the results of the mixed frequency multiplication of the I branch and the Q branch are respectively carried out with the advanced, immediate and delayed C/A codes copied by the code ring Correlation operation, the multi-channel correlation results output by the correlation operation are sent to the multi-channel integrator-clearer for coherent integration; then the multi-channel coherent integral value output by the multi-channel integrator-clearer is sent to the volumetric Kalman filter Finally, the corresponding estimated values are sent to the code loop filter and the carrier loop filter for filtering. After filtering, they are respectively fed back to the carrier numerically controlled oscillator and the C/A code numerically controlled oscillator to realize the carrier phase and The real-time adjustment of carrier frequency, code phase and code frequency finally realizes the tracking of GNSS signals.

2. GNSS receiver extremely weak signal tracking method according to claim 1, is characterized in that: GNSS digital intermediate frequency signal s _IF (n) carries out frequency mixing process with the carrier ring copy carrier signal of two-way phase difference 90 ° respectively, Among them, the GNSS digital intermediate frequency signal s _IF (n) is expressed as:

y(t _n )＝A(t _n )C(t _n -τ(t _n ))D(t _n -τ(t _n ))sin(w _IF t _n -φ(t _n ))+v _n

In the formula: t _n represents the discrete sampling time; y(t _n ) represents the digital intermediate frequency signal s _IF (n); A(t _n ) represents the amplitude of the carrier; C(t _n ) represents the C/A code broadcast by the satellite , D(t _n ) represents the data code sent by the satellite, and the level value of the two can only be ±1; τ(t _n ) represents the propagation delay of the signal; w _IF represents the angular frequency of the digital intermediate frequency; φ(t _n ) represents the carrier phase of the signal; v _n represents a Gaussian white noise sequence with a mean value of zero.

3. GNSS receiver extremely weak signal tracking method according to claim 1, is characterized in that, output multi-channel correlation result, completes according to the following steps:

① Correlate the results of the frequency mixing and multiplication of the I branch and the Q branch with the leading, immediate and lagging C/A codes copied by the code ring:

\{\begin{matrix} \begin{matrix} {I I}_{k k} ((δ δ)) = = {Σ Σ}_{n no = = {n no}_{k k} + + 11}^{{n no}_{k k} + + {N N}_{k k}} y the y (({t t}_{n no})) \cdot &Center Dot; (({C C}_{NCO NCO} (({t t}_{n no} + + δ δ - - {t t}_{NCOk NCO})) sin sin [[{w w}_{IF IF} {t t}_{n no} + + {φ φ}_{NCO NCO} (({t t}_{n no}))]])) \\ {Q Q}_{k k} ((δ δ)) = = {Σ Σ}_{n no = = {n no}_{k k} + + 11}^{{n no}_{k k} + + {N N}_{k k}} y the y (({t t}_{n no})) \cdot &Center Dot; (({C C}_{NCO NCO} (({t t}_{n no} + + δ δ - - {t t}_{NCOk NCO})) cos cos [[{w w}_{IF IF} {t t}_{n no} + + {φ φ}_{NCO NCO} (({t t}_{n no}))]])) \end{matrix} & δ δ = = - - \frac{{Δ Δ}_{e e__l l}}{22} \end{matrix}, ,, 00,, \frac{{Δ Δ}_{e e__l l}}{22}

In the formula: k represents the position of the current 1ms time interval; n represents the sampling moment of the 1ms time interval; N _k represents the number of samples per 1ms time interval; C _NCO (t _n ) represents the tracked The PRN copy code of the satellite signal; t _NCOk indicates the start time when the code NCO generates the real-time code; φ _NCO (t _n ) indicates the carrier phase copied by the receiver. Δ _{e_l} represents the distance between the leading and lagging correlators; δ represents the phase difference between the copied three-way C/A code and the real-time code; I _k (δ) and Q _k (δ) represent the I branch and the The associated cumulative value of the Q branch; where, when When , I _k (δ), Q _k (δ) respectively represent the correlation operation between the mixing results of the I branch and the Q branch and the advanced code copied by the code ring; when δ=0, I _k (δ), Q _k (δ) respectively represent the correlation operation between the mixing results of the I branch and the Q branch and the real-time code copied by the code ring; when When , I _k (δ) represents that the mixing result of the I branch and the Q branch is correlated with the lagging code copied by the code ring;

②The correlation result after the correlation calculation in step ① is expressed as:

\{\begin{matrix} \begin{matrix} {I I}_{k k} ((δ δ)) = = \frac{{N N}_{k k} {\overset{&OverBar; &OverBar;}{A A}}_{k k} {D D.}_{m m}}{22} cos cos (({Δφ Δφ}_{k k})) R R (({Δt Δt}_{k k} + + δ δ)) + + {v v}_{Ik Ik} \\ {Q Q}_{k k} ((δ δ)) = = \frac{{N N}_{k k} {\overset{&OverBar; &OverBar;}{A A}}_{k k} {D D.}_{m m}}{22} sin sin (({Δφ Δφ}_{k k})) R R (({Δt Δt}_{k k} + + δ δ)) + + {v v}_{Qk Q} \end{matrix} & δ δ = = - - \frac{{Δ Δ}_{e e__l l}}{22} \end{matrix}, 00,, \frac{{Δ Δ}_{e e__l l}}{22}

In the formula: Indicates the average value of the carrier amplitude in the entire 1ms accumulation time period, D _m represents the navigation data bit, Δφ _k represents the average value of the carrier phase error φ(t) _-φNCO (t) in the 1ms accumulation time period, Δt _k =τ (t _midk )-t _midk represents the code phase error at the middle point within the 1ms accumulation time period, and t _midk = (t _NCOk +t _NCOk+1 )2; v _Ik and v _Qk respectively represent the Gaussian white with zero mean and no correlation Noise sequence; R(Δt _k + δ) represents the autocorrelation function of the PRN code;

③ The multi-channel correlation result can be expressed as:

\{\begin{matrix} {i i}_{E E.} = = {I I}_{k k} ((- - \frac{{Δ Δ}_{e e__l l}}{22})) \\ {i i}_{P P} = = {I I}_{k k} ((00)) \\ {i i}_{L L} = = {I I}_{k k} ((\frac{{Δ Δ}_{e e__l l}}{22})) \\ {q q}_{E E.} = = {Q Q}_{k k} ((- - \frac{{Δ Δ}_{e e__l l}}{22})) \\ {q q}_{P P} = = {Q Q}_{k k} ((00)) \\ {q q}_{L L} = = {Q Q}_{k k} ((\frac{{Δ Δ}_{e e__l l}}{22})) \end{matrix}

In the formula: i _E , i _P and i _L represent the correlation values of the leading, immediate and lagging branches on the I branch, respectively; q _E , q _P and qL represent the correlation values of the leading, immediate and lagging branches on the Q branch, respectively.

4. GNSS receiver extremely weak signal tracking method according to claim 3, is characterized in that, multi-path coherent integral value is sent into volumetric Kalman filter, completes the estimation of relevant parameter, comprises: volumetric Kalman filter system Establishment of state equation x _m+1 =f _m (x _m ,w _m ) and measurement equation; where:

x_{m} = {[\begin{matrix} x_{φ_{m}} & x_{w_{m}} & x_{α_{m}} & A_{m} & t_{{the s}_{m}} \end{matrix}]}^{T},

is the state vector of the system, m represents the start time of the integration interval, here the integration time is selected as 20ms, Indicates the difference between the real carrier phase at time m and the carrier phase copied by the receiver carrier NCO; Indicates the real carrier Doppler shift at time m; Indicates the change rate of carrier Doppler drift at time m; A _m indicates the carrier amplitude at time m; Represents the code phase at time m; x _m+1 represents the system state vector at time m+1; f _m represents the nonlinear state transfer function; w _m represents the system noise vector.

5. GNSS receiver extremely weak signal tracking method according to claim 4, is characterized in that, the concrete expression of state equation is:

{[\begin{matrix} {x x}_{φ φ} \\ {x x}_{w w} \\ {x x}_{α α} \end{matrix}]}_{m m + + 11} = = [\begin{matrix} 11 & {δt δt}_{m m} & {δt δt}_{m m}^{22} / / 22 \\ 00 & 11 & {δt δt}_{m m} \\ 00 & 00 & 11 \end{matrix}] {[\begin{matrix} {x x}_{φ φ} \\ {x x}_{w w} \\ {x x}_{α α} \end{matrix}]}_{m m} - - [\begin{matrix} {δt δt}_{m m} \\ 00 \\ 00 \end{matrix}] {W W}_{{NCO NCO}_{m m}} + + [\begin{matrix} 11 & 00 & 00 & 00 \\ 00 & 11 & 00 & 00 \\ 00 & 00 & 11 & 00 \end{matrix}] {w w}_{{φ φ}_{m m}}

t_{{the s}_{m + 1}} = t_{{the s}_{m}} + \frac{w_{L 1} {δt}_{nom} - [\begin{matrix} 1 & 0 & 0 & 0 \end{matrix}] w_{φ_{m}}}{w_{L 1} + x_{w_{m}} + 0.5 {δt}_{nom} x_{α_{m}}} + w_{{ts}_{m}}

f

{A A}_{m m + + 11} = = {A A}_{m m} + + {w w}_{{A A}_{m m}}

In the formula: Indicates the cumulative time period; Indicates the value of the carrier Doppler frequency shift generated by the carrier NCO within the accumulation time period; w _L1 represents the L1 carrier angular frequency; as well as Represents a zero-mean, uncorrelated white Gaussian noise sequence.

6. GNSS receiver extremely weak signal tracking method according to claim 4, it is characterized in that, get 20ms instant coherent integral value, 20ms lead and subtract lagging coherent integral value as quantity measurement, set up measurement equation:

\begin{matrix} z_{m} = \frac{1}{σ_{no}} \sqrt{\frac{2}{N_{m}}} [\begin{matrix} Σ_{k = k_{m}}^{k_{m} + 19} I_{k} (0) \\ Σ_{k = k_{m}}^{k_{m} + 19} Q_{k} (0) \\ \frac{1}{\sqrt{η}} Σ_{k = k_{m}}^{k_{m} + 19} [I_{k} (\frac{Δ_{E._L}}{2}) - I_{k} (- \frac{Δ_{E._L}}{2})] \\ \frac{1}{\sqrt{η}} Σ_{k = k_{m}}^{k_{m} + 19} [Q_{k} (\frac{Δ_{E._L}}{2}) - Q_{k} (- \frac{Δ_{E._L}}{2})] \end{matrix}] \\ = {D.}_{m} h_{m} ({Δφ}_{m}, {Δt}_{m}, {\overset{&OverBar;}{A}}_{m}) + v_{zm} \end{matrix} = \frac{{\overset{&OverBar;}{A}}_{m} {D.}_{m}}{σ_{no}} \sqrt{\frac{N_{m}}{2}} [\begin{matrix} \cos ({Δφ}_{m}) R ({Δt}_{m}) \\ \sin ({Δφ}_{m}) R ({Δt}_{m}) \\ \frac{1}{\sqrt{η}} \cos ({Δφ}_{m}) R_{E._L} ({Δt}_{m}) \\ \frac{1}{\sqrt{η}} \sin ({Δφ}_{m}) R_{E._L} ({Δt}_{m}) \end{matrix}] + v_{zm}

In the formula: the number of samples every 20ms

N_{m} = (N_{k_{m}} + N_{k_{m + 1}} + &Center Dot; &Center Dot; &Center Dot; N_{k_{m + 19}}); η = - 2 [1 - R (Δ_{E._L})]; {\overset{&OverBar;}{A}}_{m}

Indicates the average value of 20ms carrier amplitude; Δφ _m represents the average value of 20ms carrier phase difference; Indicates the code phase error at the middle point; Indicates the lead-minus-lag correlation function; Represents the correlation function of the advanced code; Represents the correlation function of the lag code; h _m represents the measurement function; ν _zm represents the zero-mean Gaussian white noise sequence.

7. GNSS receiver extremely weak signal tracking method according to claim 6, is characterized in that, the concrete expression of each item in the measurement equation is:

{Δφ Δφ}_{m m} = = [\begin{matrix} 11 & {δt δt}_{m m} / / 22 & {δt δt}_{m m}^{22} / / 66 \end{matrix}] {[\begin{matrix} {x x}_{φ φ} \\ {x x}_{w w} \\ {x x}_{α α} \end{matrix}]}_{m m} - - \frac{{δt δt}_{m m}}{22} + + [\begin{matrix} 00 & 00 & 00 & 11 \end{matrix}] {w w}_{φm φm}

{Δt Δt}_{m m} = = (({t t}_{{s the s}_{m m + + 11}} + + {t t}_{{s the s}_{m m}})) / / 22 - - {t t}_{{mid middle}_{m m}} = = {t t}_{{s the s}_{m m}} + + \frac{11}{22} \frac{{w w}_{L L 11} {δt δt}_{nom nom} - - [\begin{matrix} 11 & 00 & 00 & 00 \end{matrix}] {w w}_{{φ φ}_{m m}}}{{w w}_{L L 11} + + {x x}_{{w w}_{m m}} + + 0.5 0.5 {δt δt}_{nom nom} {x x}_{{α α}_{m m}}} + + \frac{11}{22} {w w}_{{ts ts}_{m m}} - - {t t}_{{mid middle}_{m m}}

{\overset{&OverBar; &OverBar;}{A A}}_{m m} = = (({A A}_{m m + + 11} + + {A A}_{m m})) / / 22 = = {A A}_{m m} + + 0.5 0.5 {w w}_{{A A}_{m m}} . .

8. weak signal GNSS receiver tracking method according to claim 4, is characterized in that, according to the mathematical model that above-mentioned system equation and measurement equation set up, design corresponding volumetric Kalman filter, comprise time updating and measurement Two basic iterative processes are updated.

9. weak signal GNSS receiver tracking method according to claim 4, is characterized in that, the estimation result of multi-path correlation result filters through code loop filter and carrier loop filter respectively, after filtering, respectively as C/ The input of A-code numerical control oscillator and carrier ring numerical control oscillator realizes fast and accurate tracking of carrier frequency and phase, code phase and frequency.