CN103364801A - A method for multiplying positioning precision in a satellite navigation positioning system - Google Patents

Abstract

The invention discloses a method for doubling positioning accuracy in a satellite navigation and positioning system. In the method, each navigation satellite in the satellite navigation and positioning system downlinks pseudo-random noise codes, navigation messages and wide-area enhanced information through multiple carrier frequency points, The user terminal independently measures and corrects the orbit error, ionospheric delay, tropospheric delay and multipath error of the navigation satellite through multiple carrier frequency points at the same time, and realizes the pseudo-range measurement from the navigation satellite to the user terminal on multiple carrier frequency points. Using the pseudo-range observation equations of multiple carrier frequency points, through iterative calculation, the exact coordinates of the user terminal position can be solved. The invention can well improve the positioning accuracy of the user terminal, and significantly improve the navigation and positioning performance of the satellite navigation and positioning system.

Description

A method for doubling positioning accuracy in a satellite navigation and positioning system

technical field

The invention relates to satellite navigation and positioning technology, in particular to a method for doubling the positioning accuracy in a satellite navigation and positioning system, which is applicable to a navigation satellite that can simultaneously downlink multiple carrier frequency points and modulate pseudo-random noise codes and multi-frequency navigation messages. satellite navigation system.

Background technique

In the satellite navigation and positioning system, the positioning accuracy of the user terminal is mainly determined by the spatial layout of the system constellation and the equivalent pseudo-range measurement error. Usually, the positioning error of the satellite navigation and positioning system can be described by the following formula:

σ _i = DOP _i · σ _UERE (1)

Among them, σ _i is the positioning error of the user terminal, and i=1, 2, 3, 4, 5 respectively correspond to the plane, elevation, position, clock error and total positioning error; DOP _i is the geometrical precision attenuation factor of the system constellation, DOP _1. DOP ₂ , DOP ₃ , DOP ₄ and DOP ₅ respectively correspond to HDOP, VDOP, PDOP, TDOP and GDOP (plane, elevation, position, clock error and total geometric attenuation factor of precision); σ _UERE is equivalent pseudorange measurement error. Equation (1) requires that the pseudo-range measurement errors of navigation satellites meet the following conditions: ① independent of each other; ② equidistributed; ③ subject to Gaussian distribution with zero mean.

In the global satellite navigation and positioning system, many navigation satellites can modulate pseudo-random noise codes and navigation messages on multiple carrier frequency points. In 2002, Academician Ai Guoxiang of the Chinese Academy of Sciences led the invention of a satellite navigation and positioning system based on communication satellites (patent number: ZL 200410046064.1, invention name: transponder satellite communication navigation and positioning system, inventors: Ai Guoxiang, Shi Huli, Wu Haitao , authorized on July 29, 2009). This invention uses multiple communication frequency points on communication satellites as navigation, opening a new beginning for the development of full-frequency communication into full-frequency navigation. Observing the pseudorange and Doppler frequency shift of a navigation satellite at the same time can constrain the user terminal to the bottom circumference of a cone, which requires pseudorange measurements and Doppler frequency shifts of more than two (including two) navigation satellites. The navigation and positioning of the user terminal can be realized by shifting the measured value (application number: 201110164385.1, invention name: positioning method combined with Doppler speed measurement in satellite navigation, inventors: Ma Lihua, Ai Guoxiang, Ji Haifu). If each navigation satellite downlinks multiple navigation carriers at the same time, the equivalent pseudo-range measurement error of the navigation satellite can be effectively reduced, and the navigation and positioning accuracy of the user terminal can be improved (application number: 201110228917.3, title of invention: multi-carrier positioning method in satellite navigation , Inventors: Ma Lihua, Ai Guoxiang, Ji Haifu).

In general, the pseudo-range measurement values of multiple carrier frequency points of the same navigation satellite and the satellite ephemeris have related parts, at this time the positioning accuracy of the user terminal cannot be estimated by formula (1); at the same time, in the existing global satellite In the navigation and positioning system, the number of carrier frequency points that each navigation satellite can downlink at the same time is not the same, and the invention cannot be simply applied: the method of reducing pseudo-range measurement error in the multi-carrier positioning method in satellite navigation (patent application number: 201110228917.3). The method for doubling the positioning accuracy in the satellite navigation and positioning system of the present invention makes a new scientific exposition on the use of multiple carrier frequency points to multiply the positioning accuracy of the user terminal from the physical level, and can be used to guide the multi-frequency point satellite navigation and positioning system The carrier frequency resource is used to double the positioning accuracy of the user terminal.

Contents of the invention

The purpose of the present invention is to provide a method for doubling the positioning accuracy of a user terminal in a satellite navigation and positioning system. Multiple carrier frequency points of navigation satellites in the satellite navigation and positioning system can be used to work simultaneously, and the user terminal can measure independently through multiple carrier frequency points at the same time. And correct the orbit error and clock error of the navigation satellite, the ionospheric delay, the tropospheric delay, and the multipath error, realize the pseudo-range measurement from the navigation satellite to the user terminal at multiple carrier frequency points, and finally determine the exact coordinates of the user terminal position .

利用N个载波频点分别改正用户终端的多路径误差。最后，经过多个载波频点改正后的伪距测量中的残差互不相关。因此，对于每颗导航卫星，利用N个载波频点分别测量和改正后的伪距测量值，都具有随机特性，满足式(1)的使用条件。在使用多个载波频点的情况下，式(1)可改写为：The present invention proposes a method for doubling positioning accuracy in a satellite navigation and positioning system, which includes two aspects of physical meaning: on the one hand: each navigation satellite in the satellite navigation and positioning system downlinks navigation signals of N carrier frequency points, which The measurement noise of the time-based navigation signal is reduced to that of the single-carrier frequency point measurement noise The orbit error and clock error of the navigation satellite measured and corrected by N carrier frequency points are irrelevant; the ionospheric delay and tropospheric delay are corrected by using multiple carrier frequency points, and the residual error is correspondingly reduced as

The multipath errors of the user terminal are respectively corrected by using N carrier frequency points. Finally, the residuals in pseudorange measurements corrected by multiple carrier frequencies are not correlated with each other. Therefore, for each navigation satellite, the measured and corrected pseudo-range measurements using N carrier frequency points have random characteristics and satisfy the conditions of use in formula (1). In the case of using multiple carrier frequency points, formula (1) can be rewritten as:

σ _i = DOP _i PAFP σ _UERE (2)

另一方面：在测量同一颗导航卫星的伪距的同时，可以测量导航卫星上多个载波频点上的多普勒频移，即给出相应的伪距变化率信息，在建立观测方程组求解用户终端的位置时，多普勒频移测量与伪距测量具有等效性。因此，如果同时在多个载波频点上测量伪距与多普勒频移，PAFP数值在理论上还能进一步减小 Among them, PAFP is the enhancement factor of positioning accuracy by using multiple carrier frequency points for the same navigation satellite, which is called the physical accuracy enhancement factor. geometry structure. For the sake of intuition, it is assumed that the number of carrier frequency points downlinked by each navigation satellite is N. At this time,

On the other hand: while measuring the pseudorange of the same navigation satellite, the Doppler frequency shift at multiple carrier frequency points on the navigation satellite can be measured, that is, the corresponding pseudorange change rate information is given, and the observation equations can be established Doppler frequency shift measurements are equivalent to pseudorange measurements when solving the position of the user terminal. Therefore, if the pseudorange and Doppler frequency shift are measured on multiple carrier frequency points at the same time, the PAFP value can be further reduced theoretically.

DOP is a geometric parameter of space, and the pseudorange and Doppler frequency shift measured on multiple carrier frequency points of a navigation satellite are all physical parameters. Therefore, the present invention proposes a separate factor PAFP to evaluate multiple carrier frequency points. Enhancement of positioning accuracy due to point measurement. It is not difficult to see that PAFP is a physical precision enhancement factor, which is independent of the geometric parameter DOP, and the influence of the two on the positioning accuracy of the user terminal is independent of each other.

In order to achieve the above object, the present invention proposes a method for doubling positioning accuracy in a satellite navigation and positioning system, which is suitable for high-precision single-point positioning of user terminals, and is characterized in that the method includes the following steps:

Step 1: Modulate the navigation signals used for navigation and positioning that each of the M navigation satellites in the satellite navigation and positioning system will send to the user terminal to be positioned to a plurality of carrier frequency points, where M≥ 4. The navigation signal includes pseudo-random noise code, navigation message and wide-area enhancement information;

Step 2, sending the pseudo-random noise code and navigation message downwards with multiple carrier frequencies;

Step 3, the user terminal receives the pseudo-random noise code and the navigation message issued by all navigation satellites through multiple carrier frequency points;

Step 4, the user terminal obtains the clock correction parameters of the navigation satellite according to the received navigation message; obtains the orbital position of the navigation satellite according to the navigation satellite ephemeris in the received navigation message; The signal corrects the orbit error of the navigation satellite; the user terminal obtains the measurement pseudo-range from each navigation satellite to the user terminal on each carrier frequency point according to the pseudo-random noise code, and corrects the ionosphere in the measurement pseudo-range according to the received navigation signal Delay, tropospheric delay and multipath errors;

Step 5, the user terminal iteratively calculates the position coordinates of the user terminal according to the measured pseudo-range with corrected ionospheric delay, tropospheric delay and multipath error, and the corrected satellite orbit position, and finally obtains the accurate position of the user terminal coordinate;

Step 6, using the physical precision enhancement factor to evaluate the positioning accuracy of the user terminal.

The method of the invention can well improve the positioning accuracy of the user terminal, and can significantly improve the navigation and positioning performance of the system.

Description of drawings

Fig. 1 is a flowchart of a method for doubling positioning accuracy in the satellite navigation and positioning system of the present invention.

Detailed ways

In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be described in further detail below in conjunction with specific embodiments and with reference to the accompanying drawings.

Fig. 1 is a flowchart of a method for doubling positioning accuracy in the satellite navigation and positioning system of the present invention. As shown in Figure 1, the method for doubling positioning accuracy in a kind of satellite navigation and positioning system proposed by the present invention specifically includes the following steps:

Step 1, each of the M (M≥4) navigation satellites in the satellite navigation and positioning system will transmit the navigation signal for navigation and positioning to the user terminal to be positioned to multiple carrier frequency points , the navigation signal includes a pseudo-random noise code, navigation text and wide-area enhancement information;

The pseudo-random noise code corresponds to each navigation satellite separately, the pseudo-random noise code can be used to identify the navigation satellite, and the time difference measurement of the navigation signal transmission is realized by utilizing the autocorrelation and cross-correlation characteristics of the pseudo-random noise code, and the time difference is multiplied by The radio wave transmission speed is the pseudo-range from the navigation satellite to the user terminal; the navigation message includes system time, clock correction parameters of the navigation satellite, ionospheric delay model parameters, navigation satellite ephemeris and satellite health status; the wide-area enhancement The information contains correction data and integrity information of the navigation satellite orbit.

The M (M≥4) navigation satellites in the satellite navigation and positioning system all downlink multiple carrier frequency points at the same time, and modulate pseudo-random noise codes and navigation messages on these multiple carrier frequency points. Different navigation satellites use The number of carrier frequency points may be different.

The user terminal in the present invention may be a fixed terminal or a mobile terminal. The fixed terminal is a fixed satellite receiving device; the mobile terminal is a vehicle-mounted, ship-borne or handheld receiving device.

Step 2, sending the pseudo-random noise code and navigation message downwards with multiple carrier frequencies;

Step 3, the user terminal receives the pseudo-random noise code and the navigation message issued by all navigation satellites through multiple carrier frequency points;

Step 4, the user terminal obtains the clock correction parameters of the navigation satellite according to the received navigation message; obtains the orbital position of the navigation satellite according to the navigation satellite ephemeris in the received navigation message; The signal corrects the orbit error of the navigation satellite; the user terminal obtains the measurement pseudo-range from each navigation satellite to the user terminal on each carrier frequency point according to the pseudo-random noise code, and corrects the ionosphere in the measurement pseudo-range according to the received navigation signal Delay, tropospheric delay and multipath errors;

specifically:

The user terminal corrects the orbit error of the navigation satellite according to the satellite orbit correction data in the received wide-area enhancement information;

According to the pseudo-random noise code, the user terminal obtains the measured pseudo-range from each navigation satellite to the user terminal on each carrier frequency point as follows:

该测量伪距同时满足以下伪距观测方程：At the measurement time t _k , the user terminal measures the pseudorange from the navigation satellite S _j to the user terminal at the ith (i=1, 2, ..., N _j ) frequency point

The measured pseudorange satisfies the following pseudorange observation equation at the same time:

${\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; [</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}$

$<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; c\&delta;t</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;\&rho;</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;\&rho;</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; P</span>}}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,2</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,2</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>$

为测量伪距；(X_k，Y_k，Z_k)为待定位的用户终端在t_k的准确坐标(待求量)；(X^j，Y^j，Z^j)为导航卫星S_j在发射导航信号时的位置坐标；b_k为用户终端钟差的等效距离(待求量)；δt^j为导航卫星的时钟改正参数，可从导航卫星发送的导航电文中获得；c为真空光速，

为改正前的电离层时延，

为改正前的对流层时延，

为随机误差。In the formula,

is to measure the pseudo-range; (X _k , Y _k , Z _k ) is the exact coordinates of the user terminal to be positioned at t _k (required quantity); (X ^j , Y ^j , Z ^j ) is the launch time of the navigation satellite S _j The position coordinates of the navigation signal; b _k is the equivalent distance of the clock difference of the user terminal (to be sought); δt ^j is the clock correction parameter of the navigation satellite, which can be obtained from the navigation message sent by the navigation satellite; c is the speed of light in vacuum,

is the ionospheric delay before correction,

is the tropospheric delay before correction,

is a random error.

The user terminal corrects the ionospheric delay in the pseudorange measurement according to the ionospheric delay model and the received ionospheric delay model parameters in the navigation message; the user terminal collects local meteorological parameters, and according to the orbital position of the navigation satellite, The tropospheric time delay in the measured pseudorange is corrected by using the tropospheric delay model; according to the local environmental conditions, the multipath correction model is used to correct the multipath error in the measured pseudorange.

Step 5, the user terminal iteratively calculates the position coordinates of the user terminal according to the measured pseudo-range with corrected ionospheric delay, tropospheric delay and multipath error, and the corrected satellite orbit position, and finally obtains the accurate position of the user terminal coordinate;

Said step 5 further comprises the following steps:

Step 5.1, when calculating the positioning of the user terminal, first set an initial value of the user terminal position coordinates, that is, the approximate position coordinates of the user terminal (X _k ⁰ , Y _k ⁰ , Z _k ⁰ );

Step 5.2, then carry out first-order Taylor series expansion to the pseudo-range observation equation shown in formula (3), obtain the linearized form of the pseudo-range observation equation containing the user terminal position coordinate correction step size:

${\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; \&delta;X</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; \&delta;Y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; \&delta;Z</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}^{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c\&delta;t</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&delta;\&rho;</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&delta;\&rho;</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; P</span>}}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}$

为用户终端的概略位置坐标到导航卫星S_j的方向余弦：In the formula, (δX _k , δY, δZ _k ) is the correction step size of the user terminal position coordinates,

is the direction cosine from the approximate position coordinates of the user terminal to the navigation satellite S _j :

${\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}^{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}^{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; Y</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}^{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}^{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; Z</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}^{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}^{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

R _k ^j is the distance from the approximate position coordinates of the user terminal to the navigation satellite S _j :

R _k ^j ＝[(X ^j -X _k ⁰ ) ² +(Y ^j -Y _k ⁰ ) ² +(Z ^j -Z _k ⁰ ) ² ] ^1/2 (6)

和用户终端的概略位置坐标到导航卫星S_j的几何距离R_k ^j。According to the position coordinates and clock correction value of the navigation satellite at the time of the navigation signal transmission, the approximate position coordinates of the user terminal are used to calculate the direction cosine from the approximate position coordinates of the user terminal to the navigation satellite S _j through formulas (5) and (6)

and the geometric distance R _k ^j from the approximate position coordinates of the user terminal to the navigation satellite S _j .

Step 5.3, solving the linearized pseudorange observation equation obtained in step 5.2 to obtain the correction step size of the user terminal position coordinates;

Said step 5.3 further comprises the following steps:

Step 5.3.1, using the known items in the linearized pseudorange observation equation (4) Indicates that there are:

${\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; \&delta;X</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; \&delta;Y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; \&delta;Z</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

In the formula, is the constant term of the linearized pseudorange observation equation:

${\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}^{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; c\&delta;t</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;\&rho;</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;\&rho;</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; P</span>}}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

Step 5.3.2, write formula (7) in matrix form:

V＝AX-L (9)

In the formula, X is the undetermined parameter vector:

X＝[δX _k δY _k δZ _k b _k ] ^T (10)

A is the coefficient matrix of undetermined parameters:

Wherein, each navigation satellite S _j corresponds to a sub-matrix of N _j rows and 4 columns in matrix A.

L is a vector of constant entries:

$\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; =</span>{\left[\begin{array}{ccccccccccc}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; 1,1</span>}}& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& {\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}& {\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="L\; k"\; filenames="HDA0000148813370000011.png"\; state="\{\{state\}\}">L</figure-callout></span><figure-callout\; id="2"\; label="L\; k"\; filenames="HDA0000148813370000011.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}^{\mathrm{<span\; class="notranslate">k</span>}}& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& {\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="L\; k"\; filenames="HDA0000148813370000011.png"\; state="\{\{state\}\}">L</figure-callout></span><figure-callout\; id="2"\; label="L\; k"\; filenames="HDA0000148813370000011.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}^{\mathrm{<span\; class="notranslate">k</span>}}& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& {\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 1</span>}}& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& {\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}\end{array}\right]}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span>$

V is the random error vector:

$\mathrm{<span\; class="notranslate">\; V</span>}<span\; class="notranslate">\; =</span>{\left[\begin{array}{ccccccccccc}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; 1,1</span>}}& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& {\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}& {\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="v\; k"\; filenames="HDA0000148813370000011.png"\; state="\{\{state\}\}">v</figure-callout></span><figure-callout\; id="2"\; label="v\; k"\; filenames="HDA0000148813370000011.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}^{\mathrm{<span\; class="notranslate">k</span>}}& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& {\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="v\; k"\; filenames="HDA0000148813370000011.png"\; state="\{\{state\}\}">v</figure-callout></span><figure-callout\; id="2"\; label="v\; k"\; filenames="HDA0000148813370000011.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}^{\mathrm{<span\; class="notranslate">k</span>}}& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& {\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 1</span>}}& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& {\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}\end{array}\right]}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 13</span>}<span\; class="notranslate">\; )</span>$

Step 5.3.3, using the least square method to solve formula (9), the undetermined parameter vector X can be obtained:

X＝(A ^T A) ^-1 A ^T L (14)

Step 5.4, using the correction step size of the user terminal position coordinates obtained in step 5.3 to correct the approximate position coordinates of the user terminal;

Put the undetermined parameter vector X calculated by formula (14) into the following formula to correct the approximate position coordinates of the user terminal:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}^{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;X</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}\\ {\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>{{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}^{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;Y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}\\ {\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>{{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}^{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;Z</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 15</span>}<span\; class="notranslate">\; )</span>$

Step 5.5, using the corrected position coordinates of the user terminal as the approximate position coordinates of the user terminal to repeat steps 5.2 to 5.4 for iterative calculation until the iteration end condition is satisfied, the position coordinates of the user terminal obtained at this time are the user terminal position exact coordinates.

According to the needs of practical applications, the iteration end condition can be a number requirement (for example, the maximum number of iterations is 5) or an accuracy requirement (for example, the difference between each coordinate value of the two iterations before and after is less than a certain fixed value, such as 0.5 meters) .

Step 6, using the physical precision enhancement factor to evaluate the positioning accuracy of the user terminal.

In this step, the geometric precision attenuation matrix Q is introduced first:

$\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{cccc}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}& {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}& {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}& {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 14</span>}}\\ {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}& {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}& {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; three</span>}}& {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; four</span>}}\\ {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 31</span>}}& {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 32</span>}}& {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 33</span>}}& {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 34</span>}}\\ {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 41</span>}}& {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 42</span>}}& {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 43</span>}}& {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 44</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>$

Further, get:

${\mathrm{<span\; class="notranslate">\; DOP</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\sqrt{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}}<span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="DOP"\; filenames="HDA0000148813370000011.png"\; state="\{\{state\}\}">DOP</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\sqrt{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 33</span>}}}<span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; DOP</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>\sqrt{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 33</span>}}}<span\; class="notranslate">\; ,</span>$

${\mathrm{<span\; class="notranslate">\; DOP</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; =</span>\sqrt{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 44</span>}}}<span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; DOP</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; =</span>\sqrt{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 33</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 44</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 17</span>}<span\; class="notranslate">\; )</span>$

DOP _i is the geometric precision attenuation factor of the multi-frequency point satellite navigation and positioning constellation, and i=1, 2, 3, 4, 5 correspond to the plane (HDOP), elevation (VDOP), position (PDOP), clock difference (TDOP) and The overall Geometric Decay of Precision (GDOP).

When each navigation satellite adopts a single carrier frequency point, that is, N _j = 1 (j=1, 2, ..., M) in formula (11), the geometric precision attenuation factor obtained according to formula (16) and (17) is recorded as is DOP ₀ , then the physical precision enhancement factor PAFP can be defined as:

$\mathrm{<span\; class="notranslate">\; PAFP</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; DOP</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{{\mathrm{<span\; class="notranslate">\; DOP</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 18</span>}<span\; class="notranslate">\; )</span>$

Using the physical precision enhancement factor PAFP, the positioning error of the user terminal can be described as:

σ _i = DOP _i PAFP σ _UERE (19)

Among them, σ _i is the positioning error of the user terminal, and σ _UERE is the equivalent pseudorange measurement error.

In addition to the above-mentioned positioning method based on pseudorange measurement of multiple carrier frequency points, the physical precision enhancement factor PAFP can also be used to evaluate a positioning method based on Doppler frequency shift measurement of multiple carrier frequency points. In general, the present invention is a physical method of doubling positioning accuracy.

The specific embodiments described above have further described the purpose, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above descriptions are only specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims (10)

1. the method for multiplication bearing accuracy in the satellite navigation and location system is used for the high-precision point location of user terminal, it is characterized in that the method may further comprise the steps:

Step 1, each Navsat in M the Navsat of satellite navigation and location system inside will be modulated to a plurality of carrier frequency points to the navigation signal that is used for navigator fix that user terminal to be positioned sends, wherein, M 〉=4, described navigation signal comprise that Pseudo-Random Noise Code, navigation message and wide area strengthen information;

Step 2 sends described Pseudo-Random Noise Code and navigation message downwards with a plurality of carrier frequency points;

Step 3, user terminal receives described Pseudo-Random Noise Code and the navigation message that all Navsats issue by a plurality of carrier frequency points;

Step 4, user terminal corrects parameter according to the clock that the described navigation message that receives obtains Navsat; According to the Navsat ephemeris in the described navigation message that receives, obtain the orbital position of Navsat; Correct the orbit error of Navsat according to the described navigation signal that receives; User terminal obtains on each carrier frequency point each Navsat to the measurement pseudorange of user terminal according to Pseudo-Random Noise Code, corrects ionospheric delay, troposphere time delay and the Multipath Errors of measuring in the pseudorange according to the described navigation signal that receives;

Step 5, user terminal be according to the measurement pseudorange that has corrected ionospheric delay, troposphere time delay and Multipath Errors, and the satellite orbital position after correcting carries out Iterative to the position coordinates of user terminal, finally obtains the accurate coordinate of user terminal location;

Step 6 uses the physical accuracy enhancer that the bearing accuracy of user terminal is estimated.

2. method according to claim 1 is characterized in that, described Pseudo-Random Noise Code can identify Navsat separately corresponding to each Navsat; Utilize the auto-correlation of described Pseudo-Random Noise Code and the mistiming that their cross correlation comes the transmission of measure and navigation signal, this mistiming multiply by the electric wave transmission speed and is Navsat to the measurement pseudorange of user terminal; The clock that described navigation message includes system time, Navsat corrects parameter, ionosphere delay model parameter, Navsat ephemeris and satellite health situation; Described wide area enhancing information comprises correction data and the integrity information of Navsat track.

3. method according to claim 2 is characterized in that, described measurement pseudorange satisfies following pseudorange observation equation simultaneously:

${\mathrm{\&rho;}}_k^{j,i}={[{(X^j-X_k)}^2+{(Y^j-Y_k)}^2+{(Z^j-Z_k)}^2]}^{1/2}$

$+b_k-{\mathrm{c\&delta;t}}^j+{\mathrm{\&delta;\&rho;}}_{k_n}^{j,i}+{\mathrm{\&delta;\&rho;}}_{k_P}^{j,i}+v_k^{j,i}$

$(j=\mathrm{1,2},...,M;i=\mathrm{1,2},...,N_j)$

Wherein, For measuring constantly t _k, the Navsat S at i frequency that user terminal measurement obtains _jTo the measurement pseudorange of user terminal, i=1,2 ..., N _j, j=1,2 ..., M; (X _k, Y _k, Z _k) be that user terminal to be positioned is at moment t _kAccurate coordinate; (X ^j, Y ^j, Z ^j) be Navsat S _jPosition coordinates when the emission navigation signal; b _kEquivalent distances for user terminal clock correction; δ t ^jClock correction parameter for Navsat; C is vacuum light speed,

Be the ionospheric delay before correcting,

Be the troposphere time delay before correcting,

Be stochastic error.

4. method according to claim 1 is characterized in that, described step 4 further comprises: the orbit error that corrects the data correction Navsat according to the satellite orbit in the described wide area enhancing information that receives; Correct the ionospheric delay of measuring pseudorange according to the ionosphere delay model parameter in ionosphere delay model and the described navigation message that receives; User terminal gathers local meteorologic parameter, and according to the orbital position of Navsat, utilizes tropospheric delay to correct the troposphere time delay of measuring pseudorange; According to the environmental aspect of locality, utilize the multipath correction model to correct the Multipath Errors of measuring pseudorange.

5. method according to claim 4 is characterized in that, described step 5 further may further comprise the steps:

Step 5.1 is at first set the initial value of a user terminal location coordinate as the general location coordinate (X of user terminal _k ⁰, Y _k ⁰, Z _k ⁰);

Then step 5.2 carries out 1 rank Taylor series expansion to described pseudorange observation equation, obtains containing linearization form user terminal location coordinate modification step-length, described pseudorange observation equation;

Step 5.3 is found the solution the linearization pseudorange observation equation that described step 5.2 obtains, and obtains the correction step-length of user terminal location coordinate;

Step 5.4 uses the correction step-length of the user terminal location coordinate that described step 5.3 obtains that the general location coordinate of user terminal is revised;

Step 5.5, the position coordinates of revised user terminal is carried out iterative computation as the general location coordinate repeating step 5.2-step 5.4 of user terminal, until satisfy the iteration termination condition, the position coordinates of the user terminal that obtain this moment is the accurate coordinate of user terminal location, and described iteration termination condition is number of times requirement or accuracy requirement.

6. method according to claim 5 is characterized in that, the linearization form of described pseudorange observation equation is:

$v_k^{j,i}=l_k^j{\mathrm{\&delta;X}}_k+m_k^j{\mathrm{\&delta;Y}}_k+n_k^j{\mathrm{\&delta;Z}}_k$

$-b_k+{\mathrm{\&rho;}}_k^{j,i}-{R_k}^j+{\mathrm{c\&delta;t}}^j-{\mathrm{\&delta;\&rho;}}_{k_n}^{j,i}-{\mathrm{\&delta;\&rho;}}_{k_P}^{j,i},$

Wherein, (δ X _k, δ Y, δ Z _k) be the correction step-length of user terminal location coordinate, For the general location coordinate of user terminal to Navsat S _jDirection cosine:

$l_k^j=\frac{X^j-{X_k}^0}{{R_k}^j},$ $m_k^j=\frac{Y^j-{Y_k}^0}{{R_k}^j},$ $n_k^j=\frac{Z^j-{Z_k}^0}{{R_k}^j},$

R _k ^jFor the general location coordinate of user terminal to Navsat S _jDistance:

R _k ^j＝[(X ^j-X _k ⁰) ²+(Y ^j-Y _k ⁰) ²+(Z ^j-Z _k0) ²] ^1/2。

7. method according to claim 5 is characterized in that, described step 5.3 further may further comprise the steps:

Step 5.3.1 uses the known terms in the linearizing pseudorange observation equation Expression:

$v_k^{j,i}=l_k^j{\mathrm{\&delta;X}}_k+m_k^j{\mathrm{\&delta;Y}}_k+n_k^j{\mathrm{\&delta;Z}}_k-b_k-L_k^{j,i},$

Wherein, $L_k^{j,i}={R_k}^j-{\mathrm{\&rho;}}_k^{j,i}-{\mathrm{c\&delta;t}}^j+{\mathrm{\&delta;\&rho;}}_{k_n}^{j,i}+{\mathrm{\&delta;\&rho;}}_{k_P}^{j,i};$

Step 5.3.2, write following formula as matrix form:

V＝AX-L，

Wherein, X is the undetermined parameter vector:

X＝[δX _k δY _k δZ _k b _k] ^T，

A is the matrix of coefficients of undetermined parameter:

Each Navsat S _jCorresponding N in matrix A _jThe submatrix of row 4 row,

L is the constant term vector:

$L={\left[\begin{array}{ccccccccccc}{L}_k^{\mathrm{1,1}}& ...& L_k^{1,N_1}& L_k^{\mathrm{2,1}}& ...& L_k^{2,N_2}& ...& ...& L_k^{M,1}& ...& L_k^{M,N_M}\end{array}\right]}^T$

V is the stochastic error vector:

$V={\left[\begin{array}{ccccccccccc}{v}_k^{\mathrm{1,1}}& ...& v_k^{1,N_1}& v_k^{\mathrm{2,1}}& ...& v_k^{2,N_2}& ...& ...& v_k^{M,1}& ...& v_k^{M,N_M}\end{array}\right]}^T$

Step 5.3.3 utilizes the linearization pseudorange observation equation of least square method solution matrix form, obtains undetermined parameter vector X:

X＝(A ^TA) ^-1A ^TL。

8. method according to claim 7 is characterized in that, described physical accuracy enhancer PAFP is defined as:

$\mathrm{PAFP}=\frac{{\mathrm{DOP}}_i}{{\mathrm{DOP}}_0},$

Wherein, DOP _iBe the geometric dilution of precision of multi-frequency-point satellite navigation location constellation, i=1,2,3,4,5 is corresponding flat, elevation, position, clock correction and total geometric dilution of precision respectively:

${\mathrm{DOP}}_1=\sqrt{D_{11}+D_{22}},$ ${\mathrm{DOP}}_2=\sqrt{D_{33}},$ ${\mathrm{DOP}}_3=\sqrt{D_{11}+D_{22}+D_{33}},$ ${\mathrm{DOP}}_4=\sqrt{D_{44}},$ ${\mathrm{DOP}}_5=\sqrt{D_{11}+D_{22}+D_{33}+D_{44}},$

Wherein, D ₁₁, D ₂₂, D ₃₃, D ₄₄Be the diagonal entry of geometric accuracy damping matrix Q, described geometric accuracy damping matrix Q is expressed as:

$Q={\left(A^{T}A\right)}^{-1}=\left[\begin{array}{cccc}{D}_{11}& D_{12}& D_{13}& D_{14}\\ D_{21}& D_{22}& D_{23}& D_{24}\\ D_{31}& D_{32}& D_{33}& D_{34}\\ D_{41}& D_{42}& D_{43}& D_{44}\end{array}\right],$

DOP ₀Geometric dilution of precision when adopting the single carrier frequency for every Navsat.

9. method according to claim 8 is characterized in that, utilizes the positioning error of the user terminal that described physical accuracy enhancer PAFP obtains to be:

σ _i＝DOP _i·PAFP·σ _UERE，

Wherein, σ _iBe the positioning error of user terminal, σ _UEREBe equivalent pseudo range measurement error;

Described physical accuracy enhancer PAFP also can be used for for the evaluation based on the localization method of the Doppler shift measurement of a plurality of carrier frequency points.

10. method according to claim 1 is characterized in that, described user terminal is fixed terminal or portable terminal, and described fixed terminal is the fixed satellite receiving equipment, and described portable terminal is vehicle-mounted, boat-carrying or hand-held receiving equipment.

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