Low-cost embedded real-time high-precision positioning system based on BDS + GPS dual-system adaptive fusion RTK resolving algorithm

Abstract

The invention discloses a low-cost embedded real-time high-precision positioning system based on a BDS + GPS dual-system adaptive fusion RTK resolving algorithm. The self-designed low-cost embedded high-precision positioning system comprises an LTE-CAT1 network communication module with an embedded open source SOC processor, a low-cost GNSS satellite signal receiving module, a power management unit, a gravitational acceleration chip and a related connector, and comprises a BDS + GPS dual-system adaptive fusion RTK resolving algorithm. The algorithm comprises the following steps: establishing an RTK double-difference observation equation according to original observation data of BDS + GPS dual systems of a base station and a moving station; carrying out Kalman filtering solution and robust Kalman adaptive filtering estimation; fusing Hurmet variance component estimation; and the RTK ambiguity of the BDS + GPS dual system is fixed. According to the invention, multiple robust estimation is added, so that the low-cost embedded high-precision positioning system can achieve a centimeter-level high-precision stable positioning result in a complex environment. The invention belongs to the technical field of navigation and positioning, and particularly relates to a low-cost embedded real-time high-precision positioning system based on a BDS + GPS dual-system adaptive fusion RTK resolving algorithm.

Description

Technical Field

[0001] The invention belongs to the technical field of navigation and positioning, and specifically relates to a low-cost embedded real-time high-precision positioning system based on a BDS+GPS dual-system adaptive fusion RTK solution algorithm. Background Art

[0002] BeiDou Navigation Satellite System (BDS) is a satellite navigation and positioning system independently developed by my country with independent intellectual property rights. It is the third satellite navigation system that can be positioned internationally after the GPS of the United States and the GLONASS of Russia. With the continuous development of the global satellite navigation system, the combination of different satellite constellations has gradually increased the number of visible satellites, and the spatial geometric distribution of satellites has also become more perfect. The BDS+GPS dual-system fusion RTK solution provides a more reliable guarantee for high-precision positioning due to the introduction of more visible satellites. Single-constellation positioning has some shortcomings, such as limited visible satellites and weak stability. Therefore, the research on BDS+GPS dual-system navigation and positioning has become a new hot spot in navigation and positioning. The use of BDS+GPS dual-system combined positioning will double the number of satellites, which is conducive to enhancing the strength of satellite geometry and improving positioning accuracy and stability. At the same time, the development of BDS+GPS dual systems has also posed challenges to the compatibility and scalability of positioning models of different systems and frequencies. In the BDS+GPS combined navigation positioning, the receiver needs to receive navigation information from different satellite constellations. Since there is a certain system deviation between the two systems, the problem of time and space unification needs to be considered in the BDS+GPS combined navigation positioning. The time bases used by BDS and GPS are different. BDS uses Beidou time as the time base, while GPS uses GPS time as the time base. The Beidou start time is 00:00:00 on January 1, 2006, and the GPS start time is 00:00:00 on January 6, 1980. In addition, both time systems have no leap seconds. The start time is inconsistent, and the time needs to be converted to GPST to unify the time base. Although BDS uses the CGCS2000 coordinate system and GPS uses the WGS-84 coordinate system, the coordinate origins and orientations of the two coordinate systems are consistent. The coordinate changes of the same point in the CGCS2000 coordinate system and the WGS-84 coordinate system are caused by the difference in the flattening of the reference ellipsoids of the two coordinate systems, and they are approximately considered to belong to the same reference frame.

[0003] Due to the differences in the distribution of satellite constellations and satellite orbits of various satellite navigation systems, the navigation positioning performance and observation accuracy of each system are different. The GNSS multi-system fusion positioning only determines the weights of the observation values ​​of each system based on the prior accuracy, which is not accurate and reliable. At the same time, in cities, canyons and other areas, due to the complex observation environment, satellite signals form multipath or non-line-of-sight signals due to reflection or scattering of buildings, which increases the probability of observation values ​​containing gross errors or anomalies, and the carrier motion model under dynamic conditions is difficult to accurately model, making the conventional Kalman filter positioning solution prone to large deviations or even divergence. For BDS+GPS system fusion positioning, especially in complex environments, how to no longer rely on prior theories or empirical values ​​to determine the weights of observation values ​​between each navigation system and each satellite, and adaptively adjust the weights of observation values ​​between each navigation system and between satellites. The double difference observation value has the advantages of eliminating the receiver clock error and satellite clock error, greatly weakening the influence of satellite ephemeris error, ionospheric delay error, tropospheric delay error and other errors, and the double difference ambiguity has integer characteristics, which is of great significance to improving the accuracy and availability of GNSS multi-system fusion RTK positioning. The present invention is a low-cost embedded real-time high-precision positioning system based on a BDS+GPS dual-system adaptive fusion RTK solution algorithm. Summary of the invention

[0004] The purpose of the present invention is to provide a low-cost embedded real-time high-precision positioning system based on the BDS+GPS dual-system adaptive fusion RTK solution algorithm. The hardware platform of the embedded real-time high-precision positioning system includes an LTE CAT1 network communication module with an embedded open source SOC processor, a GNSS satellite signal receiving module, a power management unit, a gravity acceleration chip and related connectors, and a GNSS satellite signal processing module is externally connected to a GNSS helical antenna. The GNSS helical antenna improves the sensitivity of receiving satellite signals, and the satellite signals are modulated and demodulated by the satellite signal processing module to obtain satellite data in RTCM format. The power management unit provides stable voltage for each functional module and chip of the embedded platform, and the LTE CAT1 network communication module is used to obtain base station data from the network in real time.

[0005] The GNSS satellite signal receiving module uses the low-cost MXT906 module of Wuhan Mengxin Company. The MXT906B multi-system multi-frequency RTK high-precision navigation and positioning module is a professional high-precision positioning module for centimeter-level high-precision positioning applications. The module supports BDS, GPS / QZSS, GLONASS multi-systems and multi-frequency points, and has an internal integrated dual-frequency RTK algorithm, which can provide stable centimeter-level high-precision positioning services. The MXT906B has a compact size, uses LGA pads, supports standard pick-and-place and reflow soldering, has the characteristics of anti-interference, small size, low power consumption, and high precision, and is a cost-effective professional centimeter-level high-precision navigation and positioning module.

[0006] MXT906 module main features:

[0007] Can simultaneously receive multi-system multi-frequency signals (frequency bands: BDS-B1I, B2I, GPS / QZSS-L1C / A, L2C, GLONASS-L1, L2);

[0008] Support BeiDou-3 satellite signal system;

[0009] Dual-frequency RTK algorithm, centimeter-level positioning accuracy (single point positioning: 2.0m, RTK: 0.02m+1ppm);

[0010] Support raw observation output

[0011] --Pseudorange observation accuracy GPS L1C / A <= 20cm L2C <= 40cm, BDS B1I <= 20cm B2I <= 20cm, GLONASS L1 <= 40cm L2 <= 40cm);

[0012] --Carrier observation accuracy GPS L1C / A≤1mm L2C≤2mm, BDS B1I≤1mm B2I≤1mm,

[0013] GLONASS L1≤1mm L2≤1mm;

[0014] --Fixed solution convergence time ≤10s;

[0015] --Data update rate 1 / 2 / 5 / 10Hz

[0016] Smart SuppressTM anti-interference technology;

[0017] Navigation data format NMEA0183 V4.10, RTCM3.X;

[0018] The MXT906 module supports RTCM3.X protocol differential data input for RTK positioning solution. The external base station differential data can be sent to the module through the serial port to achieve RTK differential positioning.

[0019] The RTCM3.X message types supported by input are:

[0020] RTCM3.X message types Message Description 1005 / 1006 Base station coordinates 1074 GPS observations, including L1 and L2 frequency points 1084 GLONASS observations, including G1 and G2 frequencies 1114 QZSS observations, including L1 and L2 frequency points 1124 BDS observations must include B1 and B2 frequency points

[0021] The MXT906 module supports raw observation output and ephemeris output, and the data format supports the RTCM3.X protocol.

[0022] The RTCM3.X message types supported by the output are:

[0023]

[0024]

[0025] The embedded open source SOC processor LTE CAT1 network communication module adopts Hezhou's low-power and low-cost Air724, which is an ultra-small package LTE Cat.1bis module; the embedded OPENCPU adopts Unisoc's UIS8910 platform, supports secondary development, supports LTE 3GPP Rel.13 technology, and is a 4G full network access module. Air724 has built-in rich network protocols, integrates multiple industrial standard interfaces, and supports multiple drivers and software functions (such as USB drivers under Windows XP, Windows Vista, Windows7 / 8 / 8.1 / 10, Linux, Android and other operating systems), supports FOTA upgrades (supports Luat cloud background, Xinsimai custom background, Air724 supports frequency bands: LTE-TDD: B34 / B38 / B39 / B40 / B41, LTE-FDD: B1 / B3 / B5 / B8; supports data, LTE TDD--uplink and downlink ratio 2: maximum 8Mbps (DL) / maximum 2Mbps (UL), uplink and downlink ratio 1: maximum 6Mbps (DL) / maximum 4Mbps (UL); LTE FDD--maximum 10Mbps (DL) / maximum 5Mbps (UL).

[0026] The embedded real-time high-precision positioning system of the present invention uses the real-time csRTOS embedded operating system independently developed based on the LUA open platform as the operating system running on the system hardware. Through the real-time csRTOS, the open source SOC processor embedded in the LTE CAT1 network communication module is used to develop and execute the BDS+GPS dual-system adaptive fusion RTK solution algorithm in conjunction with the GNSS satellite signal receiving and processing module.

[0027] The adaptive fusion RTK solution algorithm based on the BDS+GPS dual system adopted in the present invention is used to effectively reduce the influence of the inaccurate prior random model of GNSS positioning, the observation anomaly, and the anomaly of the dynamic model on the BDS+GPS dual system fusion RTK positioning, and improve the positioning accuracy of the BDS+GPS dual system fusion RTK, so that the RTK positioning result is more stable and reliable in complex environments. The BDS+GPS dual system adaptive fusion RTK solution algorithm includes the following steps:

[0028] Step 1: Establish the conventional RTK double-difference observation equation based on the BDS+GPS dual-system observation data of the base station and the rover;

[0029] Step 2: Conventional Kalman filter solution;

[0030] Step 3: Robust Kalman adaptive filter estimation;

[0031] Step 4: Helmett variance component estimation of BDS+GPS dual system fusion;

[0032] Step 5: BDS+GPS dual system RTK ambiguity is fixed.

[0033] Further, as a preferred technical solution, the specific process of step 1 is:

[0034] Step 1-1: Establish the basic observation equation based on the original pseudorange and carrier phase observations, as follows:

[0035] In the formula, the subscripts i and r are the frequency and station of the observed quantity, respectively, and the superscript s is the number of GPS and BDS satellites;

[0036] are the pseudorange and carrier phase raw observation values, in meters, respectively. is the phase observation value (week);

[0037] is the geometric distance between the satellite and the station at the time of signal transmission, c is the speed of light in vacuum, δt r and δt j are the receiver clock error and satellite clock error respectively, T s is the tropospheric delay, is the ionospheric delay at frequency i, and are the pseudorange hardware delay bias at the receiver and satellite, and are the phase hardware delay deviations of the receiver and satellite, including the carrier phase hardware delay deviation and the initial phase deviation, λ i and is the carrier phase wavelength and integer ambiguity of frequency i, and are the measurement noise of pseudorange and carrier phase observations, respectively;

[0038] Step 1-2: According to the RTK double-difference model, the satellite clock error and receiver clock error in step 1-1 can be eliminated, and the influence of satellite orbit error, tropospheric delay error, ionospheric delay error and multipath effect can be weakened, and the carrier phase double-difference observation equation can be established, as follows:

[0039]

[0040] In the formula, the superscripts m and n represent the number of GPS satellites and BDS satellites; the subscripts r and b represent the mobile station and the base station;

[0041] is the double difference phase observation value at epoch t; is the distance from satellite s to station r; is the double difference ambiguity; since the reference coordinates are known, the above formula can be transformed into:

[0042]

[0043] Step 1-3: The prior coordinates of the mobile station are estimated using single point positioning, and the approximate estimate X r =(x r ,y r ,z r ) T , let the correction number be dX r =(dx r ,dy r ,dz r ) T , linearizing the final transformed equation in step 1-2 yields the carrier phase double difference error equation:

[0044]

[0045] In the formula,

[0046]

[0047] Similarly, the pseudorange double difference error equation can be obtained:

[0048]

[0049] in, is the double-difference pseudorange observation value.

[0050] Further, as a preferred technical solution, the specific process of step 2 is:

[0051] Step 2-1: Establish the state equation and observation equation of Kalman filter:

[0052] X k =Φ k,k-1 X k-1 +W k-1

[0053] L k =H k X k +V k

[0054] Where k represents the observation epoch time, X k represents the state vector at time k, Φ k,k-1represents the transition matrix of the system state from time k-1 to time k, W k-1 is the dynamic noise vector, L k is the observation vector at time k, H k is the observation equation coefficient matrix, V k is the observation noise vector;

[0055] Step 2-2: The observations are considered to be independent of each other. The dynamic noise and observation noise are zero-mean, uncorrelated white noises, which satisfy the following conditions:

[0056]

[0057] In the formula, Ω k is the variance matrix of process noise, Q k is the variance matrix of the observation noise;

[0058] Step 2-3: Rewrite the state equation and observation equation into error equations respectively:

[0059]

[0060] In the formula, and V k are the predicted values ​​of state parameters, and the observed value L k The residual vector of the state parameter is for:

[0061]

[0062] The covariance matrix of can be obtained:

[0063]

[0064] Construct the objective function according to the least squares criterion:

[0065]

[0066] Where P k and are the observed values ​​L k and state parameter forecast values The weight matrix of

[0067] Paired Partial derivative and set its partial derivative equal to 0, we have:

[0068]

[0069] Further we can get:

[0070]

[0071] Step 2-4: Substitute the error equation corresponding to the observation equation into formula (1) to obtain:

[0072]

[0073] Furthermore, as a preferred technical solution, the general process of Kalman filter calculation is further derived from the matrix identity transformation and matrix inversion formula:

[0074] Step 2-4-1: Calculate the Kalman filter gain matrix K based on the prediction accuracy of the previous epoch for the current epoch k ,

[0075]

[0076] Step 2-4-2: Update the current epoch observations, i.e. use the weights of the current epoch measurements for weighted correction.

[0077]

[0078] Step 2-4-3: Update time, that is, predict the observation value of the next epoch.

[0079] Further, as a preferred technical solution, the specific process of step 3 is:

[0080] Step 3-1: The adaptive Kalman filter solution is:

[0081]

[0082] In the formula, For L k The equivalent weight matrix of , which is the adaptive estimate of the observation vector weight matrix, α k is the adaptive factor, 0≤α k ≤1;

[0083] Step 3-2: Determine equivalent weights and adaptive weights.

[0084] Furthermore, as a preferred technical solution, the specific calculation process of the equivalent weight factor is:

[0085] Step 3-2-1: In the BDS+GPS dual-system fusion positioning, the observation values ​​between the systems are independent of each other, and the corresponding equivalent weights are: Where P i It is the original power array. is the adaptive weight factor;

[0086] Step 3-2-2: Determine the weight factor using the IGG-III equivalent weight factor or the double-factor equivalent weight factor function, wherein the function expression based on the IGG-III equivalent weight factor is:

[0087]

[0088] In the formula, is the standardized residual, k0, k1 are constants, generally k0 = 1.5 ~ 2.0, k1 = 3.0 ~ 8.0; the function expression based on the double factor equivalent weight factor is:

[0089]

[0090] In the formula, c is a constant, c = 2.5 ~ 3.0, i, j represents the row and column numbers of the matrix;

[0091] Step 3-2-3: Calculate standardized residuals

[0092] σ v =1.483 mede i

[0093] Step 3-2-4: For different types of observations, their standardized residuals for:

[0094]

[0095] In the formula,

[0096] σ MAD =1.483 mede i -mede i

[0097] Furthermore, as a preferred technical solution, the specific calculation process of the equivalent weight factor is:

[0098] Adopt two-segment function to calculate adaptive weight factor a k ,Right now:

[0099]

[0100] In the formula, c is a constant, ranging from 1.0 to 2.5.

[0101]

[0102] In the formula, is the standardized prediction residual, is the state parameter prediction residual, is the trace of the state parameter prediction residual covariance matrix.

[0103] Further, as a preferred technical solution, the specific process of step 4 is:

[0104] Step 4-1: During the first filtering, the BDS+GPS dual system observations are weighted according to the satellite elevation angle. C :P G ;

[0105] Step 4-2: Perform filtering and solve to obtain V i T P i V i (i=C,G);

[0106] Step 4-3: Estimation of variance components:

[0107]

[0108] In the formula,

[0109] Among them, N C 、N G are the number of BDS+GPS dual system observations respectively;

[0110] Step 4-4: Re-evaluation:

[0111]

[0112] In the formula, c is any constant, optional A value in ;

[0113] Step 4-5: Repeat steps 4-2 to 4-4 until The difference is less than 0.01.

[0114] Furthermore, as a preferred technical solution, when the iteration does not converge or converges distortedly in step 4, the satellites are re-screened or the weights of certain satellites are appropriately reduced before solving the problem.

[0115] Furthermore, as a preferred technical solution, in step 5, the BDS+GPS dual-system RTK ambiguity is fixed by using a least squares ambiguity reduction correlation adjustment method combined with a partial ambiguity fixing strategy.

[0116] Compared with the prior art, the present invention has the following beneficial effects:

[0117] The present invention aims at the BDS+GPS dual-system adaptive fusion RTK solution algorithm. Firstly, the weights of the BDS and GPS satellite observation values ​​are adjusted by adopting the robust Kalman adaptive filtering to suppress the influence of observation anomalies and dynamic model errors on RTK valuation parameters. Secondly, the variance component estimation is adopted to adaptively adjust the weights of the observation values ​​between the satellite navigation systems (BDS, GPS). The weight ratio between observation values ​​of different types or unequal precision is adaptively adjusted through iterative calculation, so that the weight distribution is more reasonable, and the GNSS multi-system fusion RTK positioning is more accurate and reliable in complex environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0118] Figure 1 This is a system hardware framework diagram of a low-cost embedded real-time high-precision positioning system based on BDS+GPS dual-system adaptive fusion RTK solution algorithm;

[0119] Figure 2 This is the flow chart of the BDS+GPS dual system adaptive fusion RTK solution algorithm; DETAILED DESCRIPTION

[0120] The present invention will be further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0121] Example:

[0122] like Figure 1As shown, the system hardware framework diagram of a low-cost embedded real-time high-precision positioning system based on the BDS+GPS dual-system adaptive fusion RTK solution algorithm described in this embodiment. The hardware platform includes an LTE CAT1 network communication module with an embedded open source SOC processor, a GNSS satellite signal receiving module, a power management unit, a gravity acceleration chip and related connectors, and the GNSS satellite signal processing module is externally connected to a GNSS spiral antenna; the GNSS spiral antenna is used to receive satellite signals, and the satellite signals are modulated and demodulated by the satellite signal processing module to obtain satellite data in RTCM format; the power management unit provides stable voltage for each functional module and chip of the embedded platform; the LTE CAT1 network communication module is used to obtain base station data from the network in real time. The GNSS satellite signal receiving module in the embodiment adopts the MXT906 module of Wuhan Mengxin Company, which provides low-cost mobile stations. The MXT906 module supports BDS, GPS, GLONASS, Galileo, and QZSS multi-system multi-frequency satellite signals. Based on the MXT906 module, not only the RTCM messages broadcast by the autonomous base station are received to achieve high-precision positioning, but also the RTCM format data can be obtained through the commercial positioning platform to achieve the positioning function; the embedded open source SOC processor LTE CAT1 network communication module adopts Hezhou's low-power and low-cost Air724; the embedded real-time high-precision positioning system selects the csRTOS embedded operating system as the operating system of the device.

[0123] like Figure 2 As shown in the flowchart of the BDS+GPS dual system adaptive fusion RTK solution algorithm described in this embodiment, the BDS+GPS dual system adaptive fusion RTK solution algorithm described in this embodiment includes the following steps:

[0124] Step 1: Establish the conventional RTK double-difference observation equation based on the BDS+GPS dual-system observation data of the base station and the rover;

[0125] Step 2: Conventional Kalman filter solution;

[0126] Step 3: Robust Kalman adaptive filter estimation;

[0127] Step 4: Helmett variance component estimation of BDS+GPS dual system fusion;

[0128] Step 5: BDS+GPS dual system RTK ambiguity is fixed.

[0129] The specific process of step 1 in this embodiment is:

[0130] Step 1-1: Establish the basic observation equation based on the original pseudorange and carrier phase observations, as follows:

[0131] In the formula, the subscripts i and r are the frequency and station of the observed quantity, respectively, and the superscript s is the number of GPS and BDS satellites;

[0132] are the pseudorange and carrier phase raw observation values, in meters, respectively. is the phase observation value (week);

[0133] is the geometric distance between the satellite and the station at the time of signal transmission, c is the speed of light in vacuum, δt r and δt j are the receiver clock error and satellite clock error respectively, T s is the tropospheric delay, is the ionospheric delay at frequency i, and are the pseudorange hardware delay bias at the receiver and satellite, and are the phase hardware delay deviations of the receiver and satellite, including the carrier phase hardware delay deviation and the initial phase deviation, λ i and is the carrier phase wavelength and integer ambiguity of frequency i, and are the measurement noise of pseudorange and carrier phase observations, respectively;

[0134] Step 1-2: According to the RTK double-difference model, the satellite clock error and receiver clock error in step 1-1 can be eliminated, and the influence of satellite orbit error, tropospheric delay error, ionospheric delay error and multipath effect can be weakened, and the carrier phase double-difference observation equation can be established, as follows:

[0135]

[0136] In the formula, the superscripts m and n represent the number of GPS satellites and BDS satellites; the subscripts r and b represent the mobile station and the base station;

[0137] is the double difference phase observation value at epoch t; is the distance from satellite s to station r; is the double difference ambiguity; since the reference coordinates are known, the above formula can be transformed into:

[0138]

[0139] Step 1-3: The prior coordinates of the mobile station are estimated using single point positioning, and the approximate estimate X r =(x r ,y r ,z r )T , let the correction number be dX r =(dx r ,dy r ,dz r ) T , linearizing the final transformed equation in step 1-2 yields the carrier phase double difference error equation:

[0140]

[0141] In the formula,

[0142]

[0143] Similarly, the pseudorange double difference error equation can be obtained:

[0144]

[0145] in, is the double-difference pseudorange observation value.

[0146] The specific process of step 2 of this embodiment is:

[0147] Step 2-1: Establish the state equation and observation equation of Kalman filter:

[0148] X k =Φ k,k-1 X k-1 +W k-1

[0149] L k =H k X k +V k

[0150] Where k represents the observation epoch time, X k represents the state vector at time k, Φ k,k-1 represents the transition matrix of the system state from time k-1 to time k, W k-1 is the dynamic noise vector, L k is the observation vector at time k, H k is the observation equation coefficient matrix, V k is the observation noise vector;

[0151] Step 2-2: The observations are considered to be independent of each other. The dynamic noise and observation noise are zero-mean, uncorrelated white noises, which satisfy the following conditions:

[0152]

[0153] In the formula, Ω k is the variance matrix of process noise, Qk is the variance matrix of the observation noise;

[0154] Step 2-3: Rewrite the state equation and observation equation into error equations respectively:

[0155]

[0156] In the formula, and V k are the predicted values ​​of state parameters, and the observed value L k The residual vector of the state parameter is for:

[0157]

[0158] The covariance matrix of can be obtained:

[0159]

[0160] Construct the objective function according to the least squares criterion:

[0161]

[0162] Where P k and are the observed values ​​L k and state parameter forecast values The weight matrix of

[0163] Paired Partial derivative and set its partial derivative equal to 0, we have:

[0164]

[0165] Further we can get:

[0166]

[0167] Step 2-4: Substitute the error equation corresponding to the observation equation into formula (1) to obtain:

[0168]

[0169] Furthermore, as a preferred technical solution, the general process of Kalman filter calculation is further derived from the matrix identity transformation and matrix inversion formula:

[0170] Step 2-4-1: Calculate the Kalman filter gain matrix K based on the prediction accuracy of the previous epoch for the current epoch k ,

[0171]

[0172] Step 2-4-2: Update the current epoch observations, i.e. use the weights of the current epoch measurements for weighted correction.

[0173]

[0174] Step 2-4-3: Update time, that is, predict the observation value of the next epoch.

[0175] The specific process of step 3 of this embodiment is:

[0176] Step 3-1: The adaptive Kalman filter solution is:

[0177]

[0178] In the formula, For L k The equivalent weight matrix of , which is the adaptive estimate of the observation vector weight matrix, α k is the adaptive factor, 0≤α k ≤1;

[0179] Step 3-2: Determine equivalent weights and adaptive weights.

[0180] The specific calculation process of the equivalent weight factor described in the embodiment is:

[0181] Step 3-2-1: In the BDS+GPS dual-system fusion positioning, the observation values ​​between the systems are independent of each other, and the corresponding equivalent weights are: Where P i It is the original power array. is the adaptive weight factor;

[0182] Step 3-2-2: Determine the weight factor using the IGG-III equivalent weight factor or the double-factor equivalent weight factor function, wherein the function expression based on the IGG-III equivalent weight factor is:

[0183]

[0184] In the formula, is the standardized residual, k0, k1 are constants, generally k0 = 1.5 ~ 2.0, k1 = 3.0 ~ 8.0; the function expression based on the double factor equivalent weight factor is:

[0185]

[0186] In the formula, c is a constant, c = 2.5 ~ 3.0, i, j represents the row and column numbers of the matrix;

[0187] Step 3-2-3: Calculate standardized residuals

[0188] σ v =1.483 mede i

[0189] Step 3-2-4: For different types of observations, their standardized residuals for:

[0190]

[0191] In the formula,

[0192] σ MAD =1.483 mede i -mede i

[0193] The specific calculation process of the equivalent weight factor described in the embodiment is:

[0194] Adopt two-segment function to calculate adaptive weight factor a k ,Right now:

[0195]

[0196] In the formula, c is a constant, ranging from 1.0 to 2.5.

[0197]

[0198] In the formula, is the standardized prediction residual, is the state parameter prediction residual, is the trace of the state parameter prediction residual covariance matrix.

[0199] The specific process of step 4 of this embodiment is:

[0200] Step 4-1: During the first filtering, the BDS+GPS dual system observations are weighted according to the satellite elevation angle. C :P G ;

[0201] Step 4-2: Perform filtering and solve to obtain V i T P i V i (i=C,G);

[0202] Step 4-3: Estimation of variance components:

[0203]

[0204] In the formula,

[0205] Among them, N C 、N G are the number of BDS+GPS dual system observations respectively;

[0206] Step 4-4: Re-evaluation:

[0207]

[0208] In the formula, c is any constant, optional A value in ;

[0209] Step 4-5: Repeat steps 4-2 to 4-4 until The difference is less than 0.01.

[0210] When the iteration does not converge or converges distortedly in step 4, the reason for analysis is that the number of observations of various types is unbalanced. If the number of observations of one type is too small, the weight ratio determined by the Helmert variance component estimation is easily distorted; second, in the process of observation data preprocessing, if the residuals of various observations differ too much, the iteration process may not converge or the number of iterations is too many, and the S matrix will be a singular matrix and cannot be located and solved. Therefore, during the solution process, it is necessary to pay attention to the number of satellites of various types in the epoch to decide whether to use the Helmert variance component estimation; when the iteration process diverges, it is necessary to analyze the residuals of each satellite, re-screen the satellites or appropriately reduce the weights of some satellites, and then solve.

[0211] In the present embodiment, the BDS+GPS dual system RTK ambiguity fixation preferably adopts the least squares ambiguity reduction correlation adjustment method combined with the partial ambiguity fixing strategy to fix. The least squares ambiguity reduction correlation adjustment method belongs to the prior art, and it is easy to implement for those skilled in the art to fix it in combination with the partial ambiguity fixing strategy. This embodiment only provides such a preferred method.

[0212] Although the present invention has been described in detail above by general description and specific embodiments, it is obvious to those skilled in the art that some modifications or improvements can be made to the present invention. Therefore, these modifications or improvements made without departing from the spirit of the present invention all belong to the scope of protection claimed by the present invention.

Claims

1. A low-cost embedded real-time high-precision positioning system based on BDS+GPS dual-system adaptive fusion RTK solution algorithm, characterized by: The hardware platform includes an LTE CAT1 network communication module with an embedded open source SOC processor, a GNSS satellite signal receiving module, a power management unit, a gravity acceleration chip and related connectors. The GNSS satellite signal processing module is connected to an external GNSS spiral antenna; the GNSS spiral antenna is used to receive satellite signals, and the satellite signals are modulated and demodulated by the satellite signal processing module to obtain satellite data in RTCM format; the power management unit provides stable voltage for each functional module and chip of the embedded platform; the LTE CAT 1 network communication module is used to obtain base station data from the network in real time.

2. According to claim 1, a low-cost embedded real-time high-precision positioning system based on BDS+GPS dual-system adaptive fusion RTK solution algorithm is characterized by: The GNSS satellite signal receiving module adopts the MXT906 module of Wuhan Mengxin Company, which provides low-cost mobile stations. The MXT906 module supports BDS, GPS, GLONASS, Galileo, and QZSS multi-system multi-frequency satellite signals. Based on the MXT906 module, it not only receives the RTCM messages broadcast by the autonomous base station to achieve high-precision positioning, but also can obtain RTCM format data through the commercial positioning platform to achieve positioning function; the embedded open source SOC processor LTE CAT1 network communication module adopts Hezhou's low-power and low-cost Air724; the embedded real-time high-precision positioning system selects the csRTOS embedded operating system as the operating system of the device.

3. According to claim 1, a low-cost embedded real-time high-precision positioning system based on BDS+GPS dual-system adaptive fusion RTK solution algorithm is characterized in that include: The BDS+GPS dual-system adaptive fusion RTK solution algorithm is executed through the LTE CAT1 network communication module’s built-in open source SOC processor and the GNSS satellite signal receiving and processing module.

4. The BDS+GPS dual system adaptive fusion RTK solution algorithm according to claim 3 is characterized in that: The following steps are involved: Step 1: Establish the conventional RTK double-difference observation equation based on the BDS+GPS dual-system observation data of the base station and the rover; Step 2: Conventional Kalman filter solution; Step 3: Robust Kalman adaptive filter estimation; Step 4: Helmett variance component estimation of BDS+GPS dual system fusion; Step 5: BDS+GPS dual system RTK ambiguity is fixed.

5. The BDS+GPS dual system adaptive fusion RTK solution algorithm according to claim 4 is characterized in that: The specific process of step 1 is as follows: Step 1-1: Establish the basic observation equation based on the original pseudorange and carrier phase observations, as follows: In the formula, the subscripts i and r are the frequency and station of the observed quantity, respectively, and the superscript s is the number of GPS and BDS satellites; are the pseudorange and carrier phase raw observation values, in meters, respectively. is the phase observation value (week); is the geometric distance between the satellite and the station at the time of signal transmission, c is the speed of light in vacuum, δt r and δt j are the receiver clock error and satellite clock error respectively, T s is the tropospheric delay, is the ionospheric delay at frequency i, and are the pseudorange hardware delay bias at the receiver and satellite, and are the phase hardware delay deviations of the receiver and satellite, including the carrier phase hardware delay deviation and the initial phase deviation, λ i and is the carrier phase wavelength and integer ambiguity of frequency i, and are the measurement noise of pseudorange and carrier phase observations, respectively; Step 1-2: According to the RTK double-difference model, the satellite clock error and receiver clock error in step 1-1 can be eliminated, and the influence of satellite orbit error, tropospheric delay error, ionospheric delay error and multipath effect can be weakened, and the carrier phase double-difference observation equation can be established, as follows: In the formula, the superscripts m and n represent the number of GPS satellites and BDS satellites; the subscripts r and b represent the mobile station and the base station; is the double difference phase observation value at epoch t; is the distance from satellite s to station r; is the double difference ambiguity; since the reference coordinates are known, the above formula can be transformed into: Step 1-3: The prior coordinates of the mobile station are estimated using single point positioning, and the approximate estimate X r =(x r ,y r ,z r ) T , let the correction number be dX r =(dx r ,dy r ,dz r ) T , linearizing the final transformed equation in step 1-2 yields the carrier phase double difference error equation: In the formula, Similarly, the pseudorange double difference error equation can be obtained: in, is the double-difference pseudorange observation value.

6. The BDS+GPS dual system adaptive fusion RTK solution algorithm according to claim 5 is characterized in that: The specific process of step 2 is: Step 2-1: Establish the state equation and observation equation of Kalman filter: X k =Φ k,k-1 X k-1 +W k-1 L k =H k X k +V k Where k represents the observation epoch time, X k represents the state vector at time k, Φ k,k-1 represents the transition matrix of the system state from time k-1 to time k, W k-1 is the dynamic noise vector, L k is the observation vector at time k, H k is the observation equation coefficient matrix, V k is the observation noise vector; Step 2-2: The observations are considered to be independent of each other. The dynamic noise and observation noise are zero-mean, uncorrelated white noises, which satisfy the following conditions: In the formula, Ω k is the variance matrix of process noise, Q k is the variance matrix of the observation noise; Step 2-3: Rewrite the state equation and observation equation into error equations respectively: In the formula, and V k are the predicted values ​​of state parameters, and the observed value L k The residual vector of the state parameter is for: The covariance matrix of can be obtained: Construct the objective function according to the least squares criterion: Where P k and are the observed values ​​L k and state parameter forecast values The weight matrix of Paired Partial derivative and set its partial derivative equal to 0, we have: Further we can get: Step 2-4: Substitute the error equation corresponding to the observation equation into formula (1) to obtain:

7. The BDS+GPS dual system adaptive fusion RTK solution algorithm according to claim 6 is characterized in that: By using the matrix identity transformation and matrix inversion formula, the general process of Kalman filter calculation is further derived as follows: Step 2-4-1: Calculate the Kalman filter gain matrix K based on the prediction accuracy of the previous epoch for the current epoch k , Step 2-4-2: Update the current epoch observations, i.e. use the weights of the current epoch measurements for weighted correction. Step 2-4-3: Update time, that is, predict the observation value of the next epoch.

8. The BDS+GPS dual system adaptive fusion RTK solution algorithm according to claim 6 or 7, characterized in that: The specific process of step 3 is as follows: Step 3-1: The adaptive Kalman filter solution is: In the formula, For L k The equivalent weight matrix of , which is the adaptive estimate of the observation vector weight matrix, α k is the adaptive factor, 0≤α k ≤1; Step 3-2: Determine equivalent weight factors and adaptive weight factors.

9. The BDS+GPS dual system adaptive fusion RTK solution algorithm according to claim 8 is characterized in that: The specific calculation process of the equivalent weight factor is: Step 3-2-1: In the BDS+GPS dual-system fusion positioning, the observation values ​​between the systems are independent of each other, and the corresponding equivalent weights are: i=C,G Where P i It is the original power array. is the adaptive weight factor; Step 3-2-2: Determine the weight factor using the IGG-III equivalent weight factor or the double-factor equivalent weight factor function, wherein the function expression based on the IGG-III equivalent weight factor is: In the formula, is the standardized residual, k0 and k1 are constants, generally k0 = 1.5 ~ 2.0, k1 = 3.0 ~ 8.0; The function expression based on the double-factor equivalent weight factor is: In the formula, c is a constant, c = 2.5 ~ 3.0, i, j represents the row and column numbers of the matrix; Step 3-2-3: Calculate standardized residuals σ v =1.483med|e i | Step 3-2-4: For different types of observations, their standardized residuals for: In the formula, σ MAD =1,483·med|e i -med|e i ||。 10. The BDS+GPS dual system adaptive fusion RTK solution algorithm according to claim 8, characterized in that: The specific calculation process of the adaptive weight factor is: Adopt two-segment function to calculate adaptive weight factor a k ,Right now: In the formula, c is a constant, ranging from 1.0 to 2.

5. In the formula, is the standardized prediction residual, is the state parameter prediction residual, is the trace of the state parameter prediction residual covariance matrix.

11. The BDS+GPS dual system adaptive fusion RTK solution algorithm according to claim 8, characterized in that: The specific process of step 4 is as follows: Step 4-1: During the first filtering, the BDS+GPS dual system observations are weighted according to the satellite elevation angle. C :P G ; Step 4-2: Perform filtering and solve to obtain V i T P i V i (i=C,G); Step 4-3: Estimation of variance components: In the formula, Among them, N C 、N G are the number of BDS+GPS dual system observations respectively; Step 4-4: Re-evaluation: In the formula, c is any constant, optional A value in ; Step 4-5: Repeat steps 4-2 to 4-4 until The difference is less than 0.

01.

12. The BDS+GPS dual system adaptive fusion RTK solution algorithm according to claim 11 is characterized in that: When the iteration does not converge or converges distortedly in step 4, re-screen the satellites or appropriately reduce the weights of some satellites before solving the problem again.

13. The BDS+GPS dual system adaptive fusion RTK solution algorithm according to claim 5 is characterized in that: In step 5, the BDS+GPS dual-system RTK ambiguity is fixed by using the least squares ambiguity reduction correlation adjustment method combined with a partial ambiguity fixing strategy.

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