An RTK / INS Embedded Real-Time Integrated Positioning System Based on Robust Estimation
By employing two-factor robust processing and Huber equivalent weight function Kalman filtering in the RTK/INS embedded real-time integrated positioning system, the problem of low positioning accuracy caused by GNSS signal interference was solved, achieving high reliability and high accuracy navigation and positioning.
Patent Information
- Application Number
- CN202310046441.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-01-31
- Publication Date
- 2026-01-30
- Estimated Expiration
- 2043-01-31
AI Technical Summary
In urban environments, GNSS signals are easily interfered with by non-line-of-sight and multipath signals, resulting in low RTK positioning accuracy, which makes it difficult to meet the requirements of high-reliability application scenarios, and the embedded integrated navigation system cannot work properly.
To develop an RTK/INS embedded real-time integrated positioning system based on robust estimation, this paper studies a two-factor robust RTK positioning method and performs robust processing based on Huber equivalent weight function during Kalman filter update, thereby improving the accuracy and reliability of integrated navigation positioning results.
By eliminating the influence of abnormal observations, the accuracy and reliability of integrated navigation and positioning are improved, ensuring that the system can work normally in complex environments.
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Figure CN116027376B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the technical field of navigation positioning, and particularly relates to an RTK / INS embedded real-time combined positioning system based on robust estimation. BACKGROUND
[0002] Global Navigation Satellite System (GNSS) can provide global and all-weather navigation positioning and timing (PNT) services. Real-time kinematic (RTK) positioning using GNSS carrier phase observation information can achieve centimeter-level positioning accuracy. GNSS has the advantages of low cost, high accuracy, and error accumulation with time. INS (Inertial Navigation System) can also provide high-frequency and high-dynamic complete navigation parameters globally and all-weather. Due to its autonomous navigation characteristics, INS has good independence and is not affected by external interference. However, due to the influence of errors such as zero offset, the navigation error of INS will accumulate with time, making it difficult to perform long-time high-precision navigation alone. GNSS / INS combined navigation system is one of the most widely used combined navigation systems, which can ensure the continuity of navigation, reduce the cost of navigation system, enhance the reliability of navigation system, and improve the anti-interference ability of the system. The accuracy of combined navigation is mainly determined by the accuracy of satellite positioning.
[0003] In urban environments, GNSS signals are easily disturbed by non-line-of-sight (NLOS) and multipath signals in the external environment, resulting in gross errors in the observation values, which causes the estimation of the least squares to deviate. The presence of gross error observation values can seriously affect the accuracy of the position and velocity obtained by RTK. In this case, the GNSS positioning result is low in accuracy and poor in reliability, and it is difficult to meet the requirements of high-reliability application scenarios. The quality of GNSS signals will directly affect the performance of the embedded combined navigation system, making the embedded real-time combined navigation positioning system unable to work normally, and the positioning accuracy cannot be guaranteed. However, with the rapid development of automatic driving and other industries, higher requirements are put forward for the accuracy, continuity and reliability of the embedded combined navigation system, so it is crucial to perform robust estimation in combined navigation. SUMMARY
[0004] To address the aforementioned issues, this invention discloses an embedded real-time integrated positioning system based on robust estimation of RTK / INS. Developed on a fusion navigation development board, this system features dual robustness. First, a robust RTK positioning method based on two-factor robustness is investigated. Then, the obtained RTK positioning results are loosely combined with INS, and robust processing based on Huber's equivalent weight function is performed during the Kalman filter update process, thereby further improving the accuracy and reliability of the fusion navigation positioning results.
[0005] To achieve the above objectives, the technical solution of the present invention is as follows:
[0006] An embedded real-time integrated positioning system based on robust estimation using RTK / INS comprises a hardware platform including an ARM core board. The ARM core board connects to a serial communication module, a network communication module, a satellite signal receiving module, a power supply module, and an inertial module. An external GNSS antenna is connected to the satellite positioning module. The GNSS antenna receives satellite signals, which are then modulated and demodulated to obtain satellite data in RTCM format. The power supply module provides stable voltage to all functional modules of the embedded platform. The serial communication module is used for communication between the embedded hardware platform and local devices, while the network communication module is used to acquire base station data from the network in real time.
[0007] The network communication module uses the A7600 and achieves network communication through a mobile SIM card.
[0008] The satellite signal processing module uses the UM482 board from Hexin Xingtong, which supports satellite signals such as BDS B1I / B2I, GPS L1 / L2, GLONASS L1 / L2, Galileo E1 / E5b, and QZSS L1 / L2.
[0009] The voltage conversion circuit of the power module uses the DC / DC switching power conversion chip TPS5430. The 12V DC power supply is used as the input power supply of TPS5430. Necessary resistors, capacitors and diodes are added around the TPS5430 chip to form two output voltages of 5V and 3.3V.
[0010] Selecting the FreeRTOS embedded operating system as the device's operating system, a robust estimation-based RTK / INS real-time integrated positioning system based on this embedded platform includes the following steps:
[0011] Step 1: Solve the ambiguity using raw observation data such as carrier pseudorange, and fix the ambiguity using the LAMBDA algorithm.
[0012] Step 2: Substitute the fixed ambiguity back to establish a robust model and perform two-factor robust RTK.
[0013] Step 3: Initialize the inertial navigation system (INS) using IMU data and the initial position. Calculate the position, velocity, and attitude at the next moment based on the INS's mechanical choreography. Then, based on the stochastic system model, derive the error propagation equation from the INS error propagation model to establish the state equation. Use the RTK results to obtain measurements and establish the measurement equation, performing Kalman filtering for state and measurement updates.
[0014] Step 4: Construct an adaptive robust factor based on the new information, update the Kalman filter gain, obtain the Kalman filter result, perform feedback correction on the predicted position, and output a highly reliable integrated navigation result.
[0015] Step 1 includes:
[0016] Step 1-1: Set the original message format output by the satellite positioning module to RTCM format and set the sampling frequency to 1Hz. After acquisition, perform real-time decoding to obtain multi-frequency pseudorange, carrier, and satellite broadcast ephemeris.
[0017] Steps 1-2 involve performing single-point positioning and obtaining real-time base station data via the 4G network;
[0018] Steps 1-3: Formulate double-difference equations for base station data and rover data, calculate and fix the ambiguity.
[0019] Steps 1-3 include:
[0020] Establish the original pseudorange and carrier non-difference observation equations for receiver m with respect to satellite i. Perform inter-station and inter-satellite double-difference on the original pseudorange and carrier equations. Inter-station and inter-satellite double-difference eliminates receiver clock errors, satellite clock errors, and reduces ionospheric and tropospheric errors (which can be ignored when the stations are close). Use coordinate changes and double-difference ambiguities as state variables x, and use the double-difference carrier observations and station-satellite distance as observations z to establish the Kalman filter equations. The RTK positioning process is as follows:
[0021] Step 1-3-1: Establish the original pseudorange and carrier differential observation equations:
[0022]
[0023] Where ρ is the pseudorange observation value. For carrier phase observations (less than one cycle), P is the geometric distance between the receiver and the satellite, and δt is the carrier phase observation value. r and δt s Vion and Vtrop represent receiver clock bias and satellite clock bias, respectively; Vion and Vtrop represent ionospheric and tropospheric corrections, respectively; N represents integer ambiguity; and ε represents observation noise.
[0024] Step 1-3-2, further double difference between stations and between satellites to the original observation equation, double difference between stations and between satellites eliminates the receiver clock error, weakens the ionosphere and troposphere error (when the distance between stations is close, it can be ignored).
[0025]
[0026] And first-order Taylor expansion:
[0027]
[0028] That is
[0029]
[0030] Step 1-3-3, Kalman filter estimation:
[0031] According to the linear random system model:
[0032]
[0033] Where X k is the state vector; Φ k / k-1 represents the state transition matrix from epoch k-1 to k; Z k is the observation vector; H k represents the measurement matrix; W k-1 and V k are the process noise vector at epoch k-1 and the observation noise vector at k, respectively; wherein W k and V k are independent of each other, and both obey the zero mean Gaussian distribution, and the covariance matrix is represented by Q k and R k , respectively.
[0034] Kalman filter estimation:
[0035]
[0036] In the formula: K k is the gain matrix; and P k / k-1 are the predicted state vector and the predicted state covariance, respectively; P k-1 and P k are the state estimation covariance matrices at k-1 and k, respectively; I is the unit matrix;
[0037] Using Kalman filter can obtain ambiguity float solution;
[0038] Step 1-3-4, using LAMBDA algorithm to fix the double difference ambiguity to obtain ambiguity fixed solution.
[0039] Step 2 includes:
[0040] Step 2-1, when the RTK result is a fixed solution, the fixed ambiguity is back-substituted, the residual and its covariance matrix are calculated;
[0041] Step 2-2, the robust processing is performed, and the state and residual after the double-factor robust processing are calculated.
[0042] Step 2-1 includes:
[0043] Step 2-1-1: the RTK is calculated to back-substitute the fixed ambiguity, and the observation equation can be obtained:
[0044] l k =A k x k +v k (7)
[0045] Wherein l k represents the double-difference observation value, A k represents the double-difference observation equation coefficient matrix, v k represents the noise vector, wherein the covariance matrix of the noise is represented by matrix , which satisfies: x k represents the parameter vector.
[0046] Step 2-1-2, the state estimation and error covariance matrix are calculated
[0047]
[0048]
[0049] Step 2-1-3, the residual V k and its covariance matrix Q Vk
[0050]
[0051] Let then
[0052]
[0053] The double-factor robust estimation is processed by constructing an equivalent weight matrix, and the variance-covariance matrix D and the weight matrix of the related observation value are calculated is a symmetric positive definite non-diagonal matrix. is the variance factor.
[0054] Step 2-2 includes:
[0055] Step 2-2-1: Calculate the difference factor.
[0056] From step 2-1, the posterior variance-covariance matrix of the parameter estimates can be obtained. Approximately expressed as:
[0057]
[0058] Estimation of variance factor in the formula for:
[0059]
[0060] In the formula, r = nm represents the number of redundant observations.
[0061] Step 2-2-2, calculate the two-factor equivalent weight matrix:
[0062]
[0063] In the formula p ij and They are the weight matrix P and the equivalent weights, respectively. The weight element in the i-th row and j-th column,
[0064]
[0065] In the formula γ ii and γ jj This is an adaptive weighting factor.
[0066] Step 2-2-3, using the IGG-Ⅲ weighting factor:
[0067]
[0068] In the formula, v i / σ i Let k be the standardized residual of the i-th observation; k0 and k1 are the corresponding critical values. Typically, k0 is taken as 2.0 to 3.0 and k1 is taken as 4.5 to 8.5, which need to be determined based on the specific application scenario.
[0069] Then calculate the state and residuals after two-factor robustness:
[0070]
[0071]
[0072] Step 3 includes:
[0073] Initial alignment is performed using the initial position obtained from the satellite and the raw IMU data to obtain the initial attitude angle. Then, based on the specific force equation and mechanical arrangement, the velocity, position, and attitude of the inertial navigation system are updated to obtain the predicted position.
[0074] The error propagation equation is obtained from the error model, and the Kalman filter state equation is established. The state quantity where φ is the misalignment angle error, δv n is the velocity error, δp n is the position error, ε b is the gyro drift and is the accelerometer bias. The observation quantity z = [(△p) T (△v) T ], where △p represents the difference between the predicted position and the measurement, and △v represents the difference between the predicted velocity and the measurement, and the Kalman filter equation is established:
[0075]
[0076] In the formula: and P k / k-1 are the predicted state vector and the predicted state covariance, respectively; and are the state estimation results of the k-1 epoch and the k epoch, respectively; P k-1 and P k are the state estimation covariance matrices at the k-1 time and the k time, respectively; I is the unit matrix;
[0077] Step 4 includes:
[0078] Step 4-1, constructing a test statistic with the innovation;
[0079] In the Kalman filter, the measurement innovation δr k is defined as the function of the difference between the state prediction value and the current measurement value, and is expressed as:
[0080]
[0081] Theoretically, the measurement innovation is a white noise sequence, which is subject to a normal distribution with a mean of zero:
[0082]
[0083] Let take the test statistic as T k , then:
[0084]
[0085] where the subscript ii represents the elements on the diagonal of the matrix
[0086] Step 4-2, constructing an adaptive factor through the Huber function;
[0087] The adaptive factor α is constructed:
[0088]
[0089] Step 4-3, calculate the Kalman filter gain;
[0090] Compared with the traditional EKF, the original filter gain update of the robust Kalman filter is:
[0091]
[0092] Wherein represents the robust Kalman gain.
[0093] Finally, the state solution is calculated according to the robust Kalman filter to obtain the attitude, velocity, position and other parameter solutions. After obtaining the Kalman filter result, the predicted position is feedback corrected, and the high-reliable integrated navigation result is output.
[0094] The beneficial effects of the present application are:
[0095] The RTK / INS embedded real-time integrated positioning system based on robust estimation provided by the present application develops an embedded real-time positioning system with double robustness on the basis of the integrated navigation development board. Firstly, in order to solve the problem of observation value deviation caused by non-line-of-sight signal (NLOS) and multipath effect and other interferences in the RTK positioning process, the RTK positioning based on double-factor robustness is researched. Based on the least square model after the ambiguity fixed solution back substitution, the double-factor robustness processing is carried out by using the post residual to eliminate the influence of part of abnormal observation values. Then, the obtained RTK positioning result is loosely combined with the INS, and the robust processing based on Huber equivalent weight function is carried out in the Kalman filter update process, so as to further improve the accuracy and reliability of the integrated navigation positioning result. BRIEF DESCRIPTION OF DRAWINGS
[0096] Figure 1 It is a kind of RTK / INS embedded real-time integrated positioning system framework based on robust estimation;
[0097] Figure 2 It is the robust algorithm execution process provided by the present application for specific embodiment. DETAILED DESCRIPTION
[0098] The present application will be further illustrated by combining the drawings and specific embodiments, and it should be understood that the following specific embodiments are only used to illustrate the present application and are not used to limit the scope of the present application.
[0099] Embodiment 1: An RTK / INS embedded real-time integrated positioning system based on robust estimation, a hardware platform comprising an ARM core board, the ARM core board being connected with a serial communication module, a network communication module, a satellite signal receiving module, a power module and an inertial module, and the satellite positioning module being externally connected with a GNSS antenna. The GNSS antenna is used for receiving satellite signals, and the satellite signals are modulated and demodulated to obtain satellite data in the RTCM format. The power module provides stable voltage for each functional module of the embedded platform. The serial communication module is used for communication of relevant data of the embedded hardware platform and local equipment, and the network communication module is used for real-time acquisition of base station data from the network.
[0100] The network communication module adopts A7600 and realizes network communication through a mobile SIM card.
[0101] The satellite signal processing module adopts a UM482 board card of HandChip Star Technology Co., Ltd., and supports satellite signals such as BDS B1I / B2I, GPS L1 / L2, GLONASS L1 / L2, Galileo E1 / E5b and QZSS L1 / L2.
[0102] The voltage conversion circuit of the power module selects a DC / DC switching power conversion chip TPS5430, takes a 12V direct current power supply as the input power supply of the TPS5430, and adds necessary resistors, capacitors and diodes to the periphery of the TPS5430 chip to form two output voltages of 5V and 3.3V.
[0103] The FreeRTOS embedded operating system is selected as the operating system of the device, and a RTK / INS real-time integrated positioning system based on robust estimation based on the embedded platform comprises the following steps:
[0104] Step 1: using carrier pseudorange and other raw observation value data to solve ambiguity, and fixing ambiguity through LAMBDA algorithm.
[0105] Step 2: substituting the fixed ambiguity, establishing a robust model, and performing double-factor robust RTK.
[0106] Step 3: using IMU data and initial position to initialize the inertial navigation system, and calculating the position, speed and attitude at the next time according to the mechanical arrangement of the inertial navigation. Then, according to the random system model, the error propagation equation is obtained from the INS error propagation model, and the state equation is established. The measurement equation is established by using the RTK result to obtain the measurement, and the Kalman filter state update and measurement update are performed.
[0107] Step 4: constructing an adaptive robust factor according to the innovation, updating the Kalman filter gain, obtaining the Kalman filter result, feeding back and correcting the predicted position, and outputting the high-reliability integrated navigation result.
[0108] Step 1 includes:
[0109] Step 1-1, set the original message format output by the satellite positioning module to RTCM format, and set the sampling frequency to 1 Hz, and after acquisition, real-time decoding is performed to obtain multi-frequency pseudorange, carrier and satellite broadcast ephemeris;
[0110] Step 1-2, single point positioning is performed, and real-time data of base stations is obtained through a 4G network;
[0111] Step 1-3, double difference equations are set for base station data and rover station data, and ambiguities are calculated and fixed
[0112] Step 1-3 includes:
[0113] The original pseudorange and carrier phase observation equations of receiver m for satellite i are established, the station-to-station and satellite-to-satellite double difference is performed on the original pseudorange and carrier phase equations, the station-to-station and satellite-to-satellite double difference eliminates the receiver clock error and satellite clock error, and weakens the ionospheric and tropospheric errors (which can be ignored when the stations are close), the coordinate change and double difference ambiguity are taken as state variables x, and the double difference carrier phase observation value and station-to-satellite distance are taken as observation variables z to establish the Kalman filter equation. The RTK positioning process is as follows:
[0114] Step 1-3-1, establish the original pseudorange and carrier phase observation equation:
[0115]
[0116] Where ρ is the pseudorange observation value, is the carrier phase observation value (less than one week), P is the geometric distance between the receiver and the satellite, δt r and δt s represent the receiver clock error and the satellite clock error, Vion and Vtrop represent the ionospheric and tropospheric corrections, N represents the integer ambiguity, and ε represents the observation noise;
[0117] Step 1-3-2, further station-to-station and satellite-to-satellite double difference is performed on the original observation equation, which eliminates the receiver clock error and weakens the ionospheric and tropospheric errors (which can be ignored when the stations are close).
[0118]
[0119] And perform first-order Taylor expansion:
[0120]
[0121] That is
[0122]
[0123] Step 1-3-3, Kalman filter estimation is performed:
[0124] According to the linear random system model:
[0125]
[0126] where X k is the state vector; Φ k / k-1 represents the state transition matrix from epoch k-1 to k; Z k is the observation vector; H k represents the measurement matrix; W k-1 and V k are the process noise vector at epoch k-1 and the observation noise vector at k, respectively; wherein W k and V k are independent of each other, and both follow a Gaussian distribution with zero mean, and the covariance matrices are represented by Q k and R k , respectively.
[0127] Kalman filter estimation is performed:
[0128]
[0129] where: K k is the gain matrix; and P k / k-1 are the predicted state vector and the predicted state covariance, respectively; P k-1 and P k are the state estimation covariance matrices at k-1 and k, respectively; I is the identity matrix;
[0130] The ambiguity float solution can be obtained by using Kalman filter;
[0131] Step 1-3-4, the double-difference ambiguity is fixed by using LAMBDA algorithm to obtain the ambiguity fixed solution.
[0132] Step 2 includes:
[0133] Step 2-1, when the RTK result is a fixed solution, the fixed ambiguity is substituted back to calculate the residual and its covariance matrix;
[0134] Step 2-2, robust processing is performed, and the state and residual after double-factor robustness are calculated.
[0135] Step 2-1 includes:
[0136] Step 2-1-1, the fixed ambiguity calculated by RTK is substituted back to obtain the observation equation:
[0137] l k = Ak x k +v k (7)
[0138] where l k denotes double-difference observations, A k denotes double-difference observation equation coefficient matrix, v k denotes noise vector, where the covariance matrix of noise is denoted by matrix , which satisfies: x k denotes parameter vector.
[0139] Step 2-1-2, calculate state estimation and error covariance matrix
[0140]
[0141] Step 2-1-3, further can calculate residual V k and its covariance matrix Q Vk
[0142]
[0143] Let then
[0144]
[0145] The double-factor robust estimation is to process outliers by constructing equivalent weight matrix, and the variance-covariance matrix D and weight matrix W of the relevant observations are calculated is a symmetric positive definite non-diagonal matrix. is the variance factor.
[0146] Step 2-2 includes:
[0147] Step 2-2-1, calculate double-difference factor.
[0148] The posterior variance-covariance matrix of parameter estimation from step 2-1 is approximately expressed as:
[0149]
[0150] In the formula, the estimation of variance factor is:
[0151]
[0152] In the formula, r=n-m is the number of redundant observations.
[0153] Step 2-2-2, calculate double-factor equivalent weight matrix:
[0154]
[0155] where p ij and are the weight matrix P and the equivalent weight of the i-th row and j-th column of the weight matrix P,
[0156]
[0157] where γ ii and γ jj are the adaptive weight reduction factors.
[0158] Step 2-2-3, using IGG-III weight reduction factor:
[0159]
[0160] where v i / σ i is the standardized residual of the i-th observation; k0 and k1 are the corresponding critical values, usually k0 takes 2.0-3.0, and k1 takes 4.5-8.5, which need to be determined according to the application scenario.
[0161] Then calculate the state and residual after double-factor robustness:
[0162]
[0163]
[0164] Step 3 includes:
[0165] The initial position obtained by satellite is used for initial alignment with the original data of IMU to obtain the initial attitude angle; then the velocity, position and attitude of the inertial navigation system are updated according to the specific force equation and mechanical arrangement to obtain the predicted position.
[0166] The error model is used to obtain the error transfer equation, and the Kalman filter state equation is established. The state quantity where φ is the misalignment angle error, δv n is the velocity error, δp n is the position error, ε b is the gyro drift, and is the acceleration bias. The observation z = [(△p) T (△v) T ], where △p represents the difference between the predicted position and the measurement, and △v represents the difference between the predicted velocity and the measurement. The Kalman filter equation is established:
[0167]
[0168] where: and Pk / k-1 respectively are the predicted state vector and the predicted state covariance; and respectively are the state estimation results of k-1 epoch and k epoch; P k-1 and P k respectively are the state estimation covariance matrix of k-1 epoch and k epoch; I is the unit matrix;
[0169] Step 4 includes:
[0170] Step 4-1, constructing a test statistic with innovation;
[0171] In Kalman filtering, the measurement innovation δr k is defined as the function of the difference between the state prediction value and the current measurement value, and is expressed as:
[0172]
[0173] In theory, the measurement innovation is a white noise sequence, which is subject to a normal distribution with a mean of zero:
[0174]
[0175] Let Take the test statistic as T k Then:
[0176]
[0177] Where subscript ii represents the elements on the diagonal of the matrix
[0178] Step 4-2, constructing an adaptive factor through Huber function;
[0179] Constructing the adaptive factor α:
[0180]
[0181] Step 4-3, calculating the Kalman filter gain;
[0182] Compared with the traditional EKF, the original filter gain update of the robust Kalman filter is:
[0183]
[0184] Where K represents the robust Kalman gain.
[0185] Finally, according to the robust Kalman filter, the state is solved to obtain the parameters such as attitude, velocity, and position. After obtaining the Kalman filter result, the predicted position is feedback corrected, and the high-reliability integrated navigation result is output.
[0186] It should be noted that the above content only illustrates the technical idea of the present application, and cannot limit the protection scope of the present application. For ordinary skilled in the art, without departing from the principle of the present application, a number of improvements and refinements can be made, which fall within the protection scope of the claims of the present application.
Claims
1. An RTK / INS embedded real-time combination positioning system based on robust estimation, characterized in that: The hardware platform comprises an ARM core board connected with a serial communication module, a network communication module, a satellite signal processing module, a power module and an inertial module, and the satellite signal processing module is externally connected with a GNSS antenna; the GNSS antenna is used for receiving satellite signals, and the satellite signals are modulated and demodulated by the satellite signal processing module to obtain satellite data in the RTCM format; the inertial module provides acceleration and angular velocity data; The power module provides stable voltage for each functional module of the embedded platform; the serial communication module is used for communication of relevant data between the embedded hardware platform and local equipment, and the network communication module is used for real-time acquisition of base station data from the network; A positioning method of an RTK / INS real-time combination positioning system based on robust estimation based on the FreeRTOS embedded operating system is selected as the operating system of the equipment, and comprises the following steps: Step 1: using carrier pseudorange original observation value data to solve ambiguity, and fixing ambiguity by LAMBDA algorithm; Step 2: substituting the fixed ambiguity, establishing a robust model, and performing double-factor robust RTK; including: Step 2-1: when the RTK result is a fixed solution, substituting the fixed ambiguity, calculating residual and its covariance matrix; Step 2-2: performing robust processing and calculating state and residual after double-factor robustness; wherein step 2-1 comprises: Step 2-1-1: substituting the RTK calculated fixed ambiguity to obtain an observation equation: (1) wherein denotes the double difference observations, denotes the double difference observation equation coefficient matrix, denotes the noise vector, wherein the covariance matrix of the noise is given by the matrix denotes, in the case of no fault, that: , denotes the parameter vector; Step 2-1-2: calculating state estimation and error covariance matrix (2) (3) Step 2-1-3, further calculate the residual error and its covariance matrix ; (4) Let then (5) The double-factor robust estimation is to process outliers by constructing an equivalent weight matrix, and the variance-covariance matrix of the relevant observations is calculated and the weight matrix is a symmetric positive definite non-diagonal matrix; is a variance factor; Step 3: initializing the inertial navigation system by using IMU data and initial position, and calculating the position, velocity and attitude at the next time according to the mechanical arrangement of the inertial navigation; then, according to the random system model, the error propagation equation is obtained from the INS error propagation model to establish the state equation; the RTK result is used to obtain the measurement to establish the measurement equation, and the Kalman filter state update and measurement update are performed; Step 4: constructing an adaptive robust factor according to the innovation, updating the Kalman filter gain, obtaining the Kalman filter result, feeding back and correcting the predicted position, and outputting the high-reliability combination navigation result; including: Step 4-1: constructing a test statistic using innovation; In Kalman filtering, the measurement innovation defined as a function of the state prediction and the current measurement, is denoted as: (6) Theoretically, the measurement innovation is a white noise sequence, which is subject to normal distribution with mean zero: (7) Let , take the test statistic as then: (8) where the subscript denotes the elements on the diagonal of the matrix; Step 4-2: constructing an adaptive factor by Huber function; Constructing an adaptive factor : (9) Step 4-3: calculating the Kalman filter gain; Compared with the traditional EKF, the original filter gain update of the robust Kalman filter is: (10) wherein denotes the robust Kalman gain; Finally, the state is solved according to the robust Kalman filter to obtain the parameter solution; after obtaining the Kalman filter result, the predicted position is fed back and corrected, and the high-reliability combination navigation result is output.
2. The RTK / INS embedded real-time integrated positioning system based on robust estimation according to claim 1, characterized in that: The satellite signal processing module adopts the UM482 board card of HandChipStar, which supports BDS B1I / B2I, GPS L1 / L2, GLONASS L1 / L2, Galileo E1 / E5b, QZSS L1 / L2 satellite signals.
3. The RTK / INS embedded real-time integrated positioning system based on robust estimation according to claim 1, characterized in that Step 1 comprises: Step 1-1, set the original message format output by the satellite positioning module to RTCM format, and set the sampling frequency to 1 Hz, and after acquisition, real-time decoding is performed to obtain multi-frequency pseudo-range, carrier and satellite broadcast ephemeris; Step 1-2, single point positioning is performed, and real-time data of base stations is obtained through a 4G network; Step 1-3, the base station data and the rover station data are listed in double difference equations, and ambiguity is calculated and fixed.
4. The RTK / INS embedded real-time integrated positioning system based on robust estimation according to claim 3, characterized in that: Step 1-3 includes: Establishing receiver For satellite The original pseudo-range, carrier phase observation equation, the original pseudo-range and carrier equation are inter-station and inter-satellite double difference, which eliminates the receiver clock error, satellite clock error, weakens the ionosphere and troposphere error, and takes the coordinate change and double difference ambiguity as the state quantity , using double difference carrier observation value and station-satellite distance as observation quantity Establish Kalman filter equation; RTK positioning process is as follows: Step 1-3-1, establish original pseudo-range, carrier non-difference observation equation: (11) wherein is a pseudorange observation, is a carrier phase observation, is a geometric distance of the receiver to the satellite, and denotes a receiver clock bias and a satellite clock bias, and denotes ionosphere and troposphere corrections, denotes a whole number ambiguity, denotes an observation noise; Step 1-3-2, further make inter-station and inter-satellite double difference on the original observation equation, which eliminates the receiver clock error and weakens the ionosphere and troposphere error; (12) And make first-order Taylor expansion: (13) That is (14) Step 1-3-3, Kalman filter estimation is performed: According to the linear random system model: (15) wherein is the state vector; denotes the state transition matrix from epoch to ; is the observation vector; denotes the measurement matrix; and denote the process noise vector at epoch and the observation noise vector at epoch , respectively; wherein and are mutually independent and both follow a Gaussian distribution with zero mean, whose covariance matrices are denoted by and , respectively; Kalman filter estimation is performed: (16) where: is a gain matrix; and are the predicted state vector and predicted state covariance, respectively; and are the state estimation covariance matrices at time and time is an identity matrix; Ambiguity float solution is obtained by using Kalman filter; Step 1-3-4, double difference ambiguity is fixed by using LAMBDA algorithm to obtain ambiguity fixed solution.
5. The RTK / INS embedded real-time integrated positioning system based on robust estimation according to claim 1, characterized in that: Step 2-2 includes: Step 2-2-1, calculate double difference factor; Posterior variance-covariance matrix of parameter estimates from step 2-1 Approximately expressed as: (17) where the estimate of the variance factor is is: (18) In the formula, is the number of redundant observations; Step 2-2-2, calculate double factor equivalent weight matrix: (19) wherein and are the weight vectors and the equivalent weights of the first row column weight elements, respectively, (20) In the formula and is an adaptive downweighting factor; Step 2-2-3, use IGG-III weight reduction factor: (21) wherein is the standardized residual for the nth observation; and is the corresponding critical value, take , take ; Then calculate the state and residual after the double factor robustness: (22) (23)。 6. The RTK / INS embedded real-time integrated positioning system based on robust estimation according to claim 5, characterized in that: Step 3 includes: The initial position obtained by using the satellite is used for initial alignment with the original data of the IMU to obtain the initial attitude angle; then the velocity, position and attitude of the inertial navigation system are updated according to the specific force equation and mechanical arrangement to obtain the predicted position; The error transfer equation is obtained from the error model, and the Kalman filter state equation is established; the state quantity wherein, is the misalignment angle error, is the velocity error, is the position error, is the gyro drift and is the accumulated bias value; the observation quantity wherein represents the difference between the predicted position and the measurement, represents the difference between the predicted velocity and the measurement, and the Kalman filter equation is established: (24) wherein: and are the predicted state vector and the predicted state covariance, respectively; and are the state estimate at epoch and state estimate at epoch, respectively; and are the state estimate covariance matrix at time and state estimate covariance matrix at time, respectively; is the identity matrix.
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Embedded real-time positioning system with fault detection and elimination functions
CN114779305A