Low-orbit enhanced BDS and INS tightly coupled navigation fault detection and isolation method

Abstract

The application provides a low-orbit enhanced BDS and INS tight combination navigation fault detection and isolation method, introduces an FDE method based on adaptive maximum correlation entropy robust filtering, constructs a unified BDS / LEO / INS tight combination mathematical model, and studies a rough error detection and elimination method under multi-source heterogeneous observation conditions. Experimental results show that the FDE method can effectively identify and eliminate rough error satellites, significantly improve the system positioning accuracy, and compared with the BDS / INS tight combination system without using FDE, the east, north and sky direction positioning accuracy is improved by 86.56%, 77.12% and 51.80% respectively after introducing FDE; under the enhancement of LEO, the BDS / LEO / INS-FDE system is further improved to 86.95%, 82.60% and 53.94%. In addition, under the environment of low observation satellites, the introduction of LEO satellites significantly improves the satellite geometric configuration and enhances the navigation ability of the system in the case of partial BDS satellite failure, providing an effective theoretical method for continuous and reliable high-precision navigation in complex environments.

Description

Technical Field

[0001] This invention belongs to the field of satellite navigation and positioning and integrated navigation technology, specifically relating to a method for fault detection and isolation of low-orbit enhanced BDS and INS tightly integrated navigation. Background Technology

[0002] Global Navigation Satellite Systems (GNSS), as core spatiotemporal information infrastructure, have achieved meter- to centimeter-level positioning accuracy on platforms such as unmanned systems and weaponry. Currently, the major GNSS systems that have been built and provide global services include the US's GPS, Russia's GLONASS, the EU's Galileo, and China's BeiDou Navigation Satellite System (BDS). BDS employs a unique hybrid constellation design, including geostationary orbit (GEO), inclined geosynchronous orbit (IGSO), and medium Earth orbit (MEO) satellites, providing global coverage and regional augmentation services. However, in typical complex scenarios such as urban canyons, under overpasses, and tree-lined roads, GNSS signals are susceptible to severe obstruction, non-line-of-sight propagation, and multipath interference, leading to a significant decrease in positioning accuracy or even positioning interruption. These challenging GNSS environments are widespread in high-precision navigation missions such as urban warfare, emergency rescue, and autonomous driving, posing a severe test to the continuity, reliability, and integrity of navigation systems. Inertial Navigation Systems (INS) can provide continuous navigation information during short-term interruptions in GNSS signals. However, the performance of traditional tightly coupled GNSS / INS systems still heavily depends on the quality of GNSS observations. In cases of long-term GNSS signal degradation or loss of lock, INS errors accumulate over time, causing a rapid decline in navigation accuracy.

[0003] To overcome the aforementioned bottlenecks, navigation enhancement using low-Earth orbit (LEO) satellites has become a research hotspot. LEO satellites typically have a receiving power approximately 30 dB higher than GNSS signals, move at high speeds, and undergo rapid geometric changes, which helps to quickly improve satellite spatial distribution. Integrating LEO-enhanced GNSS / INS navigation can effectively achieve complementary advantages and is expected to provide continuous, stable, and high-precision positioning services in complex and challenging environments.

[0004] Domestic and international scholars have conducted the following research on the compact combination of LEO and INS:

[0005] 1. Online calibration of INS was achieved using Iridium and Orbcomm satellite signals. Even after GNSS signal interruption, LEO / INS could still maintain accuracy at the hundred-meter level for several minutes.

[0006] 2. To address the LEO trajectory error problem, an adaptive federated Kalman filter framework is proposed, and the positioning capability of LEO / INS over a long period of time is verified through on-vehicle experiments.

[0007] 3. For weakly observable conditions, a LEO-SOP / INS compact combination navigation method is proposed. The trend information extracted by the Rauch–Tung–Striebel (RTS) smoothing post-processing method is used to optimize the stochastic model and state dimension of the real-time Extended Kalman Filter (EKF).

[0008] 4. Regarding the BDS and LEO collaborative enhancement mechanism, the real-time navigation accuracy of LEO satellites is improved by using BDS-3 PPP-B2b real-time correction data, thereby enhancing the real-time orbit accuracy based on BDS-3 in the Asia-Pacific region.

[0009] 5. Taking advantage of the rapid change in the geometric configuration of LEO satellites, this paper improves the problems of slow time transfer convergence and insufficient short-term stability of traditional GNSS Precise Point Positioning (PPP). By simulating polar-orbiting Walker constellations of different sizes, a multi-GNSS PPP model with LEO enhancement is constructed.

[0010] 6. The study investigated the impact of different orbital altitudes, inclinations, and satellite numbers on global coverage, number of visible satellites, accuracy attenuation factor, and PPP convergence time, and pointed out that LEO satellite-enhanced GNSS can achieve PPP convergence within 1 minute without external enhancement information;

[0011] 7. The introduction of LEO satellites can significantly shorten the PPP convergence time. Among them, the 192-satellite scheme reduces the convergence time of multi-GNSS PPP from 9.6 min to 2.1 min. Reference

[14] realizes the combined navigation simulation of multi-source heterogeneous sensors based on the federated filtering algorithm. By flexibly allocating information factors, it can adapt to the fusion requirements of sensors with different precision.

[0012] 8. A compact navigation method based on LEO satellite augmentation and factor graph optimization is proposed. In complex urban environments, LEO augmentation improves positioning accuracy by 35%–58%.

[0013] While multi-source tightly integrated navigation has significant theoretical advantages, in practical engineering applications, satellite observation data can be affected by clock errors, orbital deviations, and multipath effects, leading to gross errors. Failure to pass fault detection and exclusion (FDE) will severely impact the state estimation accuracy of the integrated navigation system, and may even cause navigation solution failure. Traditional receiver autonomous integrity monitoring methods mainly identify satellite gross errors through consistency checks of pseudorange residuals. However, in multi-source heterogeneous observation fusion scenarios, due to significant differences in the observation models and error characteristics of each system, and the time-varying cumulative nature of INS errors, a single residual check is insufficient to effectively cover all types of gross errors, easily leading to missed or false detections.

[0014] Current improvement methods mainly include:

[0015] 1. Utilize redundant information among multi-source observations to perform cross-system residual comparison;

[0016] 2. Using an adaptive robust estimation method instead of traditional least squares estimation can suppress the impact of gross errors on state estimation;

[0017] 3. Using neural networks to extract the feature differences between multipath error and star clock error can improve the efficiency and accuracy of gross error classification in complex environments.

[0018] While current research has made some progress in gross error detection and identification in multi-source compact navigation systems, research on FDE mechanisms for LEO-enhanced BDS / INS compact systems remains relatively lacking. On the one hand, existing research on LEO enhancement mainly focuses on improving the positioning performance of GNSS (especially GPS) or the convergence speed of PPP, with less in-depth exploration of its role in gross error suppression in multi-source fusion architectures and in-depth discussions of BDS. On the other hand, considering the rapid changes in LEO satellite geometry and the highly dynamic nature of observation models, the adaptability and robustness of existing FDE methods in heterogeneous observation fusion still require further in-depth research.

[0019] To address the aforementioned problems, developing a navigation system or method that is suitable for complex and challenging environments and possesses continuity, reliability, and high precision is a pressing issue that needs to be resolved by those skilled in the art. Summary of the Invention

[0020] The purpose of this invention is to propose a LEO-enhanced BDS / INS compact navigation method based on the FDE framework. By constructing a unified BDS / LEO / INS compact mathematical model, and based on a gross error detection and elimination method under multi-source heterogeneous observation conditions, the effectiveness and robustness of the proposed method in improving geometric configuration, suppressing the influence of gross errors, and enhancing navigation performance in low-observation environments are verified using a simulation experiment system. This provides a theoretical method for continuous and reliable high-precision navigation in complex environments.

[0021] To achieve the above objectives, the technical solution adopted by the present invention includes the following steps:

[0022] A method for fault detection and isolation in low-orbit enhanced BDS and INS tightly integrated navigation, the method comprising:

[0023] S1. Construct a tightly integrated navigation model of LEO-enhanced BDS and INS systems;

[0024] S2. Based on the maximum correlation entropy robust filtering, an FDE filter is constructed to detect gross errors in satellite observations.

[0025] S3. Based on the innovation vector and innovation covariance matrix of the FDE filter, construct a global test statistic to determine whether there are gross errors in the current observations;

[0026] S4. If there are no gross errors, output the navigation and positioning results directly;

[0027] If gross errors exist, the observations of each satellite are identified one by one based on the local test statistics, faulty satellites containing gross errors are located and removed; and the clean observations after removing gross errors are used to perform BDS and INS tight combination navigation calculations in combination with LEO satellites before outputting the navigation and positioning results.

[0028] Furthermore, the LEO-enhanced BDS and INS tightly coupled navigation model constructed in step S1 includes a state equation and an observation equation; the state equation is constructed based on the INS psi angle error equation; the observation equation is constructed based on the difference between the pseudorange and pseudorange rate observations of BDS and INS, and LEO and INS.

[0029] Furthermore, the state equation and observation equation are expressed as follows:

[0030] ;

[0031] Where, x k It is the state vector at time k, z k w is the observation vector at time k. k and v k These are independent process and measurement noise, hk F represents the nonlinear measurement matrix. k-1 This represents the nonlinear state transition matrix.

[0032] Furthermore, the innovation vector r of the FDE filter constructed in step S2 k With the new information covariance matrix S k for:

[0033] ;

[0034] Among them, H k h k The linear observation matrix;

[0035] P k|k-1 This represents the prior error covariance matrix at time k;

[0036] This represents the prior state at time k.

[0037] Furthermore, whether there are gross errors in the satellite observations in step S3 is determined according to the following method:

[0038] A global test is performed based on the residuals and covariance matrix of the constructed FDE filter, and a global test statistic TN is constructed. k ,as follows:

[0039] ;

[0040] When there are no gross errors in the satellite observations, the statistic TN k Obeying χ 2 distributed;

[0041] when When α is significant, there are gross errors in the satellite observations.

[0042] Furthermore, step S3 also includes: when there are gross errors in the satellite observations, the innovation vector and the innovation covariance matrix are adjusted using an adaptive kernel bandwidth selection model, the specific method of which is as follows:

[0043] S21. Construct judgment condition α based on the new information vector and the new information covariance matrix. i,k = r i,k / S ii,k , used as a function variable to adjust the kernel bandwidth for each measurement, where r i,k S represents the i-th element of the innovation vector. ii,k Representation matrix The i-th diagonal element;

[0044] S22. When gross errors exist in satellite observations, the kernel bandwidth is adjusted using an adaptive kernel bandwidth selection model, which is as follows:

[0045] .

[0046] Furthermore, the local test statistic in step S4 is constructed based on the data probing method, and the statistic for the i-th satellite observation is:

[0047] ;

[0048] Among them, e i Let i be a vector whose i-th element is 1 and all other elements are 0;

[0049] If w i If the value exceeds the set threshold, the satellite observation has gross errors and will be discarded.

[0050] Compared with the prior art, the present invention has the following beneficial effects:

[0051] 1. This invention introduces an FDE method based on adaptive maximum correlation entropy robust filtering to effectively identify and eliminate gross error satellites, significantly improving the system's positioning accuracy. Compared to the BDS / INS tightly coupled system without FDE, the positioning accuracy for East, North, and Sky directions is improved by 86.56%, 77.12%, and 51.80% respectively after introducing FDE. With LEO enhancement, the BDS / LEO / INS-FDE system further improves to 86.95%, 82.60%, and 53.94% respectively.

[0052] 2. In low-observation satellite environments, the introduction of LEO satellites significantly improves satellite geometry and enhances the system's navigation capability when some BDS satellites fail, providing an effective theoretical method for continuous and reliable high-precision navigation in complex environments;

[0053] 3. The maximum correlation entropy criterion is adopted to replace the traditional criterion, and an adaptive kernel bandwidth selection model is introduced, which effectively suppresses the influence of non-Gaussian noise and gross errors on state estimation and significantly improves the robustness of the filter.

[0054] 4. By constructing a global test statistic for detecting gross errors and a local test statistic for accurately locating faulty satellites, the accuracy and efficiency of gross error detection are improved, and the problem of missed or false detections in multi-source heterogeneous data by single residual test is avoided. Attached Figure Description

[0055] Figure 1 This is a flowchart of the method of the present invention;

[0056] Figure 2This is a flight trajectory diagram of the drone in this embodiment;

[0057] Figure 3 This is a view of the visible satellite sky in this embodiment;

[0058] Figure 4 This is a graph showing the noise parameters as a function of elevation angle in this embodiment;

[0059] Figure 5 This is a statistical chart of the number of visible satellites for BDS and LEO in this embodiment;

[0060] Figure 6 This is a comparison chart of the PDOP values ​​of BDS and BDS / LEO in this embodiment;

[0061] Figure 7 This is a diagram showing the change of LEO satellite elevation angle over time in this embodiment;

[0062] Figure 8 This is a schematic diagram of the global test statistics for gross error detection in the absence of gross errors in this embodiment;

[0063] Figure 9 This is a schematic diagram of the local test statistics for gross error identification in the absence of gross errors in this embodiment;

[0064] Figure 10 This is a schematic diagram illustrating the inclusion of global gross error test statistics in this embodiment;

[0065] Figure 11 This is a schematic diagram illustrating the inclusion of local gross error test statistics in this embodiment;

[0066] Figure 12 This is a comparison chart of positioning errors using different methods in this embodiment;

[0067] Figure 13 This embodiment presents the RMSE statistics for positioning errors of different methods.

[0068] Figure 14 This is a schematic diagram of the inertial sensor zero-bias estimation results in this embodiment;

[0069] Figure 15 This is a positioning error diagram without the FDE method in this embodiment;

[0070] Figure 16 This is a graph showing the RMSE statistics without the FDE method in this embodiment;

[0071] Figure 17 This is a positioning error diagram with the FDE method in this embodiment;

[0072] Figure 18 This is a cumulative probability distribution diagram of positioning error with FDE method in this embodiment;

[0073] Figure 19 This is a sky view of the six visible BDS satellites in this embodiment;

[0074] Figure 20 This is a schematic diagram illustrating the PDOP values ​​of BDS with different numbers of LEO satellites in this embodiment;

[0075] Figure 21 This is a diagram showing the LEO satellite-enhanced BDS positioning results in this embodiment;

[0076] Figure 22 This is a statistical chart of the RMSE (Real-Time Sequence) of LEO satellite-enhanced BDS positioning error in this embodiment;

[0077] Figure 23 This is a positioning error diagram of the LEO-enhanced BDS / INS tight combination in this embodiment;

[0078] Figure 24 This is a statistical chart of the LEO-enhanced BDS / INS positioning error RMSE in this embodiment. Detailed Implementation

[0079] The technical solutions in the embodiments of the present invention will now be clearly and completely described with reference to the accompanying drawings. Figure 1 The present invention will be described in detail with specific embodiments.

[0080] Example 1:

[0081] This embodiment provides a method for fault detection and isolation in low-orbit enhanced BDS and INS tightly integrated navigation, including:

[0082] 1. Construct a tightly integrated navigation model of LEO-enhanced BDS and INS systems.

[0083] LEO constellation parameters are represented by three integers: M, T, and F. M is the total number of satellites, T is the number of orbital planes, and F is the inter-plane phase parameter, used to describe the relative phase relationship between satellites in adjacent orbital planes. In this uniform constellation configuration, the right ascension Ω of the ascending node and the mean anomaly angle of the q-th satellite in the p-th plane are... The formula is:

[0084] ;

[0085] ;

[0086] In the formula, the subscripts p and q represent the p-th orbital plane and the q-th satellite, respectively, and S = M / T represents the number of satellites in each orbital plane.

[0087] The LEO-enhanced BDS / INS system compact navigation model includes:

[0088] (1) Equations of state

[0089] The INS uses the "Northeast-Northern Sky (ENU)" local coordinate system as the navigation coordinate system (n-frame), with the x, y, and z axes pointing to the local east, north, and vertical upward directions, respectively. The Inertial Measurement Unit (IMU) is fixed in the carrier coordinate system (b-frame), with the x, y, and z axes pointing to the right-front-upward direction, respectively. The psi angle error equation is as follows:

[0090] ;

[0091] In the formula, , and These represent the position, velocity, and attitude errors in the n-frame, respectively. It is the specific force output by the accelerometer; and This indicates the sensor error of the accelerometer and gyroscope; and This indicates that the gyroscope and accelerometer have zero bias. and It is the relevant time. and It drives white noise; It is the direction cosine matrix from the b-system to the n-system; and Let and represent the angular rates of rotation of the Earth coordinate system (e-frame) relative to the inertial coordinate system (i-frame) and the angular rates of rotation of the n-frame relative to the e-frame, respectively. , , and This corresponds to the angular rate error; This represents the local gravity error; the superscripts n and b represent the n-system and b-system, respectively.

[0092] (2) Observation equation

[0093] After ionospheric delay, tropospheric delay, and satellite clock error compensation, the pseudorange measurements of the i-th BDS and j-th LEO satellites are... and pseudorange rate The observation equation can be expressed as:

[0094] ;

[0095] ;

[0096] ;

[0097] ;

[0098] In the formula, the superscripts or subscripts B and L represent the BDS and LEO systems, respectively. and These represent receiver clock bias and clock drift, respectively. and These represent satellite clock bias and clock drift, respectively. and These represent the pseudorange and pseudorange rate measurement noise, respectively. and These are the satellite's position vector and velocity vector, respectively; r u and v u These are the receiver's true position and velocity vector, respectively; is the unit vector in the direction of the line of sight; c is the speed of light.

[0099] The pseudorange and pseudorange rate prediction values ​​of INS relative to BDS and LEO are:

[0100] ;

[0101] ;

[0102] ;

[0103] ;

[0104] In the formula, r ins and v ins These are the receiver user's position vector and velocity vector, respectively, calculated from INS dead reckoning. This is the unit vector for predicting the direction of the line of sight.

[0105] The observations are the differences between the pseudorange and pseudorange rate observations of BDS and INS, and LEO and INS. The observation equation is:

[0106] ;

[0107] In the formula, and These are the BDS pseudorange and pseudorange rate observations, respectively. and These are the LEO pseudorange and pseudorange rate observations, respectively. and , respectively, represent the INS predicted pseudorange and pseudorange rate, and m and n represent the total number of observable BDS and LEO satellites, respectively.

[0108] In constructing an LEO-enhanced BDS / INS compact combinational system in the n-system, the state vector x in the filter is defined as:

[0109] ;

[0110] In the formula, the tightly coupled system includes 15 inertial navigation states and 4 clock bias states, which are the clock biases of the BDS and LEO receivers, respectively. and BDS and LEO receiver clock drift and .

[0111] The LEO-enhanced BDS / INS compact combination model includes a state model and an observation model, expressed as follows:

[0112] ;

[0113] In the formula, x k It is the state vector at time k, z k It is the observation vector. k and v k These are independent process and measurement noise, h k F represents the nonlinear measurement matrix. k-1 This represents the nonlinear state transition matrix.

[0114] 2. Enhanced filter and local detection fault detection method

[0115] The traditional EKF method is based on the minimum mean square error criterion, which is optimal under the Gaussian assumption. However, the estimation performance of EKF deteriorates significantly when the measurement noise is non-Gaussian. To overcome this limitation, the maximum correlation entropy criterion is used instead. During the time update process, by combining the established state transition model and the state at the previous time step, the prior state and the prior error covariance matrix at time k are obtained, expressed as:

[0116] ;

[0117] In the formula, Q k-1 It is the covariance matrix of the process noise. Further, we define a representation of the true state x. k With the prediction of prior states State prediction error between the deviations:

[0118] ;

[0119] Combining the LEO-enhanced BDS / INS compact combination model state prediction error in step S1, the equation is reconstructed, resulting in the linear equation:

[0120] ;

[0121] In the formula, E represents the identity matrix, and H... k hk The linear observation matrix, α k equal:

[0122] ;

[0123] Extended error covariance matrix Δ k :

[0124] ;

[0125] In the formula, S is obtained by the Chuleski decomposition of the extended error covariance matrix. k Multiply both sides of the reconstructed linear equation by... The linear regression model can be rewritten as:

[0126] ;

[0127] Where L k , Γ k and δ k Defined as:

[0128] ;

[0129] Introducing the maximum correlation entropy criterion as the loss function to improve the filtering method, expressed as:

[0130] ;

[0131] The solution to the state estimation is obtained by maximizing the above optimization criterion:

[0132] ;

[0133] In the formula, L = mx + nz, where mx and nz are x k and z k The dimension is defined as the number of all observation states and all observable satellites, δ. k (i) represents L k -Γ k x k The i-th component. The optimal solution is:

[0134] ;

[0135] definition ,have:

[0136] ;

[0137] in:

[0138] ;

[0139] This represents the operation of constructing a diagonal matrix. Therefore, the optimal solution formula can be transformed into:

[0140] ;

[0141] Then the state can be estimated. :

[0142] ;

[0143] Vector C k The error covariance matrix is ​​reweighted and the measurement noise matrix is ​​reconstructed. The corrected error covariance matrix is ​​expressed as follows:

[0144] ;

[0145] Since the true state is unknown, we can assume that the estimate is unbiased. At that time, C P , k It equals the identity matrix. Therefore, the prior error covariance and measurement noise variance can be rewritten as:

[0146] ;

[0147] Finally, the updated covariance is introduced into the measurement update process to calculate the gain matrix, posterior state, and posterior covariance matrix:

[0148] ;

[0149] Filter innovation vector r k With the new information covariance matrix S k for:

[0150] ;

[0151] A judgment condition is constructed based on the innovation vector and the innovation covariance matrix. Used as a function variable to adjust the kernel bandwidth for each measurement, where r i,k S represents the i-th element of the innovation vector. ii,k Representation matrix The i-th diagonal element. When there are large gross errors in the satellite observations, the kernel bandwidth is appropriately adjusted using a logarithmic function. The adaptive kernel bandwidth selection model is as follows:

[0152] ;

[0153] Based on the compact combination BDS / LEO / INS positioning system, the residuals and covariance matrix of the adaptive maximum correlation entropy robust filter are used for global testing, and a global test statistic TN is constructed. k :

[0154] ;

[0155] When there are no outliers in the observations, the test statistic TN k Obeying χ 2 Distribution. When When α is the significance level, it is determined that there are gross errors in the observed values.

[0156] The proposed enhanced FDE method combines adaptive filtering and local tests. Adaptive filtering is used to eliminate undetected gross errors and further improve the accuracy of the test statistics. Local tests are performed using data probing, and the statistic for the i-th observation is:

[0157] ;

[0158] In the formula, e i Let w be a vector whose i-th element is 1 and all other elements are 0. When gross errors exist in this observation, the test statistic w is... i＞ μ 1-α⁄2 .

[0159] Example 2:

[0160] This embodiment uses the method provided in Embodiment 1 to perform simulation experiments for verification and analysis.

[0161] To evaluate the effectiveness of the proposed LEO-enhanced BDS / INS compact navigation method and FDE algorithm, multi-scenario and multi-mode verification was conducted based on a unified simulation experimental framework. The simulation experiments aimed to reproduce navigation challenges in complex and low-observation environments, including GNSS signal obstruction, observational gross errors, and insufficient satellite visibility, and to quantitatively analyze the improvement of the LEO constellation on the performance of the BDS / INS compact combination. The experiments simulated UAV reconnaissance and patrol missions in a battlefield environment, constructing error models for BDS, LEO, and IMU, and generating pseudorange observations containing noise and gross errors. The data processing workflow included:

[0162] (1) Data acquisition and quality analysis;

[0163] (2) Verification of BDS / LEO / INS tight combination FDE navigation results;

[0164] (3) LEO-enhanced BDS / INS tight combination localization results;

[0165] (4) Performance testing under low-observation satellite environment.

[0166] To compare algorithm performance, four modes were set up: BDS / INS, BDS / INS-FDE, BDS / LEO / INS, and BDS / LEO / INS-FDE. The enhancement performance of different numbers of LEO satellites was tested under the condition of limited number of BDS satellites.

[0167] 1. Data acquisition and quality analysis

[0168] The drone flew along a preset trajectory, with its initial position set at longitude 118°, latitude 32°, and altitude 15 m. The drone's horizontal flight trajectory was as follows: Figure 2 As shown, the entire process takes approximately 75 minutes.

[0169] Both BDS and LEO sampling frequencies are 1Hz, and the IMU output frequency is 100Hz. Based on the actual flight trajectory, velocity, and attitude information, noise-free ideal IMU observations are first generated, and the IMU noise shown in Table 1 is superimposed on the original observations. The LEO constellation is simulated based on my country's "Hongyun" system. The BDS constellation parameters are set according to the reference, and the constellation parameters are shown in Table 2, where the LEO orbital period is 105.82 min. The visible satellite sky distribution during the UAV flight is as follows: Figure 3 As shown, the LEO satellites are numbered PRN1–PRN156, and the BDS satellites are numbered PRN301–PRN335. The BDS satellites have shorter tracks in the sky, while the LEO satellites have longer tracks. In data processing, the cutoff elevation angle for both LEO and BDS satellites is set to 15°. The pseudorange accuracy varies with the elevation angle, as shown below. Figure 4 As shown, the zenith direction measurement accuracy is 3 m. In the FDE method, the significance level α = 0.1%, the power β = 20%, and the corresponding local test threshold is 3.29.

[0170] Table 1 Sensor Parameters

[0171]

[0172] Table 2 BDS / LEO Constellation Parameters

[0173]

[0174] During the flight period, the total number of visible satellites remained between 12 and 17. Since the flight path was within the coverage area of ​​the Asia-Pacific region's enhanced service, 5 GEO satellites were continuously visible, resulting in a relatively large number of visible satellites for the BDS system, reaching 10 to 12. Due to their high speed and low orbital altitude, the number of simultaneously visible LEO satellites was relatively small, ranging from 2 to 5, and sometimes less than 4, making it difficult to achieve independent navigation and positioning. Figure 5 and Figure 6This represents the variation in the number of visible satellites and the Position Dilution of Precision (PDOP) over approximately 4500 seconds. The maximum PDOP for a single BDS system was 2.238, the minimum was 1.495, and the average was 1.799. Since fewer than four LEO satellites were visible in 73.48% of epochs, their independent PDOP values ​​were not calculated. For the BDS / LEO combined system, the maximum PDOP was 2.165, the minimum was 1.255, and the average was 1.496. Introducing LEO augmentation significantly improved satellite spatial geometry, with PDOP values ​​below 2 in 96.8% of epochs.

[0175] Figure 7 This shows the change in the number of visible LEO satellites above an elevation angle of 15° over time, with significant changes in elevation angle. Among them, LEO satellite PRN131 had the longest visibility time, appearing from 2039s to 2711s, lasting approximately 11.53 minutes; while BDS satellite PRN 308 remained visible throughout its entire 4500-second flight period. In contrast, BDS satellites in medium and high orbits moved relatively slowly, with smaller trajectory movements in the sky view, such as... Figure 3 As shown.

[0176] 2. BDS / LEO / INS tightly coupled FDE navigation results

[0177] A 25m step error was artificially added to the pseudorange observations from the PRN329 satellite, and the FDE algorithm under different combination modes was compared and analyzed. The following four modes were used for comparison and verification: BDS / INS compact combination mode (without FDE); BDS / INS-FDE compact combination mode (with FDE); BDS / LEO / INS compact combination mode (without FDE); and BDS / LEO / INS-FDE compact combination mode (with FDE). Figure 8 and Figure 9 The results are the global test statistic and the local test statistic for PRN 329 without the inclusion of gross errors. Without the influence of gross errors, the global test statistic is lower than the preset threshold; there are a few false alarms in the local test statistic. Figure 10 and Figure 11 These represent the global and local test values ​​after adding a 25m step gross error to the pseudorange observations of PRN 329, respectively. Both the global and local tests effectively detect the gross error and can identify and remove it. The system as a whole has good gross error sensitivity, although there are still some missed detections in a few epochs.

[0178] Figure 12 and Figure 13The data presents positioning results and RMSE statistics for four modes: BDS / INS, BDS / INS-FDE, BDS / LEO / INS, and BDS / LEO / INS-FDE. After introducing the FDE algorithm, the positioning performance of both the BDS / INS-FDE and BDS / LEO / INS-FDE combined modes is significantly improved. The BDS / INS-FDE method has an eastward error of 0.72 m, a northward error of 0.92 m, and an astronomical error of 1.34 m, representing accuracy improvements of 86.56%, 77.12%, and 51.80%, respectively, compared to the BDS / INS method without FDE. The BDS / LEO / INS-FDE method has an eastward error of 0.60 m, a northward error of 0.69 m, and an astronomical error of 1.23 m, representing accuracy improvements of 86.95%, 82.60%, and 53.94%, respectively. Without FDE, the BDS / INS tightly combined mode is most significantly affected by gross errors and has the worst positioning accuracy. The BDS / LEO / INS mode, with the introduction of LEO satellites, has enhanced observation geometry and redundancy, resulting in improved positioning accuracy. Furthermore, by combining it with the FDE algorithm, the system's ability to suppress gross errors is significantly enhanced, further improving positioning accuracy.

[0179] Figure 14 The figure shows the zero-bias estimation results for the BDS / LEO / INS-FDE tightly coupled accelerometer and gyroscope. As can be seen from the figure, the zero biases of the three-axis accelerometer and three-axis gyroscope converged stably after several minutes, eventually converging to approximately 500 μg and 5° / h, respectively. The continuous and reliable BDS / LEO navigation solution can be used to correct the accumulated errors of the inertial sensors and achieve accurate estimation of the errors of the inertial navigation devices. During the experiment, the gross errors that were detected and eliminated in a timely manner did not cause filter divergence or lead to a decrease in positioning performance; the system maintained good dead reckoning capability, verifying the effectiveness of the adopted FDE model.

[0180] 3. LEO-enhanced BDS / INS tight-binding localization results

[0181] After adding a 25 m gross error to the pseudorange observations from BDS satellite PRN 329, the positioning performance of the LEO-enhanced single BDS system and the BDS / INS tightly coupled navigation system was further evaluated in both FDE-free and FDE-enabled scenarios. Figure 15 and Figure 16 The figures show the positioning errors and their RMSE statistics in the East, North, and Sky directions without the FDE method.

[0182] The results of a single BDS system are significantly affected by gross errors, with positioning errors exceeding 5 m in both the horizontal and vertical directions. Introducing LEO satellite augmentation significantly improves positioning performance; the LEO-enhanced BDS system achieves 14.00%, 31.85%, and 22.26% higher accuracy in the east, north, and sky directions compared to the single BDS system, respectively. Comparing the positioning results of BDS / INS and BDS / LEO / INS modes, LEO enhancement improves accuracy in the three directions by 14.09%, 2.12%, and 21.56%, respectively. Under conditions where gross errors exist in the observations, the addition of LEO satellites effectively suppresses the impact of these gross errors on navigation solutions.

[0183] Figure 17 and Figure 18 These are the positioning results and their cumulative distribution function (CDF) of positioning errors for the four combined modes after applying the FDE algorithm. Figure 17 It is evident that the single BDS system is significantly affected by gross errors, with the maximum horizontal error exceeding 10 m and the maximum vertical error exceeding 50 m. Although the FDE algorithm detects and eliminates these gross errors, the reduced number of available satellites leads to a weakened geometric configuration, resulting in a decline in positioning performance. For the BDS, BDS / LEO, BDS / INS, and BDS / LEO / INS modes, the percentages of epochs with eastward errors better than 2 m are 61.57%, 75.29%, 98.79%, and 99.89%, respectively; the corresponding percentages for northward errors are 52.73%, 73.95%, 96.49%, and 98.93%; and the percentages for celestial errors better than 4 m are 55.12%, 69.90%, 100%, and 100%. The overall trend of the cumulative distribution function shows that the positioning accuracy of the three combined modes—BDS / LEO, BDS / INS, and BDS / LEO / INS—is significantly improved compared to the single BDS mode.

[0184] 4. LEO enhances BDS / INS tight-binding positioning performance under low observation conditions

[0185] In practical applications, LEO satellite signals have stronger received power, typically about 30dB higher than BDS signals, providing stronger anti-interference capabilities, while BDS signals are prone to partial or complete failure. To evaluate the FDE navigation performance of LEO-enhanced BDS and BDS / INS tightly coupled systems under such conditions, a BDS scenario with a low number of observation satellites was simulated. Figure 5 As shown, there were originally 10–12 BDS satellites visible. In this embodiment, only 6 satellites (PRN315, 316, 322, 323, 329, 332) are selected as visible satellites, and the remaining satellites are set to invisible. The sky distribution is as follows. Figure 19As shown. A 25 m step error was injected into the pseudorange observations of the PRN 329 satellite, and the positioning results were compared with those of BDS satellites augmented with 1 LEO satellite, 2 LEO satellites, and all available LEO satellites (2–5), as well as with BDS / INS tight combination.

[0186] Figure 20 The variation of the Geometric Accuracy Factor (PDOP) of BDS satellites with different numbers of LEO satellites was investigated. Using only 6 BDS satellites, the PDOP value ranged from 2 to 4. After introducing one LEO satellite for enhancement, the system had a total of 6 BDS satellites and 1 LEO satellite available. After detecting and removing gross observations from PRN 329, the available satellites decreased to 5 BDS satellites and 1 LEO satellite. Due to the high orbital velocity and poor spatial geometry of this LEO satellite, the satellite configuration strength weakened, resulting in a significant jump in PDOP, with 18.43% of epochs showing a PDOP value exceeding 4. Using two LEO satellites for enhancement improved the geometry, further reducing the PDOP value, with only 3.02% of epochs showing a PDOP greater than 4. When more than two LEO satellites were introduced, the PDOP variation tended to stabilize, with a mean of approximately 2, indicating that multi-satellite LEO enhancement significantly improves the stability of the BDS system.

[0187] Figure 21 and Figure 22 The positioning results of a single BDS system with different numbers of LEO satellites and their corresponding RMSE statistics are presented. When only one LEO satellite is introduced, the maximum horizontal positioning error exceeds 50 m, and the elevation error exceeds 100 m. The RMSEs for the east, north, and sky directions are 6.38 m, 10.22 m, and 30.56 m, respectively. After using two LEO satellites for augmentation, the RMSEs in the corresponding directions decrease to 4.33 m, 4.69 m, and 14.19 m. When using 2–5 LEO satellites for augmentation, the RMSEs in each direction further decrease to 2.40 m, 3.41 m, and 3.50 m. In satellite-constrained environments, compared to one LEO satellite, two LEO satellites improve the positioning accuracy in the east, north, and sky directions by 35.25%, 54.07%, and 53.59%, respectively. Compared to using only two LEO satellites, using two or more LEO satellites further improves the accuracy in the three directions by 41.82%, 54.98%, and 65.20%, respectively. Due to its low orbit and high speed, the LEO satellite effectively improves the satellite's spatial geometry and increases observation redundancy, thereby significantly enhancing the system's positioning accuracy and reliability. Especially in single BDS mode, the elevation direction error is drastically reduced from 30.56 m to 4.94 m, fully demonstrating the role of LEO in enhancing error accuracy.

[0188] Figure 23 and Figure 24The positioning results of the BDS / INS compact combination system with different numbers of LEO satellites and their corresponding RMSE statistics are presented.

[0189] With the increase in the number of LEO satellites and the enhancement of the BDS / INS system using fault detection and elimination algorithms, the positioning results become more stable. The positioning errors in the east, north, and sky directions all show a significant decreasing trend, with the maximum error in the horizontal direction being better than 3 m and the maximum error in the vertical direction not exceeding 5 m. Compared to using one LEO satellite, the positioning accuracy in the east, north, and sky directions is improved by 3.85%, 9.54%, and 12.58%, respectively, when enhanced by two LEO satellites. Further increasing the number of LEO satellites to two or more improves the accuracy in the corresponding directions by 9.87%, 12.34%, and 34.70%. Under simulation conditions based on the "Hongyun" constellation setup, using all visible LEO satellites (2–5) to enhance the BDS / INS-FDE tightly coupled system, the positioning accuracies in the three directions are 0.81 m, 0.87 m, and 1.32 m, respectively.

[0190] 4. Conclusion

[0191] To address the issues of gross error interference and insufficient satellite signal quantity in complex observation environments, the low-Earth orbit enhanced BDS / LEO / INS tightly coupled navigation fault detection and isolation method proposed in Example 1 constructs a unified BDS / LEO / INS observation model and employs the maximum correlation entropy criterion to enhance the robustness of the filter, thereby achieving effective detection and elimination of gross errors in multi-source observations. The following conclusions are drawn:

[0192] (1) The proposed FDE method can significantly suppress the impact of gross errors on navigation solutions, and achieves a positioning accuracy improvement of more than 50% in BDS / INS-FDE and BDS / LEO / INS-FDE systems respectively;

[0193] (2) The introduction of LEO satellites not only improved the satellite's spatial geometry, but also provided important observation redundancy when BDS observations were limited, significantly enhancing the system's fault tolerance and navigation continuity;

[0194] (3) In a low-observation-satellite environment, even adding only 1-2 LEO satellites can significantly improve the system's positioning accuracy and stability, demonstrating LEO's ability to enhance applications in complex environments.

[0195] The above embodiments are for illustrative purposes only and are not intended to limit the scope of this invention. Although this invention has been described in detail with reference to the embodiments, those skilled in the art should understand that various combinations, modifications, or equivalent substitutions of the technical solutions of this invention do not depart from the spirit and scope of the technical solutions of this invention and should be covered within the scope of the claims of this invention.

Claims

1. A method for fault detection and isolation in low-orbit enhanced BDS and INS tightly integrated navigation, characterized in that, The methods include: S1. Construct a tightly integrated navigation model of LEO-enhanced BDS and INS systems; S2. Based on the maximum correlation entropy robust filtering, an FDE filter is constructed to detect gross errors in satellite observations. S3. Based on the innovation vector and innovation covariance matrix of the FDE filter, construct a global test statistic to determine whether there are gross errors in the current observations; S4. If there are no gross errors, output the navigation and positioning results directly; If gross errors exist, the observations of each satellite are identified one by one based on the local test statistics, faulty satellites containing gross errors are located and removed; and the clean observations after removing gross errors are used to perform BDS and INS tight combination navigation calculations in combination with LEO satellites before outputting the navigation and positioning results.

2. The method for fault detection and isolation of low-orbit enhanced BDS and INS tightly integrated navigation according to claim 1, characterized in that, The LEO-enhanced BDS and INS tightly coupled navigation model constructed in step S1 includes a state equation and an observation equation; the state equation is constructed based on the INS psi angle error equation; the observation equation is constructed based on the difference between the pseudorange and pseudorange rate observations of BDS and INS, and LEO and INS.

3. The method for fault detection and isolation of low-orbit enhanced BDS and INS tightly integrated navigation according to claim 2, characterized in that, The state equations and observation equations are expressed as follows: ； Where, x k It is the state vector at time k, z k w is the observation vector at time k. k and v k These are independent process and measurement noise, h k F represents the nonlinear measurement matrix. k-1 This represents the nonlinear state transition matrix.

4. The method for fault detection and isolation of low-orbit enhanced BDS and INS tightly integrated navigation according to claim 1, characterized in that, The innovation vector r of the FDE filter constructed in step S2 k With the new information covariance matrix S k for: ； Among them, H k h k The linear observation matrix; P k|k-1 This represents the prior error covariance matrix at time k; This represents the prior state at time k.

5. The method for fault detection and isolation of low-orbit enhanced BDS and INS tightly integrated navigation according to claim 1, characterized in that, Whether there are gross errors in the satellite observations in step S3 is determined according to the following method: A global test is performed based on the residuals and covariance matrix of the constructed FDE filter, and a global test statistic TN is constructed. k ,as follows: ； When there are no gross errors in the satellite observations, the statistic TN k Obeying χ 2 distributed; when When α is significant, there are gross errors in the satellite observations.

6. The method for fault detection and isolation of low-orbit enhanced BDS and INS tightly integrated navigation according to claim 1, characterized in that, Step S3 further includes: when there are gross errors in the satellite observations, the innovation vector and the innovation covariance matrix are adjusted using an adaptive kernel bandwidth selection model, as follows: S21. Construct judgment condition α based on the new information vector and the new information covariance matrix. i,k = r i,k / S ii,k , used as a function variable to adjust the kernel bandwidth for each measurement, where r i,k S represents the i-th element of the innovation vector. ii,k Representation matrix The i-th diagonal element; S22. When gross errors exist in satellite observations, the kernel bandwidth is adjusted using an adaptive kernel bandwidth selection model, which is as follows: 。 7. A method for fault detection and isolation of low-orbit enhanced BDS and INS tightly integrated navigation according to claim 1, characterized in that, The local test statistic in step S4 is constructed based on the data probing method, and the statistic for the i-th satellite observation is: ； Among them, e i Let i be a vector whose i-th element is 1 and all other elements are 0; If w i If the value exceeds the set threshold, the satellite observation has gross errors and will be discarded.

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