A pseudo-observation-based heterogeneous flight cluster inertial navigation error cooperative correction method

Abstract

The application discloses a heterogeneous flight cluster inertial navigation error cooperative correction method based on pseudo observation, which is composed of multiple unmanned aerial vehicles (UAVs) and the UAVs observe each other, and comprises the following steps: S1, acquiring inertial navigation positions of the UAVs at a current time and inertial navigation position estimation noises; S2, selecting a reference anchor point, and obtaining relative distance observation, relative azimuth observation and relative pitch angle observation among the UAVs in the cluster; S3, establishing an observation equation of the heterogeneous cluster UAVs according to the observation data obtained in the step S2; S4, constructing a pseudo observation equation according to whether the observation equation is sufficient; S5, classifying according to the rank of an observation matrix, and solving the observation equation; and S6, updating the inertial navigation position, attitude and speed of each UAV. The inertial navigation position information after correction is combined with the inertial navigation information to correct and update the navigation position, attitude and speed, and better overall positioning precision of the cluster can be obtained when the available observation quantity is insufficient.

Description

Technical Field

[0001] This invention relates to a method for collaborative correction of inertial navigation errors, and more particularly to a method for collaborative correction of inertial navigation errors in heterogeneous flight clusters based on pseudo-observations. Background Technology

[0002] Drone swarm technology is one of the future development directions of drone technology, characterized by high reliability, high mission completion rate, and the ability to perform more complex tasks. Drone swarm technology is not simply multiple drones flying in formation, but rather multiple drones forming a highly ordered intelligent group that collaborates and autonomously adjusts to jointly complete a complex and ever-changing task.

[0003] The high mission completion rate of swarm drones relies heavily on high-precision navigation technology. However, under current technological conditions, high-precision inertial navigation equipment is expensive, making it economically difficult to equip every drone in a swarm with it. Relying on GNSS (Global Navigation Satellite System) to correct inertial navigation errors is also affected by GNSS signal rejection in urban environments. In such cases, drones equipped with low-precision inertial navigation in heterogeneous multi-drone swarms often experience rapid navigation error divergence. For some drone swarms equipped with low-precision inertial navigation, it is difficult to obtain good position information in GNSS signal rejection environments, and their positioning errors will diverge over time. Traditional cooperative methods mainly focus on fusing positioning information under stable error conditions. However, in GNSS rejection environments, the inertial navigation error in a swarm drones is constantly diverging rapidly, making it difficult for traditional methods to effectively correct the error and even exacerbating the error divergence rate. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide a method for collaborative correction of inertial navigation errors in heterogeneous flight clusters based on pseudo-observations, which can solve the problem of divergence in inertial navigation positioning errors caused by insufficient observations.

[0005] Technical Solution: A collaborative correction method for inertial navigation errors in heterogeneous flight swarms based on pseudo-observations, comprising multiple UAVs forming a UAV swarm, with mutual observation among the UAVs, including the following steps:

[0006] S1, obtain the current inertial navigation position and inertial navigation position estimation noise of each UAV;

[0007] S2, Select the reference anchor point to obtain relative distance observation, relative azimuth angle observation and relative pitch angle observation among UAVs within the cluster;

[0008] S3. Based on the observation data obtained in step S2, establish the observation equation for the heterogeneous cluster UAV.

[0009] S4. Construct pseudo-observation equations based on whether the observation equations are sufficient;

[0010] S5. Classify the observations based on the rank of the observation matrix in the observation equations of step S3, and solve the observation equations.

[0011] S6 updates the inertial navigation position, attitude, and velocity of each UAV.

[0012] Furthermore, in step S1, the specific steps for obtaining the current inertial navigation position and inertial navigation position estimation noise of each UAV are as follows:

[0013] S11, using the onboard inertial navigation data of the UAVs, obtain the current inertial navigation position of each UAV, represented in the geocentric coordinate system as follows: Where i represents the i-th drone, i = 1, ..., n, and n is the number of drones in the cluster;

[0014] S12, obtain the inertial navigation position estimation noise of the UAV at the current moment, which is represented in the geocentric coordinate system as:

[0015] Furthermore, in step S2, the principles for selecting anchor points are as follows:

[0016] In high-altitude non-GNSS denied areas, UAVs with autonomous GNSS information in high altitude are used as anchor points k.

[0017] Within the GNSS denied area, the UAV obtains the geocentric coordinates (x, y, x) of anchor point k via its onboard communication system. k ,y k ,z k The relative distance between anchor point k and UAV i is obtained through an airborne ranging sensor. Relative azimuth observation and relative pitch angle observation m represents the number of reference anchor points;

[0018] The relative distance between UAV i and UAV j within the cluster is obtained by using the range and angle measuring sensors equipped on each UAV. Relative azimuth observation and relative pitch angle observation

[0019] Furthermore, in step S3, the expression for the heterogeneous cluster UAV observation model is established as follows:

[0020] Y = HX + V

[0021] Where H is the ranging observation matrix, V is the ranging observation error matrix, Y is the ranging observation vector, and X is the inertial navigation position error state vector of the swarm UAV, expressed as follows:

[0022]

[0023]

[0024] Among them, (x i ,y i ,z i () indicates the actual location of the drone.

[0025] Furthermore, in step S4, the detailed steps for constructing the pseudo-observation equation based on whether the observation equation is sufficient are as follows:

[0026] S41, calculate the rank r of the observation matrix obtained in step S3, then r = rank[H];

[0027] If r ≥ 3 × n, there are sufficient anchor points and sufficient observation equations, and the solution formula is as follows:

[0028]

[0029] Measurement weight matrix P Y It is expressed as follows:

[0030] These are distance measurement noise, azimuth measurement noise, and elevation measurement noise, respectively.

[0031] If r < 3 × n, the observation equation is insufficient and a pseudo-observation equation needs to be constructed. Then, step S42 is executed.

[0032] S42, calculate the number of insufficient observation equations t = 3 × nr, which is the number of pseudo-observation equations;

[0033] S43, find H T P Y The eigenvectors of H containing all zero eigenvalues ​​are e1, e2, ..., e t ;

[0034] S44, the pseudo-observation equation is constructed as follows:

[0035]

[0036] Among them, H e V is a pseudo-observation matrix. e This is the pseudo-observation error matrix.

[0037] Furthermore, in step S5, the observation matrix is ​​classified according to its rank, and the observation equation is solved. The detailed implementation steps are as follows:

[0038] S51, estimate noise based on the acquired UAV inertial navigation position. The transformation matrix of the inertial navigation error weight matrix is ​​then set as follows:

[0039]

[0040] S52, Solve for the inertial navigation position error of each UAV in the cluster:

[0041] If the rank r of the observation matrix is ​​greater than or equal to 3×n, the solution formula is as follows:

[0042]

[0043] If the rank r of the observation matrix is ​​less than 3×n, the problem of insufficient observations can be solved using the pseudo-observation equation constructed in step S44. The solution formula is as follows:

[0044]

[0045] in, This is the estimated value of the state vector of the inertial navigation position error of the swarm UAV;

[0046] Will The representation in the geocentric coordinate system is converted into longitude error, latitude error, and altitude error: The expression is as follows:

[0047]

[0048] Where λ, L, and h are the longitude, latitude, and altitude of the UAV, respectively, and R... N f and f represent the Earth's radius of curvature around the circumference and the Earth's oblateness, respectively.

[0049] The corrected UAV inertial navigation position was obtained. The solution formula is as follows:

[0050]

[0051] in, This represents the uncorrected inertial navigation position of UAV i.

[0052] Furthermore, in step S6, the detailed steps for updating the inertial navigation position, attitude, and velocity of each UAV are as follows:

[0053] S61, If ​​the rank r of the observation matrix is ​​greater than or equal to m, then proceed to step S62;

[0054] If the rank r of the observation matrix is ​​less than m, the inertial navigation position, attitude and velocity of each UAV will not be updated.

[0055] S62, based on the inertial navigation information of the aircraft to be assisted, establishes an 18-dimensional state equation:

[0056]

[0057] Among them, F I G is the state coefficient matrix. I Let W be the error coefficient matrix.I The white noise random error vector; the state vector X I :

[0058]

[0059] in, These are the components of the inertial platform error angle in the east, north, and celestial directions of the geographic system, respectively. δL, δλ, and δh represent the components of the velocity error angle in the east, north, and celestial directions of the geographic system, respectively; δL, δλ, and δh represent the longitude error, latitude error, and altitude error, respectively; εL bx ε by ε bz These represent the random constant errors of the gyroscopes in the east, north, and sky directions, respectively; ε rx ε ry ε rz These represent the first-order Markov process random noise of the gyroscopes in the east, north, and sky directions, respectively; Δ x Δ y Δ z These represent the first-order Markov random noise errors of the accelerometers in the east, north, and sky directions, respectively.

[0060] S63, correct the UAV i-inertial navigation position With uncorrected inertial navigation position Combined, the measurement equations for slack integrated navigation are constructed as follows:

[0061]

[0062] Among them, R M R is the radius of curvature in the meridional plane. N N is the radius of curvature of the Earth's geoid; E N N N U The corrected inertial navigation positions of the UAV are as follows: Errors along the east, north, and sky directions;

[0063] S64. Using the state equation and measurement equation obtained in steps S62 and S63, Kalman filtering is used to estimate the position, velocity, and attitude errors, and the inertial navigation position, attitude, and velocity are corrected.

[0064] Compared with the prior art, the significant advantages of this invention are as follows:

[0065] 1. Make full use of the ranging information between UAVs, and introduce pseudo-observation equations for the positioning of heterogeneous UAV clusters to solve the problem of divergence in inertial navigation positioning errors caused by insufficient observations.

[0066] 2. Select UAVs in high-altitude GNSS non-denied environments as anchor points to solve the problem of UAV inertial navigation positioning error divergence in GNSS denied environments and improve the overall navigation performance of heterogeneous UAV clusters.

[0067] 3. To address the differences and variations in the divergence amplitude of inertial navigation systems in heterogeneous unmanned swarms, inertial navigation position noise is introduced for real-time adjustment within the pseudo-observation network, further improving the accuracy of cooperative navigation. Attached Figure Description

[0068] Figure 1 This is a schematic diagram of the overall process of the present invention;

[0069] Figure 2 This is a schematic diagram of the inter-UAV ranging and angular measurement coordinate system in this invention;

[0070] Figure 3 (a) is a comparison of the average position error of the UAV cluster in the east direction after optimization using the method of this invention and the unoptimized UAV cluster when observations are insufficient; (b) is a comparison of the average position error of the UAV cluster in the north direction after optimization using the method of this invention and the unoptimized UAV cluster when observations are insufficient; and (c) is a comparison of the average position error of the UAV cluster in the sky direction after optimization using the method of this invention and the unoptimized UAV cluster when observations are insufficient.

[0071] Figure 4 (a) is a comparison of the average position error of the UAV cluster eastward after optimization and without optimization using the method of this invention when sufficient observations are available; (b) is a comparison of the average position error of the UAV cluster northward after optimization and without optimization using the method of this invention when sufficient observations are available; and (c) is a comparison of the average position error of the UAV cluster daytime after optimization and without optimization using the method of this invention when sufficient observations are available.

[0072] Figure 5 (a) is a comparison of the average pitch angle error of the UAV swarm optimized and unoptimized using the method of this invention when sufficient observations are available; (b) is a comparison of the average roll angle error of the UAV swarm optimized and unoptimized using the method of this invention when sufficient observations are available; and (c) is a comparison of the average heading angle error of the UAV swarm optimized and unoptimized using the method of this invention when sufficient observations are available.

[0073] Figure 6 (a) shows a comparison of the average eastward velocity error of the UAV swarm optimized using the method of this invention and the unoptimized UAV swarm when sufficient observations are available; (b) shows a comparison of the average northward velocity error of the UAV swarm optimized using the method of this invention and the unoptimized UAV swarm when sufficient observations are available; and (c) shows a comparison of the average celestial velocity error of the UAV swarm optimized using the method of this invention and the unoptimized UAV swarm when sufficient observations are available. Detailed Implementation

[0074] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0075] Single UAVs are inefficient, have low redundancy, and are susceptible to interference, making them unsuitable for the demands of large-scale modern swarm operations. The trend from single UAVs to UAV swarms represents a future advanced approach. Addressing the GNSS rejection problem in large cities, this invention proposes a collaborative correction method for inertial navigation errors in heterogeneous flight swarms based on distributed pseudo-observations and solutions. By utilizing mutual measurements between swarm UAVs and observation information from multiple inertial units, more navigation observations can be provided, further improving the accuracy of integrated navigation.

[0076] This invention significantly improves the observability of swarm cooperative positioning by making full use of the mutual ranging information among swarm UAVs. At the same time, the proposed inertial navigation error cooperative correction method based on pseudo-observation solution solves the problem of inertial navigation positioning error divergence caused by insufficient observations, and can effectively enhance the adaptability of swarm UAVs to harsh observation conditions.

[0077] like Figure 1 As shown, the heterogeneous flight swarm inertial navigation error collaborative correction method of the present invention includes the following steps:

[0078] Step 1 involves forming a drone swarm, where multiple drones can observe each other to obtain the current inertial navigation position and estimated inertial navigation position noise of each drone. This includes the following specific steps:

[0079] Step 11: Obtain the current position of each UAV using its onboard inertial navigation data, i.e., the inertial navigation position, represented in the geocentric coordinate system as follows: Where i represents the i-th drone, i = 1, ..., n, and n is the number of drones in the cluster.

[0080] Step 12: Based on the accuracy parameters of the onboard inertial navigation system of each UAV, obtain the position estimation noise of the UAV's onboard inertial navigation system at the current moment, which is represented by the coordinate axes of the geocentric-ground-fixed coordinate system as follows:

[0081] Step 2, obtain the observation data required for co-correction of inertial navigation errors, including the following specific steps:

[0082] Step 21, as follows Figure 2 As shown, in the high-altitude non-GNSS denied area, a UAV capable of autonomously accessing GNSS information in the high altitude serves as anchor point k; within the GNSS denied area, the UAV obtains a high-precision estimate of the geocentric and geofixed coordinates (x, k) of anchor point k through its onboard communication system. k ,y k ,z k The relative distance between anchor point k and UAV i is obtained through an airborne ranging sensor. Relative angle observations are relative azimuth angle observations. and relative pitch angle observation m is the number of anchor points;

[0083] Step 22: Obtain the relative distance between UAVs within the cluster using the ranging and angle measuring sensors equipped on each UAV. Relative azimuth observation and relative pitch angle observation Let j represent the distance and angle measurements between drone i and drone j, where j ≠ i and j = i, ..., n.

[0084] Step 3, establish the observation equations for heterogeneous cluster UAVs, including the following specific steps:

[0085] The distance and angle values ​​obtained in steps 21 and 22 and The distance and angle estimates are subtracted from the distance and angle estimates obtained using the inertial navigation position estimation provided by the airborne inertial navigation equipment, and a first-order Taylor expansion is performed to establish the heterogeneous swarm UAV observation model as follows:

[0086]

[0087] in,

[0088]

[0089]

[0090]

[0091] This indicates the measurement errors of distance, azimuth, and pitch angle between UAV i and UAV j. These represent the measurement errors of the distance, azimuth, and pitch angle between UAV i and anchor point k, respectively. Indicates the inertial navigation position of UAV i, (x i ,y i ,z i () indicates the actual location of the drone.

[0092] H is the ranging observation matrix, V is the ranging observation error matrix, Y is the ranging observation vector, and X is the inertial navigation position error state vector of the swarm UAV. Based on the accuracy of the range and angle measuring sensors of the equipment, the distance measurement noise, azimuth measurement noise, and pitch measurement noise are obtained as follows: Therefore, the measurement weight matrix P Y It is expressed as follows:

[0093]

[0094] Step 4: Construct a pseudo-observation equation based on the insufficient observation equation, including the following specific steps:

[0095] Step 41: Calculate the rank r of the observation matrix established in step 3, r = rank[H]. If r ≥ 3 × n, the anchor points are sufficient and the observation equation is sufficient, then proceed to step 52; otherwise, the observation equation is insufficient and a pseudo-observation equation needs to be constructed, then proceed to step 42.

[0096] Step 42, calculate the number of insufficient observation equations t = 3 × nr, which is the number of pseudo-observation equations;

[0097] Step 43, calculate H T P Y The eigenvectors of H containing all zero eigenvalues ​​are e1, e2, ..., e t This is used to construct the pseudo-observation equation in step 44;

[0098] Step 44, construct the pseudo-observation equation as follows:

[0099]

[0100] Among them, H e V is a pseudo-observation matrix. e This is the pseudo-observation error matrix.

[0101] Step 5: Classify the observations based on the rank of the observation matrix and solve the observation equations, including the following specific steps:

[0102] Step 51: Estimate the noise based on the UAV's onboard inertial navigation position obtained in Step 12. The transformation matrix of the inertial navigation error weight matrix is ​​then set as follows:

[0103]

[0104] Step 52: Solve for the inertial navigation position error of each UAV in the cluster. If the rank r of the observation matrix in step 41 is greater than or equal to 3×n, the solution formula is as follows:

[0105]

[0106] If the rank r of the observation matrix in step 41 is less than 3×n, the problem of insufficient observations can be solved using the pseudo-observation equation constructed in step 44. The solution formula is as follows:

[0107]

[0108] in, The estimated value of the state vector of the inertial navigation position error of the swarm UAV; The representation in the geocentric coordinate system is converted into longitude error, latitude error, and altitude error. The expression is as follows:

[0109]

[0110] Where λ, L, and h are the longitude, latitude, and altitude of the UAV, respectively; R N f and f represent the Earth's circumpolar curvature radius and Earth's oblateness, respectively.

[0111] Corrected UAV inertial navigation position The solution formula is as follows:

[0112]

[0113] in, This represents the uncorrected inertial navigation position of UAV i.

[0114] Step 6: Update the inertial navigation position, attitude, and velocity of each UAV by category, including the following specific steps:

[0115] Step 61: If r ≥ m in step 41, then proceed to step 62; otherwise, do not update the inertial navigation position, attitude, and velocity of each UAV.

[0116] Step 62: Based on the inertial navigation information of the aircraft to be assisted, establish an 18-dimensional state equation:

[0117]

[0118] Among them, F I G is the state coefficient matrix. I Let W be the error coefficient matrix. I The white noise random error vector; the state vector X I :

[0119]

[0120] in, These are the components of the inertial platform error angle in the east, north, and celestial directions of the geographic system, respectively. δL, δλ, and δh represent the components of the velocity error angle in the east, north, and celestial directions of the geographic system, respectively; δL, δλ, and δh represent the longitude, latitude, and altitude errors, respectively; ε bx ε by ε bz These represent the random constant errors of the gyroscopes in the east, north, and sky directions, respectively; ε rx ε ry ε rz These represent the first-order Markov process random noise of the gyroscopes in the east, north, and sky directions, respectively; Δ x Δ y Δ z These represent the first-order Markov random noise errors of the accelerometers in the east, north, and celestial directions, respectively.

[0121] Step 63: Obtain the corrected UAV i-inertial navigation position from step 52. With uncorrected inertial navigation position Combined, the measurement equations for slack integrated navigation are constructed as follows:

[0122]

[0123] Among them, R M N is the radius of curvature in the meridional plane; E N N N U The corrected inertial navigation positions of the UAV are as follows: Errors along the east, north, and sky directions.

[0124] Step 64: Using the state equations and measurement equations obtained in steps 62 and 63, Kalman filtering is used to estimate the position, velocity, and attitude errors, and the inertial navigation position, attitude, and velocity are corrected.

[0125] To verify the effectiveness of the proposed method for collaborative correction of inertial navigation errors in heterogeneous flight swarms based on pseudo-observations, digital simulation analysis was conducted. In the simulation, the number of available anchor nodes was either 1 or none, the number of swarm UAVs was 7, the standard deviation of the ranging noise of the used ranging sensor was 0.01m, and the standard deviation of the angular noise of the used angle measuring sensor was 0.01°. Figure 3 In the figure, (a), (b), and (c) are curves showing the changes in the average east, north, and sky position errors of the swarm UAVs as a function of navigation time before and after using the method of the present invention when no available anchor points are available. Figure 4 In the figure, (a), (b), and (c) are curves showing the changes in the average east, north, and sky position errors of the swarm UAVs before and after using the method of the present invention with navigation time when the number of available anchor points is 1. Figure 5 In the figure, (a), (b), and (c) are curves showing the changes in the average pitch angle, roll angle, and heading angle error of the swarm UAVs before and after using the method of the present invention, respectively, when the number of available anchor points is 1. Figure 6 In the figure, (a), (b), and (c) are curves showing the changes in the average east, north, and sky speed errors of the clustered UAVs with navigation time before and after using the method of the present invention when the number of available anchor points is 1.

[0126] Depend on Figure 3 As shown in (a), (b), and (c), when the number of UAVs in the cluster is 7 and the number of anchor points is 0, the insufficient number of observation equations is 6, indicating insufficient cluster observation information. After correction using the heterogeneous UAV cluster distributed inertial navigation error collaborative correction method based on pseudo-observation solutions, the average positioning error of the UAVs in the cluster is significantly reduced within a 600s navigation time compared to before correction. Figure 4 (a), (b), and (c) in the text. Figure 5 (a), (b), and (c) in the text. Figure 6 As shown in (a), (b), and (c), when the number of UAVs in the cluster is 7 and the number of anchor points is 1, the observation equations are sufficient, and the cluster observation information is abundant. High positioning accuracy can still be achieved without constructing pseudo-observation equations. The attitude and velocity errors are also corrected after using the loosely combined navigation algorithm. The positioning error obtained by using the method of this invention for collaborative correction of inertial navigation errors can consistently maintain a low average positioning error level for clustered UAVs and high cluster collaborative navigation accuracy. It can effectively improve the collaborative positioning performance under cluster conditions and has good application value.

[0127] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for collaborative correction of inertial navigation errors in heterogeneous flight swarms based on pseudo-observations, characterized in that, A drone swarm, consisting of multiple drones, observes each other, including the following steps: S1, obtain the current inertial navigation position and inertial navigation position estimation noise of each UAV; S2, Select the reference anchor point to obtain relative distance observation, relative azimuth angle observation and relative pitch angle observation among UAVs within the cluster; S3. Based on the observation data obtained in step S2, establish the observation equation for the heterogeneous cluster UAV. S4. Construct pseudo-observation equations based on whether the observation equations are sufficient; S5. Classify the observations based on the rank of the observation matrix in the observation equations of step S3, and solve the observation equations. S6, update the inertial navigation position, attitude and velocity of each UAV; In step S1, the specific steps for obtaining the current inertial navigation position and inertial navigation position estimation noise of each UAV are as follows: S11, using the onboard inertial navigation data of the UAVs, obtain the current inertial navigation position of each UAV, represented in the geocentric coordinate system as follows: ,in Indicates the first One drone, , The number of drones in the cluster; S12, obtain the inertial navigation position estimation noise of the UAV at the current moment, which is represented in the geocentric coordinate system as: ; In step S2, the principles for selecting anchor points are as follows: In high-altitude non-GNSS denied areas, drones using autonomous high-altitude GNSS information serve as anchor points. ; Within GNSS denied areas, the UAV obtains anchor points via its onboard communication system. Earth-centered and Earth-fixed coordinates Anchor points are obtained through airborne ranging sensors. For drones Relative distance observation Relative azimuth observation and relative pitch angle observation , , The number of reference anchor points; By using the range and angle measuring sensors equipped on each drone, the data of the drones within the cluster can be obtained. With drones Relative distance observation Relative azimuth observation and relative pitch angle observation , , ; In step S3, the expression for the heterogeneous cluster UAV observation model is established as follows: in, This is the distance measurement observation matrix. This is the distance measurement observation error matrix. This is the distance measurement observation vector; The inertial navigation position error state vector of the swarm UAV is expressed as follows: in, Indicates the actual location of the drone; In step S4, the detailed steps for constructing the pseudo-observation equation based on whether the observation equation is sufficient are as follows: S41, Calculate the rank of the observation matrix obtained in step S3. Then there is ; like With sufficient anchor points and observation equations, the solution formula is as follows: ； Measurement weight matrix P Y It is expressed as follows: , , , These are distance measurement noise, azimuth measurement noise, and elevation measurement noise, respectively. like The observation equations are insufficient, so it is necessary to construct pseudo-observation equations and execute step S42. S42, Calculate the insufficient number of the observation equation. , where is the number of pseudo-observation equations; S43, please obtain All zero eigenvalue eigenvectors ; S44, the pseudo-observation equation is constructed as follows: ， in, This is a pseudo-observation matrix. This is the pseudo-observation error matrix.

2. The method for collaborative correction of inertial navigation errors in heterogeneous flight clusters based on pseudo-observations according to claim 1, characterized in that, In step S5, the observation matrix is ​​classified according to its rank, and the observation equation is solved. The detailed implementation steps are as follows: S51, estimate noise based on the acquired UAV inertial navigation position. Then the transformation matrix of the inertial navigation error weight matrix is ​​set as follows: ； S52, Solve for the inertial navigation position error of each UAV in the cluster: If the rank of the observation matrix The solution formula is as follows: ； If the rank of the observation matrix The problem of insufficient observations is solved by using the pseudo-observation equation constructed in step S44. The solution formula is as follows: in, , is the estimated value of the state vector of the inertial navigation position error of the clustered UAVs; Will The representation in the geocentric coordinate system is converted into longitude error, latitude error, and altitude error: The expression is as follows: in, These are the longitude, latitude, and altitude of the drone. These are the Earth's radius of curvature along its circumference and its oblateness, respectively. The corrected drone Inertial navigation position The solution formula is as follows: in, For drones Uncorrected inertial navigation position.

3. The method for collaborative correction of inertial navigation errors in heterogeneous flight clusters based on pseudo-observations according to claim 2, characterized in that, In step S6, the detailed steps for updating the inertial navigation position, attitude, and velocity of each UAV are as follows: S61, if the rank of the observation matrix Then proceed to step S62; If the rank of the observation matrix No updates to the inertial navigation position, attitude, and velocity of each UAV are performed; S62, based on the inertial navigation information of the aircraft to be assisted, establishes an 18-dimensional state equation: in, The state coefficient matrix, The error coefficient matrix is... White noise random error vector; state vector : in, These are the components of the inertial platform error angle in the east, north, and celestial directions of the geographic system, respectively. These are the components of the velocity error angle in the east, north, and sky directions of the geographic system, respectively. These are longitude error, latitude error, and altitude error, respectively. These are the random constant errors of the gyroscopes in the east, north, and sky directions, respectively. These represent the first-order Markov process random noise of the gyroscopes in the east, north, and sky directions, respectively. These represent the first-order Markov random noise errors of the accelerometers in the east, north, and sky directions, respectively. S63, the corrected drone Inertial navigation position With uncorrected inertial navigation position Combined, the measurement equations for slack integrated navigation are constructed as follows: in, Let be the radius of curvature within the meridional plane. The radius of curvature of the Earth's geoid; , , The corrected drones Inertial navigation position Errors along the east, north, and sky directions; S64. Using the state equation and measurement equation obtained in steps S62 and S63, Kalman filtering is used to estimate the position, velocity, and attitude errors, and the inertial navigation position, attitude, and velocity are corrected.

Images