Aircraft cluster relative navigation method based on common-view target in denial environment

Abstract

The invention discloses an aircraft cluster relative navigation method based on a common-view target in a denial environment, and the method comprises the steps: obtaining a corresponding flight state and inertia measurement information through a generated trajectory, and building a relative motion state equation to carry out the updating and evolution of a relative state between members of an aircraft cluster; and introducing constant deviation and random walk into the generated inertial measurement information to simulate actual measurement information. The method comprises the following steps: constructing a measurement model of airborne measurement equipment, constructing relative position measurement between aircrafts according to guidance information of the aircrafts to a target, fusing relative states, inertial measurement information and measurement data by using extended Kalman filtering to obtain prior estimation and posteriori estimation of the states, constructing physical constraints for state quantities between the aircrafts, and obtaining the state parameters between the aircrafts. Consistency constraint is constructed by using state prior estimation and is incorporated into posteriori estimation of extended Kalman filtering, and the relative navigation method of the aircraft cluster based on the common-view target in the denial environment is completed.

Description

Technical Field

[0001] This invention relates to the field of autonomous relative navigation technology for unmanned aerial vehicle (UAV) swarms, and more specifically to a relative navigation method for UAV swarms based on common-view targets in a denied environment. Background Technology

[0002] In recent years, inspired by the flocking behavior of animals such as geese and bees, research on the theory and practical application of swarm aircraft has been carried out in both military and civilian fields. Compared to a single large aircraft, the coordinated operation of multiple small and medium-sized aircraft can reduce application costs and accomplish more complex tasks. Furthermore, due to their advantages in quantity and size, they can reduce losses when attacked and improve the overall stability of the system in the event of emergencies. The primary prerequisite for applying swarm aircraft is achieving precise relative positioning between the aircraft.

[0003] Existing unmanned aerial vehicles (UAVs) are generally equipped with inertial navigation systems. By integrating measured acceleration and angular velocity data, the aircraft's velocity and attitude information can be obtained, and the velocity can be further integrated to determine its position. However, because inertial measurement systems record noise during measurement, the continuous integration process leads to noise accumulation and significant errors in the final position and attitude information. Therefore, it is necessary to introduce other measurement devices to correct these errors. The traditional method is to use Global Navigation Satellite Systems (GNSS), which can directly obtain the aircraft's position and accurately estimate its velocity. Combined with inertial navigation systems, this creates a significant complementary effect, effectively suppressing errors introduced by integration. However, in complex environments, GNSS signals may become unusable due to multipath effects, object obstruction, and interference. Therefore, a relative navigation scheme for GNSS-denied environments is urgently needed.

[0004] Relative navigation in GNSS-denied environments mainly falls into two categories: visual information-based and radio information-based. Visual information-based relative navigation acquires images and extracts feature points to build a map in real time, enabling precise self-positioning of aircraft and relative positioning among crew members. Furthermore, since visual information can be directly measured without inter-aircraft communication, it is more suitable for relative measurement of hostile targets. However, it cannot acquire obvious information when there are no clear features in the environment, and relying solely on visual information may render aircraft swarms unsuitable in complex environments. Radio-based relative measurement methods include data links, UWB, and radar. UWB can be used to measure relative distances. By establishing anchor points and measuring the distance between aircraft and these anchor points, the positions of each aircraft can be accurately located, thus achieving relative navigation. However, fixed anchor points cannot be established in unknown environments, and due to the limited signal transmission distance of UWB, it is not suitable for long-distance distance measurement. Data links can also measure distances, with a longer range and are less susceptible to interference, making them more widely used for long-distance flight in GNSS-denied environments.

[0005] For relative navigation in long-range, unknown combat environments, existing anchor point methods or observable trajectory maneuvering methods are usually ineffective. Therefore, it is urgent to introduce new physical constraints to solve the problem of swarm relative navigation in denied environments.

[0006] Typically, some aircraft within a swarm possess target detection capabilities. When collaborative detection of a common target yields distance and angle measurements, this information can also be used for relative navigation among swarm members. However, establishing an autonomous spatiotemporal reference within the swarm, based on the detection of the same target, is a problem that needs to be solved. Therefore, existing autonomous relative navigation technologies for aircraft swarms do not fully utilize enemy measurement information to achieve relative navigation within the swarm. Furthermore, in unknown environments, existing GNSS navigation, visual navigation, or traditional anchor-point-based relative navigation technologies cannot guarantee the normal operation of the system. Summary of the Invention

[0007] The purpose of this invention is to provide a relative navigation method for aircraft swarms based on common-view targets in GNSS-denied environments. This method is applicable to open sea areas in GNSS-denied environments and can quickly solve the relative pose between aircraft without external auxiliary equipment. It can achieve autonomous relative navigation between aircraft swarms using only airborne seekers, data links, and common airborne equipment.

[0008] Technical solution:

[0009] A method for relative navigation of aircraft swarms based on common-view targets in a denied environment includes:

[0010] Step 1, Dynamic State Prediction: Based on the angular velocity and acceleration information collected by inertial sensors, the relative pose of the aircraft swarm members is predicted using the relative motion state equation, and the relative position vector is output. Speed ​​of this system and attitude transformation matrix

[0011]

[0012] Step 2, Sensor Noise Injection: In the ideal trajectory data generated in Step 1, constant bias and random walk noise are added to the inertial measurement values ​​to generate noisy accelerometer data f. A f B and gyroscope data

[0013] Step 3, Multi-source measurement fusion: Fusion of ranging and angle measurement data of the seeker to the common target, inter-aircraft ranging data of the data link, attitude angle data of the attitude instrument and velocity data of the pitot tube to construct the observation vector y, wherein the seeker data is converted into indirect measurement values ​​of the relative position between the aircraft through geometric relationships;

[0014] Step 4, Extended Kalman Filter Estimation: Using the state prediction results from Step 1 and the observation vectors from Step 3, the posterior state estimate is calculated using the extended Kalman filter algorithm to correct the relative pose error;

[0015] Step 5, Consistency Constraint Compensation: To address the inconsistency problem in distributed estimation across multiple aircraft, closed geometric constraints are introduced. A consistent Kalman filter is used to correct the posterior estimate, ensuring the output satisfies... The final state estimate.

[0016] Preferably, the relative motion state equations established in step 1 are as follows:

[0017]

[0018] The state equations include the relative position of the aircraft, the real-time states of velocity and attitude within the system, and the aircraft's dynamic input. The relative position vector in the previous time-series state variables is: The speeds of the aircraft are respectively The control input U is the gyroscope and accelerometer information collected by the inertial devices. The angular velocity information collected by aircraft A and B are respectively, f A f B These are the specific forces collected by the accelerometers of aircraft A and B, respectively. This represents the angular velocity of the geocentric fixed coordinate system relative to the inertial frame; the superscript n indicates projection onto the navigation coordinate system. These are the local gravity forces for aircraft A and aircraft B, respectively. Let be the attitude transformation matrix between aircraft B and aircraft A. Let A be the attitude transformation matrix between aircraft A and B and the geographic coordinate system. Update the corresponding pose matrix.

[0019] Preferably, in step 2, noise is added to the data corresponding to the ideal trajectory generated in step 1, including the zero bias and random walk of the gyroscope and accelerometer, to simulate the error when the sensor is measured, and to be used for state update recursion. The reference true value is given by the trajectory in step 1, and the noise level is added based on the reference true value.

[0020] Preferably, in step 3, the ranging and angle measurement data of the seeker to the common target, the inter-aircraft ranging data of the data link, the attitude angle data of the attitude instrument and the velocity data of the pitot tube are fused to construct the observation vector y, wherein the seeker data is converted into indirect measurement values ​​of the relative positions between the aircraft through geometric relationships.

[0021] Preferably, in step 3, the measurement model of the airborne measurement equipment with respect to the relative state quantity is as follows: The first item The relative position vector between the two aircraft is obtained by converting guidance information from a common target. The seeker is at a distance d. At d Bt Azimuth α At α Bt and pitch angle β At β Bt At that time, all measured values ​​will be affected by noise interference, as shown below:

[0022] The superscript ^ indicates a measured value; the observation noise δ is determined by the seeker measuring the distance r to the target. t Azimuth α, Pitch β, and distance r between aircraft measured by data link d The error is composed of the Euler angles of attitude measured by the attitude instrument and the rate measured by the pitot tube, and is expressed as δ=[δr t δα δβ δr d δθ δγ δφ δv] T δ follows a Gaussian distribution with standard deviations σ(r) and σ(r) respectively. t ), σ(α), σ(β), σ(r) d ), σ(θ), σ(γ), σ(φ), σ(v), and in addition, the pitot tube measurement of speed also includes a constant deviation Δv, where, Let be the relative position vector between the two aircraft A and B and the target. Let A be the relative position vector between aircraft A and B. Let A and B be the velocities of aircraft A and B, respectively; θ, γ, and φ be the pitch, roll, and yaw angles of the aircraft, respectively; subscripts A and B are the aircraft designations; and || represents the modulus of the vector. This method converts target guidance information into relative position measurements between aircraft, avoiding the possibility of multiple solutions when only distance measurements are available between aircraft.

[0023] Preferably, in step 4, the relative pose error is corrected by fusing the predicted and observed quantities using Kalman gain, as expressed as... in K is the prior estimate obtained by integrating the relative motion state equations in step 1. k For Kalman gain, y k For the actual observations, corresponding to the mutual estimation among the three aircraft A, B, and C, their prior estimates are as follows:

[0024]

[0025] In the formula, For state prior estimation, p is the position vector, and the subscripts AB, BC, and CA represent the relationship between aircraft A and B, aircraft B and C, and aircraft C and A, respectively. v is the velocity of the aircraft, and θ, γ, and φ are the pitch angle, roll angle, and yaw angle of the aircraft, respectively. The subscripts A, B, and C are the aircraft designations.

[0026] Preferably, in step 5, based on the prior estimates and covariance matrices of each aircraft, the mathematical constraint model for the consensus extended Kalman filter is calculated:

[0027]

[0028] By modifying the constraint model, the corrected state estimate is obtained:

[0029]

[0030] in, All of these are prior estimates of the extended Kalman filter in step 4, representing the prior state estimates between aircraft A and aircraft B, between aircraft B and aircraft C, and between aircraft C and aircraft A, respectively. and Let be a generalized transformation matrix, such that the actual state satisfies P k / k-1 For the prior estimate of covariance, ε is the coefficient of the consistency constraint, || || F This represents the Frobenius norm.

[0031] Beneficial effects

[0032] This invention indirectly measures the relative positions of cluster aircraft by introducing objects observed by the seeker into the cluster members and performing corresponding coordinate transformations on the guidance measurement information of each member to obtain the relative position measurement between the aircraft. Simultaneously, it transforms the physical constraints between aircraft states into mathematical forms and applies them to the Kalman filter, effectively improving the estimation accuracy of the distributed filter. Specifically, it uses the relative motion equation as the state equation, seeker measurement information, data link ranging information, pitot tube measurement information, and attitude instrument measurement information as measured values, and geometric constraints between member states as consistency constraints. A consistent Kalman filter is then used to estimate the relative positions, velocities, and attitudes between the aircraft. Attached Figure Description

[0033] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0034] Figure 1 This is a schematic diagram showing the relative positions of the aircraft and the target in an embodiment of the present invention;

[0035] Figure 2 This is a diagram showing the trajectory of the aircraft and the location of the target in an embodiment of the present invention;

[0036] Figure 3 This is a graph showing the relative distance estimation error between aircraft 1 and aircraft 2 in an embodiment of the present invention;

[0037] Figure 4 This is a graph showing the relative distance estimation error between aircraft 2 and aircraft 3 in an embodiment of the present invention;

[0038] Figure 5 This is a graph showing the relative distance estimation error between aircraft 3 and aircraft 1 in an embodiment of the present invention;

[0039] Figure 6 This is a graph showing the attitude estimation error of aircraft 1 in this embodiment of the invention;

[0040] Figure 7 This is a graph showing the attitude estimation error of the aircraft 2 in this embodiment of the invention;

[0041] Figure 8 This is a graph showing the attitude estimation error of the aircraft 3 in this embodiment of the invention. Detailed Implementation

[0042] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many different ways as described herein, and those skilled in the art can make similar modifications without departing from the spirit of the invention; therefore, the present invention is not limited to the specific embodiments disclosed below. Embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0043] Example

[0044] This invention provides a relative navigation method for aircraft swarms based on guidance information. Addressing the issue that methods relying solely on ranging in GNSS-denied environments lack reliable spatial coordinates for aircraft, requiring multiple friendly UAVs to solve for formation configuration and failing to fully utilize guidance information about common-view targets, this invention constructs relative position information among swarm members using their guidance information about common-view targets as observations. It then uses a consistent extended Kalman filter to estimate the relative state of the swarm aircraft, enabling relative navigation of aircraft swarms.

[0045] This invention takes the swarm flight mission of aircraft as the background, and uses data from airborne inertial navigation equipment to perform relative position, attitude and velocity evolution, and guide information for common-view targets. It uses the distance between aircraft, the airspeed and attitude of aircraft as measurement information, and the geometric topology information between aircraft as constraints. It uses consistent Kalman filtering to estimate relative position, attitude and velocity information, and realizes relative navigation of aircraft swarm.

[0046] like Figure 1 As shown, the specific solution is as follows:

[0047] Step 1: Generate the corresponding flight trajectory under the aircraft's trajectory system, thereby obtaining the corresponding flight state, simulating the aircraft's flight mission in space, and constructing a model including the aircraft's relative position. Speed ​​in this system attitude The dynamic model includes the aircraft's power input.

[0048] The dynamic state equations are expressed as follows:

[0049]

[0050] This includes the relative position vector in the preceding time state quantities of the aircraft. aircraft speed The control input U is the information from the gyroscope and accelerometer collected by the inertial devices, where... The angular velocity information collected by aircraft A and B are respectively, fA f B These are the specific forces collected by the accelerometers of aircraft A and B, respectively. This represents the angular velocity of the geocentric fixed coordinate system relative to the inertial frame; the superscript n indicates projection onto the navigation coordinate system. These are the local gravity forces for aircraft A and aircraft B, respectively. Let be the attitude transformation matrix between aircraft B and aircraft A. The attitude transformation matrix between aircraft A, B and the geographic coordinate system. Update the corresponding pose matrix.

[0051] Step 2: Add noise to the control input corresponding to the trajectory generated in Step 1, including gyroscope and accelerometer zero bias and random walk, to simulate the error of sensor measurement and to be used for state update recursion. Its reference truth value is given by the trajectory in Step 1), and the noise level is added based on the reference truth value.

[0052] Step 3: Set the relevant parameters for the aircraft's onboard attitude control system, pitot tube, seeker, data link, and other airborne equipment. Use the attitude control system to obtain the aircraft's attitude relative to the navigation system, i.e., pitch angle θ, roll angle γ, and yaw angle φ. Use the pitot tube to measure the aircraft's speed ||v||. Use the seeker to measure the relative position r between the aircraft and the target. Convert the measurement information of the two aircraft relative to the target into the relative position between the aircraft. Use the data link to measure the distance ||r|| between the aircraft. Add observation noise to the trajectory and aircraft navigation status data to simulate and generate observation values.

[0053] The airborne equipment measurement model is

[0054]

[0055] The first item The relative position vector between the two aircraft is obtained by converting guidance information from a common target. The seeker is at a distance d. At d Bt Azimuth α At α Bt and pitch angle β At β Bt At that time, all measured values ​​will be affected by noise interference, that is

[0056]

[0057] The observation noise consists of the range, azimuth, and pitch angles measured by the seeker, the inter-aircraft distances measured by the data link, the Euler angles of the attitude measured by the attitude instrument, and the rate error measured by the pitot tube, i.e., δ=[δr t δαδβδr d δθδγδφδv] TIt follows a Gaussian distribution with standard deviations σ(r) and σ(r) respectively. t ), σ(α), σ(β), σ(r) d ), σ(θ), σ(γ), σ(φ), σ(v), and in addition, the airspeed tube also includes the constant deviation Δv when measuring the speed; This is the relative position vector between the two aircraft and the target. This represents the relative position vector between the aircraft. θ represents the velocity of the aircraft; θ, γ, and φ represent the pitch, roll, and yaw angles of the aircraft, respectively; subscripts A and B are the aircraft designations; and || represents the modulus of the vector.

[0058] Step 4: The relative state is estimated a priori by fusing the spacecraft relative state and inertial device control input from previous time steps using the extended Kalman filter algorithm, and then updated using the prior estimate of the observation data with errors.

[0059] The relative pose error is corrected by fusing the predictions and observations using Kalman gain, as follows:

[0060]

[0061] In the formula, This is the prior estimate obtained by integrating the equations of state of relative motion in step 1, i.e. dt is the sampling interval time, K k For Kalman gain, y k For the actual observations, corresponding to the mutual estimation among the three aircraft A, B, and C, their prior estimates are as follows:

[0062]

[0063] In the formula, These represent the prior state estimates for the path from aircraft A to B (the state predicted at time k-1), the prior state estimates for the path from aircraft B to C, and the prior state estimates for the path from aircraft C to A, respectively. Position parameters. These represent the displacement vectors of aircraft B relative to A (with A as the coordinate reference system), aircraft C relative to B (with B as the coordinate reference system), and aircraft A relative to C (with C as the coordinate reference system). Let A be the velocity of aircraft A in coordinate system A, B be the velocity of aircraft B in coordinate system B, and C be the velocity of aircraft C in coordinate system C.

[0064] Step 5 addresses the issue of inconsistent estimation results for the same state across the three aircraft by introducing a consistency constraint compensation in the posterior estimation of the extended Kalman filter, thereby further improving accuracy. The specific form of the consistency constraint is as follows:

[0065]

[0066] The specific form of the corrected state estimate obtained after introducing consistency constraints is as follows: in All of these are prior estimates from the extended Kalman filter in step 4, representing the prior state estimates between aircraft A and aircraft B, between aircraft B and aircraft C, and between aircraft C and aircraft A, respectively. and Let be a generalized transformation matrix, such that the actual state satisfies P k / k-1 For the prior estimate of covariance, ε is the coefficient of the consistency constraint, || || F This represents the Frobenius norm.

[0067] Examples of the present invention:

[0068] Set the following calculation conditions and technical parameters:

[0069] 1) The initial coordinates of spacecraft 1 are 31.8959°N, 118.7934°E, and an altitude of 20m. Using the initial point of spacecraft 1 as the origin, the initial and target points of spacecraft 2 and 3, established in a geographic coordinate system with a northeastern sky, are [-3792.72m, 3812.67m, -2.27m], [-3794.26m, -634.62m, -1.16m], and [-5411.08m, 17155.4m, -45.46m], respectively. Their speeds are all 20m / s, and the corresponding flight trajectories are as follows: Figure 2 As shown.

[0070] 2) The initial relative position estimation error is 100m across all three axes, the velocity error is 1m / s across all axes, and the attitude error is 1° in all directions. The data link and seeker have an error of 10m (1σ) for ranging, 2° (1σ) for angle measurement, a pitot tube constant deviation of 1m / s, random noise of 0.1m / s (1σ), an accelerometer zero bias of 10ug, a random walk of 1ug, a gyroscope constant drift of 10° / h, and a random walk of 1° / √h. For aircraft attitude measurement, the noise is 1° in roll and pitch, and 2° in yaw.

[0071] Based on the relative navigation method of this invention and the above-mentioned calculation conditions and technical parameters, numerical simulation verification was performed, with a simulation time of 830 seconds. Figures 3 to 8 The figures show the relative positions and attitude error curves among the cluster members. As can be seen from the curves, the estimation errors converge. Using the root mean square error (RMSE) of the relative position estimation errors calculated between 100s and 830s of flight as a benchmark, the RMSEs of the relative position estimation errors between aircraft 1 and 2, aircraft 2 and 3, and aircraft 3 and 1 are [16.8729m, 10.2202m, 26.5555m], [38.2075m, 21.1601m, 20.8171m], and [14.2040m, 12.8100m, 38.5551m], respectively. The RMSEs of the distance estimation errors between the three aircraft are 0.6%, 1%, and 1.1% of the actual distances, respectively. The attitude measurements of the three aircraft are approximately 84.48%, 84.24%, and 88.41% higher than the direct measurements.

[0072] Therefore, by using the method of this invention, relative navigation tasks of swarm unmanned aerial vehicles can be achieved in GNSS-denied environments by relying solely on the combination of airborne inertial unit, seeker and data link TOA ranging, attitude reference instrument and pitot tube, making full use of the guidance information of the target.

[0073] This invention has many specific applications. The above description is only a preferred embodiment of this invention. It should be noted that for those skilled in the art, several improvements can be made without departing from the principle of this invention, and these improvements should also be considered within the scope of protection of this invention.

Claims

1. A relative navigation method for aircraft swarms based on common-view targets in a denied environment, characterized in that, Includes the following steps: Step 1: Generate the aircraft trajectory, obtain the corresponding flight state, and use the angular velocity and acceleration information collected by the inertial sensor to update and evolve the relative pose of the aircraft cluster members using the relative motion state equation to obtain the relative pose prediction value. Step 2: Add constant deviation and random walk to the real information of the inertial sensor to simulate the measurement information of the tolerance error; Step 3: Establish a measurement model for relative state quantities using airborne measurement equipment, integrate guidance information for common targets to generate indirect measurement values ​​between aircraft, and construct the observation vector y; Step 4: Based on the predicted values ​​from Step 1 and the observed vector y from Step 3, the relevant states are estimated using an extended Kalman filter. Step 5: Based on the principle of consistent Kalman filtering, the estimated relative position, attitude, velocity and other information among the members of the aircraft cluster are unified, and the above mathematical constraint model is added as a consistency constraint to the feedback of the filtering process to obtain the corrected state estimate.

2. The relative navigation method according to claim 1, characterized in that, In step 1, input the raw data from the inertial sensors, including the angular velocities collected by aircraft A and B. and acceleration f A f B By recursively applying differential equations, the relative poses between the aircraft at the next moment are predicted, including the relative position vector of aircraft B relative to A. The system velocities of aircraft A and B and attitude transformation matrix Provide prior estimates for step 3.

3. The relative navigation method according to claim 2, characterized in that, In step 1, the relative motion state equations are established as follows: The state equations include the relative position of the aircraft, the real-time states of velocity and attitude within the system, and the aircraft's dynamic input. The relative position vector in the previous time-series state variables is: The speeds of the aircraft are respectively The control input U is the gyroscope and accelerometer information collected by the inertial devices. The angular velocity information collected by aircraft A and B are respectively, f A f B These are the specific forces collected by the accelerometers of aircraft A and B, respectively. This represents the angular velocity of the geocentric fixed coordinate system relative to the inertial frame; the superscript n indicates projection onto the navigation coordinate system. These are the local gravity forces for aircraft A and aircraft B, respectively. Let be the attitude transformation matrix between aircraft B and aircraft A. Let A be the attitude transformation matrix between aircraft A and B and the geographic coordinate system. Update the corresponding pose matrix.

4. The relative navigation method according to claim 1, characterized in that, In step 2, noise is added to the data corresponding to the ideal trajectory generated in step 1, including the zero bias and random walk of the gyroscope and accelerometer, to simulate the error when the sensor is measured, and to be used for state update recursion. The reference true value is given by the trajectory in step 1, and the noise level is added based on the reference true value.

5. The relative navigation method according to claim 1, characterized in that, In step 3, the ranging and angle measurement data of the seeker to the common target, the inter-aircraft ranging data of the data link, the attitude angle data of the attitude instrument and the velocity data of the pitot tube are fused to construct the observation vector y. The seeker data is converted into indirect measurement values ​​of the relative positions between the aircraft through geometric relationships.

6. The relative navigation method according to any one of claims 1-5, characterized in that, In step 3, the measurement model of the airborne measurement equipment for relative state quantities is as follows: The first item The relative position vector between the two aircraft is obtained by converting guidance information from a common target. The seeker is at a distance d. At d Bt Azimuth α At α Bt and pitch angle β At β Bt At that time, all measured values ​​will be affected by noise interference, as shown below: The superscript ^ indicates a measured value; The observation noise δ is determined by the seeker measuring the distance r to the target. t Azimuth α, Pitch β, and distance r between aircraft measured by data link d The error is composed of the Euler angles of attitude measured by the attitude instrument and the rate measured by the pitot tube, and is expressed as δ=[δr t δα δβ δr d δθ δγ δφδv] T δ follows a Gaussian distribution with standard deviations σ(r) and σ(r) respectively. t ), σ(α), σ(β), σ(r) d ), σ(θ), σ(γ), σ(φ), σ(v), and in addition, the pitot tube measurement of speed also includes a constant deviation Δv, where, Let be the relative position vector between the two aircraft A and B and the target. Let A be the relative position vector between aircraft A and B. Let A and B be the velocities of aircraft A and B, respectively; θ, γ, and φ be the pitch, roll, and yaw angles of the aircraft, respectively; subscripts A and B are the aircraft designations; and |||| represents the modulus of the vector.

7. The relative navigation method according to claim 6, characterized in that, In step 4, the relative pose error is corrected by fusing the predicted and observed quantities using Kalman gain, as expressed as... in K is the prior estimate obtained by integrating the relative motion state equations in step 1. k For Kalman gain, y k For the actual observations, corresponding to the mutual estimation among the three aircraft A, B, and C, their prior estimates are as follows: In the formula, For state prior estimation, p is the position vector. The subscripts AB, BC, and CA represent the relationship between aircraft A and B, aircraft B and C, and aircraft C and A, respectively. θ, γ, and φ are the pitch, roll, and yaw angles of the aircraft, respectively. The subscripts A, B, and C are the aircraft designations. Let be the speeds of aircraft A, B, and C.

8. The relative navigation method according to claim 1 or 7, characterized in that, In step 5, based on the prior estimates and covariance matrices of each aircraft, the mathematical constraint model for the consensus extended Kalman filter is calculated: By modifying the constraint model, the corrected state estimate is obtained: in, All of these are prior estimates of the extended Kalman filter in step 4, representing the prior state estimates between aircraft A and aircraft B, between aircraft B and aircraft C, and between aircraft C and aircraft A, respectively. and Let be a generalized transformation matrix, such that the actual state satisfies For the prior estimate of covariance, ε is the coefficient of the consistency constraint, || || F This represents the Frobenius norm.

Images