Unmanned aerial vehicle clock synchronization and ranging method and system based on two-way delay estimation

Abstract

This invention relates to the field of clock synchronization technology, and discloses a method and system for UAV clock synchronization and ranging based on bidirectional delay estimation. The method includes: calculating a state prediction matrix based on a state matrix and a state equation; calculating the covariance of the process noise vector in the state equation; calculating the prediction error based on the covariance of the process noise vector; constructing a sensor observation matrix, a state observation matrix, and an observation equation; calculating the covariance of the discrete-time observation noise term in the observation equation; calculating the Kalman gain based on the prediction error and the covariance of the discrete-time observation noise term; calculating a corrected prediction value based on the Kalman gain, the state prediction matrix, the sensor observation matrix, and the state observation matrix; and performing clock correction and relative distance correction on the slave node based on the corrected prediction value. This invention can improve the synchronization accuracy of UAV clocks and relative distances.

Description

Technical Field

[0001] This invention relates to the field of clock synchronization technology, and in particular to a method and system for clock synchronization and ranging of unmanned aerial vehicles based on bidirectional delay estimation. Background Technology

[0002] With the rapid development of UAV systems in areas such as target tracking, environmental perception, cooperative navigation, and communication support, high-precision clock synchronization between nodes has become one of the key technologies for stable system operation and functional collaboration. Currently, the mainstream synchronization mechanism is based on a master-slave structure, which uses timestamp exchange to estimate and compensate for clock offset and frequency error.

[0003] However, in highly dynamic UAV networks, the high-speed relative motion between nodes, the constantly changing propagation paths, and environmental factors lead to asymmetric round-trip propagation delays, resulting in synchronization errors. Therefore, improving the accuracy and stability of clock synchronization in UAV networks under scenarios with asymmetric round-trip delays is a problem that needs to be solved.

[0004] Existing technologies employ statistical filtering methods (such as maximum likelihood estimation (MLE) and Kalman filtering (KF)) to estimate and track clock parameters. Some studies have also attempted to incorporate node motion information into the synchronization system, using simplified motion models for motion compensation. However, existing technologies still suffer from the following problems: a lack of joint estimation of node motion parameters and clock parameters, making it difficult to adapt to dynamically changing scenarios; node motion modeling typically uses ideal uniform velocity models, which are insufficient to represent complex node motions; and a lack of modeling and compensation mechanisms for wireless propagation characteristics such as link asymmetry, leading to decreased synchronization accuracy in highly dynamic environments. Summary of the Invention

[0005] This invention provides a method and system for UAV clock synchronization and ranging based on bidirectional delay estimation, the main purpose of which is to improve the synchronization accuracy of UAV clock and relative distance.

[0006] To achieve the above objectives, this invention provides a UAV clock synchronization and ranging method based on bidirectional delay estimation, comprising:

[0007] A state matrix is ​​obtained using a pre-constructed state equation, and a state prediction matrix is ​​calculated based on the state matrix and the state equation.

[0008] Calculate the covariance of the process noise vector in the state equation, and calculate the prediction error based on the covariance of the process noise vector;

[0009] Construct the sensor observation matrix, state observation matrix, and observation equation, and calculate the covariance of the discrete-time observation noise term in the observation equation;

[0010] The Kalman gain is calculated based on the prediction error and the covariance of the discrete-time observation noise term.

[0011] The corrected prediction value is calculated based on the Kalman gain, state prediction matrix, sensor observation matrix, and state observation matrix.

[0012] Based on the corrected prediction values, clock and relative distance corrections are performed on the pre-constructed slave nodes to complete UAV clock synchronization and ranging based on bidirectional delay estimation.

[0013] Optionally, obtaining the state matrix using pre-constructed state equations includes:

[0014] N rounds of timestamps are obtained by using a pre-constructed bidirectional time message exchange, and timestamps are extracted sequentially from the N rounds of timestamps;

[0015] The state equation is used to obtain the state matrix corresponding to the timestamp, wherein the state matrix is ​​as follows:

[0016]

[0017] in, Indicates the first The distance between the master drone node and the slave drone node during round-trip bidirectional message exchange. Indicates the first The radial relative velocity between the master UAV node and the slave UAV node during bidirectional message exchange. Indicates the first The radial relative acceleration between the master UAV node and the slave UAV node during bidirectional message exchange. Indicates the first The clock offset between the master drone node and the slave drone node for each filtering step. Indicates the first The clock drift between the master drone node and the slave drone node for each filtering step.

[0018] Optionally, the state equation is as follows:

[0019]

[0020] in, Indicates the first The predicted distance between the master drone node and the slave drone node during round-trip bidirectional message exchange. Indicates the first The predicted radial relative velocity between the master UAV node and the slave UAV node during round-trip bidirectional message exchange. Indicates the first The predicted radial relative acceleration between the master UAV node and the slave UAV node during round-trip bidirectional message exchange. Indicates the first The predicted clock offset between the master UAV node and the slave UAV node for each filtering step. Indicates the first The predicted clock drift between the master and slave drone nodes in each filtering step. Indicates the first The time interval during round-trip message exchange. Indicates the clock skew attenuation factor. This represents the coupling time constant between clock offsets. Indicates the first The rate of change of radial relative acceleration between the master UAV node and the slave UAV node during two-way message exchange. Indicates the first The noise intensity during the acceleration process of two-way message exchange. Indicates the first Clock noise intensity during round-trip message exchange.

[0021] Optionally, calculating the covariance of the process noise vector in the state equation includes:

[0022] The covariance of the process noise vector in the state equation is calculated using the following formula:

[0023]

[0024] in, Indicates the first The covariance of the process noise vector in each filtering step Represents the expectation operator. Indicates the first The noise vector of each filtering step Indicates the first The transpose of the noise vector in each filtering step. Indicates the first The process noise covariance matrix of the motion parameters for each filtering step Indicates the first The process noise covariance matrix of the clock parameters for each filtering step. Indicates the first The variance of the acceleration process noise in each filtering step. Indicates the first The reference time interval for updating the clock parameters of each filtering step. Indicates the first The variance of clock process noise for each filtering step.

[0025] Optionally, calculating the prediction error based on the covariance of the process noise vector includes:

[0026] The prediction error is calculated based on the covariance of the process noise vector using the following formula:

[0027]

[0028] in, Indicates the first The prediction error of each filtering step. Represents the state transition matrix. Indicates the first The posterior error covariance matrix of each filtering step The transpose of the state transition matrix;

[0029] The state transition matrix is ​​shown below:

[0030]

[0031] in, This represents the state transition matrix.

[0032] Optionally, acquiring observation information includes:

[0033] Build timestamp and timestamp The timestamp and timestamp As shown below:

[0034]

[0035] in, Indicates the first The timing of the master drone node sending a SYNC / Response message to the slave drone node during round-trip bidirectional message exchange. Indicates the first The moment when the UAV node receives the ACK / Response message sent by the master UAV node during round-trip bidirectional message exchange. Indicates the first Clock drift during round-trip message exchange. Represents the speed of light. Indicates from the drone node at Relative to the radial relative velocity of the master drone node, express The radial acceleration of the drone node relative to the master drone node is measured at all times. Indicates in The distance between the drone node and the master drone node is constantly measured. Indicates the first Clock offset during round-trip message exchange. Indicates the first The random transmission delay from the master UAV node to the slave UAV node during round-trip bidirectional message exchange. Indicates the first The moment when the master drone node receives the request sent by the slave drone node during round-trip bidirectional message exchange. Indicates the first The timing of the request sent from the drone node to the master drone node during round-trip bidirectional message exchange. Indicates in The distance between the drone node and the master drone node is constantly measured. Indicates the first Random transmission delay from the UAV node to the master UAV node during round-trip bidirectional message exchange;

[0036] According to the timestamp and timestamp Construct the first timestamp interval based on the preset timestamp. and timestamp Construct a second timestamp interval, where the first timestamp interval refers to the timestamp. and timestamp The time interval, the second timestamp interval refers to the timestamp and timestamp The time interval;

[0037] A first timestamp expression is constructed based on the first timestamp interval and the second timestamp interval, wherein the first timestamp expression is as follows:

[0038]

[0039] in, Indicates the first The first timestamp interval during round-trip bidirectional message exchange Indicates the first The second timestamp interval during round-trip bidirectional message exchange Indicates the first Asymmetric bidirectional propagation delay during round-trip bidirectional message exchange Indicates the first Composite random measurement noise during round-trip message exchange;

[0040] Based on the first timestamp interval and the second timestamp interval, a timestamp interval difference formula is constructed using the first timestamp expression, wherein the timestamp interval difference formula is as follows:

[0041]

[0042] in, Indicates the first The first timestamp interval during round-trip bidirectional message exchange Indicates the first The second timestamp interval during round-trip bidirectional message exchange Indicates the first Asymmetric bidirectional propagation delay during round-trip bidirectional message exchange Indicates the first Composite random measurement noise during round-trip message exchange. This represents the difference between the first timestamp interval. This represents the difference between the second timestamp intervals. This represents the difference in asymmetric bidirectional propagation delay. This represents the noise difference in composite random measurements;

[0043] The observation information is calculated based on the first timestamp interval difference, the second timestamp interval difference, the asymmetric two-way propagation delay difference, and the composite random measurement noise difference in the timestamp interval difference formula. The observation information is as follows:

[0044]

[0045] in, The observation vector at each observation time. For the first The state observation matrix at the nth observation time represents the nonlinear observation function at the nth observation time. The values ​​of the state vector at each observation time. Indicates the first Observational information at each observation time, Indicates the first The radial relative velocity between the UAV node and the master UAV node at each observation moment. Indicates the first The actual clock offset at each observation time Indicates the first The radial relative velocity prediction values ​​between the UAV node and the master UAV node at each observation time point. Indicates the first Predicted clock offset at each observation time, Indicates the first Velocity observation noise at each observation time Indicates the first Clock offset observation noise at each observation time.

[0046] Optionally, calculating the covariance of the discrete-time observation noise term in the observation equation includes:

[0047]

[0048] in, Indicates the first The covariance of the discrete-time observation noise term in the observation equation for each filtering step. Indicates the first Discrete-time observation noise term for each filtering step Indicates the first The transpose vector of the discrete-time observation noise term for each filtering step. Indicates the first The variance of the velocity observation noise for each filtering step. Indicates the first The variance of the clock offset observation noise for each filtering step. Indicates the first The variance of noise measured in a single timestamp during each filtering step;

[0049] The observation equation is as follows:

[0050]

[0051] in, Indicates the first Sensor observation matrix for each filtering step, Indicates the first The state observation matrix for each filtering step Indicates the first The observation information of each filtering step.

[0052] Optionally, calculating the Kalman gain based on the prediction error and the covariance of the discrete-time observation noise term includes:

[0053] The Kalman gain is calculated using the following formula, based on the prediction error and the covariance of the discrete-time observation noise term:

[0054]

[0055] in, Indicates the first Kalman gain for each filtering step Indicates the first The transpose of the state observation matrix for each filtering step.

[0056] Optionally, the step of calculating the corrected prediction value based on the Kalman gain, state prediction matrix, sensor observation matrix, and state observation matrix includes:

[0057] Based on the Kalman gain, state prediction matrix, sensor observation matrix, and state observation matrix, the corrected prediction value is calculated using the following formula:

[0058]

[0059] in, Indicates the first The corrected prediction value corresponding to each filter step wave. Indicates the first The state prediction matrix corresponding to each filter step wave.

[0060] To achieve the above objectives, the present invention also provides a UAV clock synchronization and ranging system based on bidirectional delay estimation, comprising:

[0061] The state prediction matrix prediction error calculation module is used to obtain a state matrix using a pre-constructed state equation, calculate a state prediction matrix based on the state matrix and the state equation, calculate the covariance of the process noise vector in the state equation, and calculate the prediction error based on the covariance of the process noise vector.

[0062] The observation equation covariance calculation module is used to construct the sensor observation matrix, the state observation matrix, and the observation equation, and to calculate the covariance of the discrete-time observation noise term in the observation equation.

[0063] The corrected prediction calculation module is used to calculate the Kalman gain based on the prediction error and the covariance of the discrete-time observation noise term; and to calculate the corrected prediction value based on the Kalman gain, the state prediction matrix, the sensor observation matrix, and the state observation matrix.

[0064] The slave node clock correction module is used to correct the clock and relative distance of the pre-built slave nodes according to the correction prediction value.

[0065] To address the above problems, the present invention also provides an electronic device, the electronic device comprising:

[0066] A memory that stores at least one instruction; and a processor that executes the instructions stored in the memory to implement the UAV clock synchronization and ranging method based on bidirectional delay estimation described above.

[0067] To address the aforementioned issues, the present invention also provides a computer-readable storage medium storing at least one instruction, which is executed by a processor in an electronic device to implement the aforementioned UAV clock synchronization and ranging method based on bidirectional delay estimation.

[0068] To address the problems described in the background art, this invention first requires constructing a state prediction matrix and calculating its prediction error. When constructing the state prediction matrix, the state matrix is ​​first obtained using the state equation, and then the state prediction matrix is ​​calculated based on the state matrix and the state equation. Since the process noise vector in the state matrix reflects the prediction error of the state prediction matrix, the covariance of the process noise vector in the state equation can be calculated, and then the prediction error is calculated based on the covariance of the process noise vector. At this point, it is necessary to calculate the covariance of the discrete-time observation noise term in the observation equation. First, the sensor observation matrix needs to be obtained, and then... An observation equation is constructed based on the state prediction matrix and the sensor observation matrix. Since the discrete-time observation term in the observation equation contains covariance information, the covariance of the discrete-time observation noise term in the observation equation is calculated. After obtaining the prediction error and the covariance of the discrete-time observation noise term, the Kalman gain can be calculated based on these covariances. Then, a corrected prediction value can be calculated based on the Kalman gain, the state prediction matrix, the sensor observation matrix, and the state observation matrix. Finally, clock correction and relative distance correction are applied to the pre-constructed slave nodes based on the corrected prediction value. Therefore, this invention can improve the synchronization accuracy of the UAV clock and relative distance. Attached Figure Description

[0069] Figure 1 This is a flowchart illustrating a UAV clock synchronization and ranging method based on bidirectional delay estimation provided in an embodiment of the present invention.

[0070] Figure 2 A flowchart illustrating the bidirectional message exchange process between a master node and a slave node according to an embodiment of the present invention;

[0071] Figure 3 A flowchart of clock synchronization and ranging between master and slave nodes provided in an embodiment of the present invention;

[0072] Figure 4 This is a flowchart of an EKF filtering process provided in an embodiment of the present invention;

[0073] Figure 5 This is a functional block diagram of a UAV clock synchronization and ranging system based on bidirectional delay estimation provided in an embodiment of the present invention;

[0074] Figure 6 This is a schematic diagram of the structure of an electronic device that implements the UAV clock synchronization and ranging method based on bidirectional delay estimation, according to an embodiment of the present invention.

[0075] Explanation of reference numerals in the attached figures:

[0076] 10. Electronic device; 11. Processor; 12. Memory; 13. Bus.

[0077] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0078] It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0079] This application provides a method for UAV clock synchronization and ranging based on bidirectional delay estimation. The execution entity of the UAV clock synchronization and ranging method based on bidirectional delay estimation includes, but is not limited to, at least one of the following electronic devices that can be configured to execute the method provided in this application: a server, a terminal, etc. In other words, the UAV clock synchronization and ranging method based on bidirectional delay estimation can be executed by software or hardware installed on a terminal device or a server device, and the software can be a blockchain platform. The server includes, but is not limited to, a single server, a server cluster, a cloud server, or a cloud server cluster.

[0080] Reference Figure 1 The diagram shown is a flowchart illustrating a UAV clock synchronization and ranging method based on bidirectional delay estimation according to an embodiment of the present invention. In this embodiment, the UAV clock synchronization and ranging method based on bidirectional delay estimation includes:

[0081] S1. Obtain the state matrix using the pre-constructed state equation, and calculate the state prediction matrix based on the state matrix and the state equation.

[0082] Understandably, the bidirectional time-based message exchange refers to the application technology of the Two-Way Message Exchange Protocol. Further, the bidirectional delay estimation technology is used to estimate and compensate for the asymmetric propagation delay between the master and slave drone nodes. The state matrix refers to the matrix composed of the motion parameters between the master and slave drone nodes when completing one round of bidirectional message exchange and the clock parameters between the master and slave drone nodes when completing one filtering step. The state equation refers to the equation for predicting the motion and clock parameters of the master and slave drone nodes. The state prediction matrix refers to the matrix composed of the motion and clock parameters between the master and slave drone nodes predicted based on the state equation.

[0083] In this embodiment of the invention, obtaining the state matrix using a pre-constructed state equation includes:

[0084] N rounds of timestamps are obtained by using a pre-constructed bidirectional time message exchange, and timestamps are extracted sequentially from the N rounds of timestamps;

[0085] The state equation is used to obtain the state matrix corresponding to the timestamp, wherein the state matrix is ​​as follows:

[0086]

[0087] in, Indicates the first The distance between the master drone node and the slave drone node during round-trip bidirectional message exchange. Indicates the first The radial relative velocity between the master UAV node and the slave UAV node during bidirectional message exchange. Indicates the first The radial relative acceleration between the master UAV node and the slave UAV node during bidirectional message exchange. Indicates the first The clock offset between the master drone node and the slave drone node for each filtering step. Indicates the first The clock drift between the master drone node and the slave drone node for each filtering step.

[0088] Understandably, the N-round timestamps refer to the timestamps corresponding to specific rounds of bidirectional message exchange preset by the user. For example, when N is 3, the timestamp for the first round is... , , , The second round of timestamps is , , , The third round of timestamps is , , , ,in, This represents the timestamp of the master drone node sending the SYNC / Response message to the slave drone node during the first round of bidirectional message exchange. This represents the timestamp of the ACK / Response message received from the master drone node during the first round of bidirectional message exchange. This represents the timestamp of the Request message sent from the drone node to the master drone node during the first round of bidirectional message exchange. This indicates the timestamp at which the master drone node received the Request message sent by the drone node during the first round of bidirectional message exchange. , , , , , , , The meaning follows the same logic and will not be repeated here. The bidirectional message exchange process between the master and slave drone nodes can be found in [reference needed]. Figure 2 As shown, specifically, during the initialization phase, the slave node maintains its local clock through the RTC module, using the master node's clock as the network reference clock. During the communication link establishment phase, the master node initiates a SYNC message, and the slave node replies with an ACK message, indicating successful link establishment. Subsequently, the synchronization node enters, where the slave node sends a Request message and records the master node's local transmission time T1. The master node records the time T4 when it receives the Request message. After the master node's processing delay, it replies with a Response message, recording its local transmission time. The Response message carries times T2 and T3 and arrives at the slave node. After N rounds of interaction, the slave node receives N sets of timestamp information. Simultaneously, during this phase, the IMU module measures and records the observed values. Then, the information processing unit executes the EKF filtering process. The EKF flowchart is shown below. Figure 4 As shown, the EKF filtering module obtains the state equation and observation equation through the preliminary mathematical modeling process, and performs prediction updates, gain calculations, corrections and other processes until the EKF loop ends, outputting the predicted state value. At the same time, the effectiveness of the algorithm is evaluated based on the calculated PCRB value. Finally, the slave node adjusts its local RTC according to the predicted value to achieve synchronization between the two nodes.

[0089] Furthermore, the clock offset refers to the absolute time difference between the clock of the master drone node and the clock of the slave drone node, and the clock skew refers to the frequency ratio deviation between the clock of the master drone node and the clock of the slave drone node.

[0090] In this embodiment of the invention, the state equation is as follows:

[0091]

[0092] in, Indicates the first The predicted distance between the master drone node and the slave drone node during round-trip bidirectional message exchange. Indicates the first The predicted radial relative velocity between the master UAV node and the slave UAV node during round-trip bidirectional message exchange. Indicates the first The predicted radial relative acceleration between the master UAV node and the slave UAV node during round-trip bidirectional message exchange. Indicates the first The predicted clock offset between the master UAV node and the slave UAV node for each filtering step. Indicates the first The predicted clock drift between the master and slave drone nodes in each filtering step. Indicates the first The time interval during round-trip message exchange. Indicates the clock skew attenuation factor. This represents the coupling time constant between clock offsets. Indicates the first The rate of change of radial relative acceleration between the master UAV node and the slave UAV node during two-way message exchange. Indicates the first The noise intensity during the acceleration process of two-way message exchange. Indicates the first Clock noise intensity during round-trip message exchange.

[0093] Specifically, the clock offset attenuation factor refers to the autoregressive attenuation characteristic factor describing clock drift, with a value range of 0-1. The coupling time constant refers to a constant representing the coupling scale of clock parameters.

[0094] Further, the predicted distance refers to the predicted distance between the master drone node and the slave drone node; the predicted radial relative velocity refers to the predicted radial relative velocity between the master drone node and the slave drone node; the predicted radial relative acceleration refers to the predicted radial relative acceleration between the master drone node and the slave drone node; the predicted clock offset refers to the predicted clock offset between the master drone node and the slave drone node; and the predicted clock drift refers to the predicted clock drift between the master drone node and the slave drone node.

[0095] In detail, and This represents Gaussian process noise with a mean of 0 and variances of [missing information]. and See the following examples for details.

[0096] S2. Calculate the covariance of the process noise vector in the state equation, and calculate the prediction error based on the covariance of the process noise vector.

[0097] Specifically, the process noise vector refers to the vector representing process noise in the state equation, and the process noise vector is shown below:

[0098]

[0099] in, Indicates the first The process noise vector of each filtering step.

[0100] Furthermore, the prediction error refers to the prior estimation error covariance matrix of the estimation error generated by predicting the current state based on all information from the previous observation time.

[0101] In this embodiment of the invention, calculating the covariance of the process noise vector in the state equation includes:

[0102] The covariance of the process noise vector in the state equation is calculated using the following formula:

[0103]

[0104] in, Indicates the first The covariance of the process noise vector in each filtering step Represents the expectation operator. Indicates the first The noise vector of each filtering step Indicates the first The transpose of the noise vector in each filtering step. Indicates the first The process noise covariance matrix of the motion parameters for each filtering step Indicates the first The process noise covariance matrix of the clock parameters for each filtering step. Indicates the first The variance of the acceleration process noise in each filtering step. Indicates the first The reference time interval for updating the clock parameters of each filtering step. Indicates the first The variance of clock process noise for each filtering step.

[0105] In detail, the acceleration process noise refers to the random disturbance value introduced due to the uncertainty of acceleration changes.

[0106] Furthermore, the expectation operator refers to the operator that calculates the statistical average of the outer product of the noise vector and its transpose. The filtering step refers to one complete iteration of the Extended Kalman Filter (EKF). The time interval of one filtering step is as follows:

[0107]

[0108] in, Indicates the first The time interval of each filtering step Indicates the first The timestamp of the master drone node sending SYNC / Response messages to the slave drone node during the round-trip bidirectional message exchange process. In the The timestamp of the Request message sent from the drone node to the master drone node during the round-trip bidirectional message exchange. Indicates the first The timestamp of the Request message sent from the drone node to the master drone node during the round-trip bidirectional message exchange.

[0109] Furthermore, a round of bidirectional message exchange includes two filtering steps, when When the number is odd, the time interval between filtering steps is the first step. The start of round-trip bidirectional message exchange and the first The time interval between round-trip message exchanges, when When the number is even, the time interval between filtering steps is the th step. The internal time interval for bidirectional message exchange.

[0110] In this embodiment of the invention, calculating the prediction error based on the covariance of the process noise vector includes:

[0111] The prediction error is calculated based on the covariance of the process noise vector using the following formula:

[0112]

[0113] in, Indicates the first The prediction error of each filtering step. Represents the state transition matrix. Indicates the first The posterior error covariance matrix of each filtering step The transpose of the state transition matrix;

[0114] The state transition matrix is ​​shown below:

[0115]

[0116] in, This represents the state transition matrix.

[0117] S3. Construct the sensor observation matrix, state observation matrix, and observation equation, and calculate the covariance of the discrete-time observation noise term in the observation equation.

[0118] Understandably, the sensor observation matrix refers to the observation matrix constructed from sensor observations. The observation equation refers to the equation describing the relationship between the state prediction matrix and the sensor observation matrix. The discrete-time observation noise term refers to the random error term introduced during the observation of motion parameters and clock parameters, which follows a Gaussian noise distribution with covariance R, i.e. .

[0119] The construction of the sensor observation matrix, state observation matrix, and observation equation includes:

[0120] Build timestamp and timestamp The timestamp and timestamp As shown below:

[0121]

[0122] in, Indicates the first The timing of the master drone node sending a SYNC / Response message to the slave drone node during round-trip bidirectional message exchange. Indicates the first The moment when the UAV node receives the ACK / Response message sent by the master UAV node during round-trip bidirectional message exchange. Indicates the first Clock drift during round-trip message exchange. Represents the speed of light. Indicates from the drone node at Relative to the radial relative velocity of the master drone node, express The radial acceleration of the drone node relative to the master drone node is measured at all times. Indicates in The distance between the drone node and the master drone node is constantly measured. Indicates the first Clock offset during round-trip message exchange. Indicates the first The random transmission delay from the master UAV node to the slave UAV node during round-trip bidirectional message exchange. Indicates the first The moment when the master drone node receives the request sent by the slave drone node during round-trip bidirectional message exchange. Indicates the first The timing of the request sent from the drone node to the master drone node during round-trip bidirectional message exchange. Indicates in The distance between the drone node and the master drone node is constantly measured. Indicates the first Random transmission delay from the UAV node to the master UAV node during round-trip bidirectional message exchange;

[0123] According to the timestamp and timestamp Construct the first timestamp interval based on the preset timestamp. and timestamp Construct a second timestamp interval, where the first timestamp interval refers to the timestamp. and timestamp The time interval, the second timestamp interval refers to the timestamp and timestamp The time interval;

[0124] A first timestamp expression is constructed based on the first timestamp interval and the second timestamp interval, wherein the first timestamp expression is as follows:

[0125]

[0126] in, Indicates the first The first timestamp interval during round-trip bidirectional message exchange Indicates the first The second timestamp interval during round-trip bidirectional message exchange Indicates the first Asymmetric bidirectional propagation delay during round-trip bidirectional message exchange Indicates the first Composite random measurement noise during round-trip message exchange;

[0127] Based on the first timestamp interval and the second timestamp interval, a timestamp interval difference formula is constructed using the first timestamp expression, wherein the timestamp interval difference formula is as follows:

[0128]

[0129] in, Indicates the first The first timestamp interval during round-trip bidirectional message exchange Indicates the first The second timestamp interval during round-trip bidirectional message exchange Indicates the first Asymmetric bidirectional propagation delay during round-trip bidirectional message exchange Indicates the first Composite random measurement noise during round-trip message exchange. This represents the difference between the first timestamp interval. This represents the difference between the second timestamp intervals. This represents the difference in asymmetric bidirectional propagation delay. This represents the noise difference in composite random measurements;

[0130] The observation equation is calculated based on the first timestamp interval difference, the second timestamp interval difference, the asymmetric two-way propagation delay difference, and the composite random measurement noise difference in the timestamp interval difference formula, wherein the observation equation is as follows:

[0131]

[0132] in, The observation vector at each observation time. For the first The state observation matrix at the nth observation time represents the nonlinear observation function at the nth observation time. The values ​​of the state vector at each observation time. Indicates the first Observational information at each observation time, Indicates the first The radial relative velocity between the UAV node and the master UAV node at each observation moment. Indicates the first The actual clock offset at each observation time Indicates the first The radial relative velocity prediction values ​​between the UAV node and the master UAV node at each observation time point. Indicates the first Predicted clock offset at each observation time, Indicates the first Velocity observation noise at each observation time Indicates the first Clock offset observation noise at each observation time.

[0133] Understandably, the radial relative velocity refers to the relative motion velocity from the UAV node along the line connecting it to the master UAV node, and the radial acceleration refers to the acceleration from the UAV node along the line connecting it to the master UAV node. The random transmission delay refers to the time fluctuation delay caused by factors such as medium, multipath effect, and hardware jitter.

[0134] Specifically, the asymmetric bidirectional propagation delay refers to the delay caused by the unequal propagation times of the forward and reverse signals due to the relative motion of the UAV. The composite random measurement noise refers to the total observation noise resulting from the superposition of multiple independent random noise sources. The asymmetric bidirectional propagation delay difference refers to the... Wheel and the first The difference in asymmetric bidirectional propagation delay during round-trip bidirectional message exchange. The composite random measurement noise difference refers to the difference in the first round of bidirectional message exchange. Wheel and the first The difference in composite random measurement noise during round-trip bidirectional message exchange.

[0135] Furthermore, the asymmetric bidirectional propagation delay refers to the delay caused by the unequal propagation times of the forward and reverse signals due to the relative motion between the master UAV node and the slave UAV node. The composite random measurement noise difference refers to the... Round-trip bidirectional message exchange and the first The difference in total observation noise, which is the sum of random noise sources from round-trip bidirectional message exchange.

[0136] Specifically, the observation time refers to the point in time when the motion parameters and clock parameters are measured. The predicted radial relative velocity refers to the predicted value of the radial relative velocity, and the predicted clock offset refers to the predicted value of the clock offset. The clock offset observation noise refers to the zero-mean Gaussian random error introduced in the process of obtaining the actual clock offset. Because... Since it is a nonlinear observation function, an extended Kalman filter is used for filtering. The extended Kalman filter can track changes in clock slope and relative velocity. In this embodiment of the invention, calculating the covariance of the discrete-time observation noise term in the observation equation includes:

[0137]

[0138] in, Indicates the first The covariance of the discrete-time observation noise term in the observation equation for each filtering step. Indicates the first Discrete-time observation noise term for each filtering step Indicates the first The transpose vector of the discrete-time observation noise term for each filtering step. Indicates the first The variance of the velocity observation noise for each filtering step. Indicates the first The variance of the clock offset observation noise for each filtering step. Indicates the first The variance of noise measured in a single timestamp during each filtering step;

[0139] In detail, the discrete-time observation noise term refers to the parameter term in the observation equation that represents the discrete-time observation noise.

[0140] The observation equation is as follows:

[0141]

[0142] in, Indicates the first Sensor observation matrix for each filtering step, Indicates the first The state observation matrix for each filtering step Indicates the first The observation information of each filtering step.

[0143] Furthermore, the velocity observation noise refers to the random error introduced by measuring relative velocity through a motion sensor. The clock offset observation noise refers to the random error introduced by acquiring clock offset observation values, and the single timestamp measurement noise refers to the random error introduced by factors such as hardware clock resolution, software delay jitter, and trigger uncertainty. The state observation matrix refers to the matrix that linearly maps the state space to the observation space.

[0144] S4. Calculate the Kalman gain based on the prediction error and the covariance of the discrete-time observation noise term.

[0145] Furthermore, the Kalman gain refers to the weight matrix used for optimally fusing the state prediction matrix and the state observation matrix, and is used to determine the calculation weights of the state prediction matrix and the state observation matrix.

[0146] In this embodiment of the invention, calculating the Kalman gain based on the covariance of the prediction error and the discrete-time observation noise term includes:

[0147] The Kalman gain is calculated using the following formula, based on the prediction error and the covariance of the discrete-time observation noise term:

[0148]

[0149] in, Indicates the first Kalman gain for each filtering step Indicates the first The transpose of the state observation matrix for each filtering step.

[0150] S5. Calculate the corrected prediction value based on the Kalman gain, state prediction matrix, sensor observation matrix, and state observation matrix.

[0151] Understandably, the observation information refers to the difference between the actual observed value and the expected observed value based on the predicted state, also known as observational innovation. The corrected predicted value refers to the correction value for adjusting the clock parameters of the UAV node.

[0152] In this embodiment of the invention, the step of calculating the corrected prediction value based on the Kalman gain, the state prediction matrix, the sensor observation matrix, and the state observation matrix includes:

[0153] Based on the Kalman gain, state prediction matrix, sensor observation matrix, and state observation matrix, the corrected prediction value is calculated using the following formula:

[0154]

[0155] in, Indicates the first The corrected prediction value corresponding to each filter step wave. Indicates the first The state prediction matrix corresponding to each filter step wave.

[0156] In detail, the state prediction matrix refers to the prediction matrix for motion parameters and clock parameters.

[0157] S6. Based on the corrected prediction value, perform clock correction and relative distance correction on the pre-constructed slave node to complete UAV clock synchronization and ranging based on bidirectional delay estimation.

[0158] Understandably, the term "slave node" refers to a slave drone node, "clock correction" refers to clock correction of the slave drone node's real-time clock module, and "relative distance correction" refers to correction of the relative distance between the slave drone node and the master drone node. The real-time clock module refers to the slave drone node's local clock, abbreviated as RTC. See the flowchart for clock synchronization and ranging between the master node (master drone node) and slave nodes (slave drone nodes). Figure 3 As shown.

[0159] Furthermore, after clock correction is completed, the posterior error covariance matrix can be calculated using a pre-constructed posterior error covariance formula, wherein the posterior error covariance formula is as follows:

[0160]

[0161] in, Denotes the posterior error covariance matrix. Represents the identity matrix. express The Jacobian matrix is ​​shown below:

[0162]

[0163] in, Indicates the first The state vector of the slave drone node relative to the master drone node at each observation time. Indicates the first Each observation moment is determined by the clock drift of the UAV node relative to the master UAV node. Indicates the first The change in distance between the UAV node and the master UAV node at each observation time point. This represents the state matrix corresponding to the k-th filtering step.

[0164] Understandably, the lower bound of the mean square error (MSE) for discrete-time nonlinear filtering problems can be expressed as a posterior version of the Cramer-Rhodes inequality (PCRB) based on the VanTrees method. This MSE lower bound is applicable to multidimensional nonlinear dynamic systems that may have non-Gaussian distributions. For the PCRB evaluation metrics of clock skew and clock drift, this MSE lower bound can measure the performance of UAV clock synchronization methods for bidirectional delay estimation.

[0165] To address the problems described in the background art, this invention first requires constructing a state prediction matrix and calculating its prediction error. When constructing the state prediction matrix, the state matrix is ​​first obtained using the state equation, and then the state prediction matrix is ​​calculated based on the state matrix and the state equation. Since the process noise vector in the state matrix reflects the prediction error of the state prediction matrix, the covariance of the process noise vector in the state equation can be calculated, and then the prediction error is calculated based on the covariance of the process noise vector. At this point, it is necessary to calculate the covariance of the discrete-time observation noise term in the observation equation. First, the sensor observation matrix needs to be obtained, and then... An observation equation is constructed based on the state prediction matrix and the sensor observation matrix. Since the discrete-time observation term in the observation equation contains covariance information, the covariance of the discrete-time observation noise term in the observation equation is calculated. After obtaining the prediction error and the covariance of the discrete-time observation noise term, the Kalman gain can be calculated based on these covariances. Then, a corrected prediction value can be calculated based on the Kalman gain, the state prediction matrix, the sensor observation matrix, and the state observation matrix. Finally, clock correction and relative distance correction are applied to the pre-constructed slave nodes based on the corrected prediction value. Therefore, this invention can improve the synchronization accuracy of the UAV clock and relative distance.

[0166] like Figure 5 The diagram shown is a functional block diagram of a UAV clock synchronization and ranging system based on bidirectional delay estimation provided in an embodiment of the present invention.

[0167] The UAV clock synchronization and ranging system 100 based on bidirectional delay estimation described in this invention can be installed in an electronic device. Depending on the functions implemented, the UAV clock synchronization and ranging system 100 may include a state prediction matrix prediction error calculation module 101, an observation equation covariance calculation module 102, a corrected prediction value calculation module 103, and a slave node clock correction module 104. The module described in this invention can also be referred to as a unit, which refers to a series of computer program segments that can be executed by the processor of an electronic device and can perform a fixed function, and are stored in the memory of the electronic device.

[0168] The state prediction matrix prediction error calculation module 101 is used to obtain a state matrix using a pre-constructed state equation, calculate a state prediction matrix based on the state matrix and the state equation, calculate the covariance of the process noise vector in the state equation, and calculate the prediction error based on the covariance of the process noise vector.

[0169] The observation equation covariance calculation module 102 is used to construct the sensor observation matrix, the state observation matrix and the observation equation, and to calculate the covariance of the discrete-time observation noise term in the observation equation.

[0170] The corrected prediction value calculation module 103 is used to calculate the Kalman gain based on the prediction error and the covariance of the discrete-time observation noise term; and to calculate the corrected prediction value based on the Kalman gain, the state prediction matrix, the sensor observation matrix, and the state observation matrix.

[0171] The slave node clock correction module 104 is used to perform clock correction and relative distance correction on the pre-constructed slave nodes according to the correction prediction value.

[0172] In detail, the modules in the UAV clock synchronization and ranging system 100 based on bidirectional delay estimation described in this embodiment of the invention employ the same methods as described above. Figure 1 The UAV clock synchronization and ranging methods based on bidirectional delay estimation described herein are the same techniques used and can produce the same technical effects, so they will not be elaborated here.

[0173] like Figure 6 The diagram shown is a schematic representation of an electronic device for implementing a UAV clock synchronization and ranging method based on bidirectional delay estimation, according to an embodiment of the present invention.

[0174] The electronic device 1 may include a processor 10, a memory 11 and a bus 12, and may also include a computer program stored in the memory 11 and capable of running on the processor 10, such as a UAV clock synchronization and ranging method program based on bidirectional delay estimation.

[0175] The memory 11 includes at least one type of readable storage medium, such as flash memory, portable hard drive, multimedia card, card-type memory (e.g., SD or DX memory), magnetic memory, magnetic disk, optical disk, etc. In some embodiments, the memory 11 can be an internal storage unit of the electronic device 1, such as the portable hard drive of the electronic device 1. In other embodiments, the memory 11 can be an external storage device of the electronic device 1, such as a plug-in portable hard drive, smart media card (SMC), secure digital card (SD), flash card, etc., equipped on the electronic device 1. Furthermore, the memory 11 includes both internal storage units and external storage devices of the electronic device 1. The memory 11 can be used not only to store application software and various types of data installed on the electronic device 1, such as the code of a UAV clock synchronization and ranging method program based on bidirectional delay estimation, but also to temporarily store data that has been output or will be output.

[0176] In some embodiments, the processor 10 may be composed of integrated circuits, such as a single packaged integrated circuit or multiple integrated circuits with the same or different functions, including combinations of one or more central processing units (CPUs), microprocessors, digital processing chips, graphics processors, and various control chips. The processor 10 is the control unit of the electronic device, connecting various components of the entire electronic device through various interfaces and lines. It executes programs or modules stored in the memory 11 (e.g., a UAV clock synchronization and ranging method program based on bidirectional delay estimation) and calls data stored in the memory 11 to perform various functions of the electronic device 1 and process data.

[0177] The bus 12 can be a peripheral component interconnect (PCI) bus or an extended industry standard architecture (EISA) bus, etc. The bus 12 can be divided into an address bus, a data bus, a control bus, etc. The bus 12 is configured to realize the connection and communication between the memory 11 and at least one processor 10, etc.

[0178] Figure 6 Only electronic devices with components are shown; it will be understood by those skilled in the art that... Figure 6The structure shown does not constitute a limitation on the electronic device 1, and may include fewer or more components than shown, or combine certain components, or have different component arrangements.

[0179] For example, although not shown, the electronic device 1 may also include a power supply (such as a battery) to power the various components. Preferably, the power supply can be logically connected to the at least one processor 10 through a power management device, thereby enabling functions such as charging management, discharging management, and power consumption management. The power supply may also include one or more DC or AC power supplies, recharging devices, power fault detection circuits, power converters or inverters, power status indicators, and other arbitrary components. The electronic device 1 may also include various sensors, Bluetooth modules, Wi-Fi modules, etc., which will not be described in detail here.

[0180] Furthermore, the electronic device 1 may also include a network interface. Optionally, the network interface may include a wired interface and / or a wireless interface (such as a Wi-Fi interface, a Bluetooth interface, etc.), which is typically used to establish communication connections between the electronic device 1 and other electronic devices.

[0181] Optionally, the electronic device 1 may further include a user interface, which may be a display, an input unit (such as a keyboard), and optionally, a standard wired interface or a wireless interface. Optionally, in some embodiments, the display may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, or an OLED (Organic Light-Emitting Diode) touchscreen, etc. The display may also be appropriately referred to as a screen or display unit, used to display information processed in the electronic device 1 and to display a visual user interface.

[0182] The UAV clock synchronization and ranging method program based on bidirectional delay estimation, stored in the memory 11 of the electronic device 1, is a combination of multiple instructions. When run in the processor 10, it can achieve the following:

[0183] A state matrix is ​​obtained using a pre-constructed state equation, and a state prediction matrix is ​​calculated based on the state matrix and the state equation.

[0184] Calculate the covariance of the process noise vector in the state equation, and calculate the prediction error based on the covariance of the process noise vector;

[0185] Construct the sensor observation matrix, state observation matrix, and observation equation, and calculate the covariance of the discrete-time observation noise term in the observation equation;

[0186] The Kalman gain is calculated based on the prediction error and the covariance of the discrete-time observation noise term.

[0187] The corrected prediction value is calculated based on the Kalman gain, state prediction matrix, sensor observation matrix, and state observation matrix.

[0188] Based on the corrected prediction values, clock and relative distance corrections are performed on the pre-constructed slave nodes to complete UAV clock synchronization and ranging based on bidirectional delay estimation.

[0189] Specifically, the processor 10's implementation method for the above instructions can be found in [reference needed]. Figures 1 to 6 The descriptions of the relevant steps in the corresponding embodiments are not repeated here.

[0190] Furthermore, if the modules / units integrated in the electronic device 1 are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. The computer-readable storage medium can be volatile or non-volatile. For example, the computer-readable medium may include: any entity or device capable of carrying the computer program code, a recording medium, a USB flash drive, a portable hard drive, a magnetic disk, an optical disk, a computer memory, or a read-only memory (ROM).

[0191] The present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor of an electronic device, can perform the following:

[0192] A state matrix is ​​obtained using a pre-constructed state equation, and a state prediction matrix is ​​calculated based on the state matrix and the state equation.

[0193] Calculate the covariance of the process noise vector in the state equation, and calculate the prediction error based on the covariance of the process noise vector;

[0194] Construct the sensor observation matrix, state observation matrix, and observation equation, and calculate the covariance of the discrete-time observation noise term in the observation equation;

[0195] The Kalman gain is calculated based on the prediction error and the covariance of the discrete-time observation noise term.

[0196] The corrected prediction value is calculated based on the Kalman gain, state prediction matrix, sensor observation matrix, and state observation matrix.

[0197] Based on the corrected prediction values, clock and relative distance corrections are performed on the pre-constructed slave nodes to complete UAV clock synchronization and ranging based on bidirectional delay estimation.

[0198] In the embodiments provided by this invention, it should be understood that the disclosed devices, systems, and methods can be implemented in other ways. For example, the system embodiments described above are merely illustrative, and actual implementations may have other classification methods.

[0199] The modules described as separate components may or may not be physically separate. The components shown as modules may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0200] Furthermore, the functional modules in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or in the form of hardware plus software functional modules.

[0201] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the present invention.

[0202] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for drone clock synchronization and ranging based on two-way delay estimation, characterized in that, The method includes: A state matrix is ​​obtained using a pre-constructed state equation, and a state prediction matrix is ​​calculated based on the state matrix and the state equation. Calculate the covariance of the process noise vector in the state equation, and calculate the prediction error based on the covariance of the process noise vector; Construct the sensor observation matrix, state observation matrix, and observation equation, and calculate the covariance of the discrete-time observation noise term in the observation equation; The Kalman gain is calculated based on the prediction error and the covariance of the discrete-time observation noise term. The corrected prediction value is calculated based on the Kalman gain, state prediction matrix, sensor observation matrix, and state observation matrix. Based on the corrected prediction values, clock and relative distance corrections are performed on the pre-constructed slave nodes to complete UAV clock synchronization and ranging based on bidirectional delay estimation.

2. The UAV clock synchronization and ranging method based on two-way delay estimation of claim 1, wherein, The process of obtaining the state matrix using pre-constructed state equations includes: N rounds of timestamps are obtained by using a pre-constructed bidirectional time message exchange, and timestamps are extracted sequentially from the N rounds of timestamps; The state equation is used to obtain the state matrix corresponding to the timestamp, wherein the state matrix is ​​as follows: ； in, Indicates the first The distance between the master drone node and the slave drone node during round-trip bidirectional message exchange. Indicates the first The radial relative velocity between the master UAV node and the slave UAV node during bidirectional message exchange. Indicates the first The radial relative acceleration between the master UAV node and the slave UAV node during bidirectional message exchange. Indicates the first The clock offset between the master drone node and the slave drone node for each filtering step. Indicates the first The clock drift between the master drone node and the slave drone node for each filtering step.

3. The UAV clock synchronization and ranging method based on bidirectional delay estimation as described in claim 2, characterized in that, The state equation is as follows: ； in, Indicates the first The predicted distance between the master drone node and the slave drone node during round-trip bidirectional message exchange. Indicates the first The predicted radial relative velocity between the master UAV node and the slave UAV node during round-trip bidirectional message exchange. Indicates the first The predicted radial relative acceleration between the master UAV node and the slave UAV node during round-trip bidirectional message exchange. Indicates the first The predicted clock offset between the master UAV node and the slave UAV node for each filtering step. Indicates the first The predicted clock drift between the master and slave drone nodes in each filtering step. Indicates the first The time interval during round-trip message exchange. Indicates the clock skew attenuation factor. This represents the coupling time constant between clock offsets. Indicates the first The rate of change of radial relative acceleration between the master UAV node and the slave UAV node during two-way message exchange. Indicates the first The noise intensity during the acceleration process of two-way message exchange. Indicates the first Clock noise intensity during round-trip message exchange.

4. The UAV clock synchronization and ranging method based on bidirectional delay estimation as described in claim 3, characterized in that, The calculation of the covariance of the process noise vector in the state equation includes: The covariance of the process noise vector in the state equation is calculated using the following formula: ； in, Indicates the first The covariance of the process noise vector in each filtering step Represents the expectation operator. Indicates the first The noise vector of each filtering step Indicates the first The transpose of the noise vector in each filtering step. Indicates the first The process noise covariance matrix of the motion parameters for each filtering step Indicates the first The process noise covariance matrix of the clock parameters for each filtering step. Indicates the first The variance of the acceleration process noise in each filtering step. Indicates the first The reference time interval for updating the clock parameters of each filtering step. Indicates the first The variance of clock process noise for each filtering step.

5. The UAV clock synchronization and ranging method based on bidirectional delay estimation as described in claim 4, characterized in that, The calculation of prediction error based on the covariance of the process noise vector includes: The prediction error is calculated based on the covariance of the process noise vector using the following formula: ； in, Indicates the first The prediction error of each filtering step. Represents the state transition matrix. Indicates the first The posterior error covariance matrix of each filtering step The transpose of the state transition matrix; The state transition matrix is ​​shown below: ； in, This represents the state transition matrix.

6. The UAV clock synchronization and ranging method based on bidirectional delay estimation as described in claim 5, characterized in that, The construction of the sensor observation matrix, state observation matrix, and observation equation includes: Build timestamp and timestamp The timestamp and timestamp As shown below: ； in, Indicates the first The timing of the master drone node sending a SYNC / Response message to the slave drone node during round-trip bidirectional message exchange. Indicates the first The moment when the UAV node receives the ACK / Response message sent by the master UAV node during round-trip bidirectional message exchange. Indicates the first Clock drift during round-trip message exchange. Represents the speed of light. Indicates from the drone node at Relative to the radial relative velocity of the master drone node, express The radial acceleration of the drone node relative to the master drone node is measured at all times. Indicates in The distance between the drone node and the master drone node is constantly measured. Indicates the first Clock offset during round-trip message exchange. Indicates the first The random transmission delay from the master UAV node to the slave UAV node during round-trip bidirectional message exchange. Indicates the first The moment when the master drone node receives the request sent by the slave drone node during round-trip bidirectional message exchange. Indicates the first The timing of the request sent from the drone node to the master drone node during round-trip bidirectional message exchange. Indicates in The distance between the drone node and the master drone node is constantly measured. Indicates the first Random transmission delay from the UAV node to the master UAV node during round-trip bidirectional message exchange; According to the timestamp and timestamp Construct the first timestamp interval based on the preset timestamp. and timestamp Construct a second timestamp interval, where the first timestamp interval refers to the timestamp. and timestamp The time interval, the second timestamp interval refers to the timestamp and timestamp The time interval; A first timestamp expression is constructed based on the first timestamp interval and the second timestamp interval, wherein the first timestamp expression is as follows: ； in, Indicates the first The first timestamp interval during round-trip bidirectional message exchange Indicates the first The second timestamp interval during round-trip bidirectional message exchange Indicates the first Asymmetric bidirectional propagation delay during round-trip bidirectional message exchange Indicates the first Composite random measurement noise during round-trip message exchange; Based on the first timestamp interval and the second timestamp interval, a timestamp interval difference formula is constructed using the first timestamp expression, wherein the timestamp interval difference formula is as follows: ； in, Indicates the first The first timestamp interval during round-trip bidirectional message exchange Indicates the first The second timestamp interval during round-trip bidirectional message exchange Indicates the first Asymmetric bidirectional propagation delay during round-trip bidirectional message exchange Indicates the first Composite random measurement noise during round-trip message exchange. This represents the difference between the first timestamp interval. This represents the difference between the second timestamp intervals. This represents the difference in asymmetric bidirectional propagation delay. This represents the noise difference in composite random measurements; The observation equation is calculated based on the first timestamp interval difference, the second timestamp interval difference, the asymmetric two-way propagation delay difference, and the composite random measurement noise difference in the timestamp interval difference formula, wherein the observation equation is as follows: ； in, The observation vector at each observation time. For the first The state observation matrix at the nth observation time represents the nonlinear observation function at the nth observation time. The values ​​of the state vector at each observation time. Indicates the first Observational information at each observation time, Indicates the first The radial relative velocity between the UAV node and the master UAV node at each observation moment. Indicates the first The actual clock offset at each observation time Indicates the first The radial relative velocity prediction values ​​between the UAV node and the master UAV node at each observation time point. Indicates the first Predicted clock offset at each observation time, Indicates the first Velocity observation noise at each observation time Indicates the first Clock offset observation noise at each observation time.

7. The UAV clock synchronization and ranging method based on bidirectional delay estimation as described in claim 6, characterized in that, The calculation of the covariance of the discrete-time observation noise term in the observation equation includes: ； in, Indicates the first The covariance of the discrete-time observation noise term in the observation equation for each filtering step. Indicates the first Discrete-time observation noise term for each filtering step Indicates the first The transpose vector of the discrete-time observation noise term for each filtering step. Indicates the first The variance of the velocity observation noise for each filtering step. Indicates the first The variance of the clock offset observation noise for each filtering step. Indicates the first The variance of noise measured in a single timestamp during each filtering step; The observation equation is as follows: ； in, Indicates the first Sensor observation matrix for each filtering step, Indicates the first The state observation matrix for each filtering step Indicates the first The observation information of each filtering step.

8. The UAV clock synchronization and ranging method based on bidirectional delay estimation as described in claim 7, characterized in that, The calculation of the Kalman gain based on the covariance of the prediction error and the discrete-time observation noise term includes: The Kalman gain is calculated using the following formula, based on the prediction error and the covariance of the discrete-time observation noise term: ； in, Indicates the first Kalman gain for each filtering step Indicates the first The transpose of the state observation matrix for each filtering step.

9. The UAV clock synchronization and ranging method based on bidirectional delay estimation as described in claim 8, characterized in that, The step of calculating the corrected prediction value based on the Kalman gain, state prediction matrix, sensor observation matrix, and state observation matrix includes: Based on the Kalman gain, state prediction matrix, sensor observation matrix, and state observation matrix, the corrected prediction value is calculated using the following formula: ； in, Indicates the first The corrected prediction value corresponding to each filter step wave. Indicates the first The state prediction matrix corresponding to each filter step wave.

10. A UAV clock synchronization and ranging system based on bidirectional delay estimation, characterized in that, The system includes: The state prediction matrix prediction error calculation module is used to obtain a state matrix using a pre-constructed state equation, calculate a state prediction matrix based on the state matrix and the state equation, calculate the covariance of the process noise vector in the state equation, and calculate the prediction error based on the covariance of the process noise vector. The observation equation covariance calculation module is used to construct the sensor observation matrix, the state observation matrix, and the observation equation, and to calculate the covariance of the discrete-time observation noise term in the observation equation. The corrected prediction calculation module is used to calculate the Kalman gain based on the prediction error and the covariance of the discrete-time observation noise term; and to calculate the corrected prediction value based on the Kalman gain, the state prediction matrix, the sensor observation matrix, and the state observation matrix. The slave node clock correction module is used to correct the clock and relative distance of the pre-built slave nodes according to the correction prediction value.

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