Multi-unmanned aerial vehicle spinning phase difference and time difference combined passive positioning method

Abstract

The invention discloses a multi-unmanned aerial vehicle spinning phase difference and time difference combined passive positioning method. A plurality of unmanned aerial vehicles are used for formation flight, each unmanned aerial vehicle is provided with a horizontally rotating long baseline interferometer to measure the arrival phase difference of radiation source signals, and each unmanned aerial vehicle measures the arrival time difference of the radiation source signals; and establishing a phase difference and time difference combined passive model according to the positioning model, determining a positioning equation, and resolving by adopting a multi-stage multi-hypothesis extended Kalman filtering algorithm to obtain position estimation of the radiation source. The method is low in implementation difficulty, low in manufacturing cost and system complexity and high in positioning precision, and can be well applied to electronic reconnaissance and other military and civil fields.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of passive location technology, in particular to a multi-UAV spin phase difference time difference joint passive location method. BACKGROUND

[0002] Multi-station passive location technology that receives non-cooperative radiation source signals through multiple observation stations to determine the position of the radiation source has important application value in military and civilian fields such as investigation, monitoring, early warning, and personnel search and rescue, and has been widely concerned and researched.

[0003] In recent years, platform technologies such as unmanned aerial vehicles (UAVs) have been increasingly widely used. Such platforms have characteristics such as low cost and miniaturization, and multi-station passive location based on such miniaturized platform formations has important research and application value. However, the application of existing multi-station passive location systems on such platforms may face difficulties in implementation, poor positioning accuracy, high cost, and high system complexity. Therefore, it is of great significance to research new multi-station passive location systems.

[0004] The solution method of the passive location equation usually has a closed-form analytical method represented by pseudo-linear least squares and two-step weighted least squares, an optimization algorithm represented by grid search and particle swarm, and a filter recursive algorithm such as extended Kalman filter and particle filter. Under different location systems, the positioning effect obtained by using different location algorithms is different, so it is of great theoretical and engineering application value to research location algorithms suitable for a particular location system based on the location system. SUMMARY

[0005] To solve the above problems, the present application provides a multi-UAV spin phase difference time difference joint passive location method, which includes a new system of multi-UAV spin phase difference time difference joint location and a new algorithm of multi-level multi-hypothesis extended Kalman filter (MLMH-EKF). A multi-UAV formation flight (i.e., the UAVs are relatively stationary, and the UAV group flies at a certain height) is used, and a horizontal rotating long baseline interferometer is installed on each UAV to measure the phasedifference of arrival (PDOA) of the radiation source signal. At the same time, each UAV measures the timedifference of arrival (TDOA) of the radiation source signal. According to the location model, a phase difference time difference joint location equation is established, and a multi-level multi-hypothesis extended Kalman filter algorithm is used to solve it to obtain the position estimate of the radiation source.

[0006] The technical solution of the present application is:

[0007] A multi-UAV spin-phase-difference and time-difference combined passive localization method is proposed. This method utilizes multiple UAVs flying in formation, with each UAV equipped with a horizontally rotating long baseline interferometer to measure the arrival phase difference of the radiation source signal. Simultaneously, each UAV measures the arrival time difference of the radiation source signal. Based on the localization model, a phase-difference and time-difference combined passive model is established to determine the localization equation. A multi-level, multi-hypothesis extended Kalman filter algorithm is then used to solve the equation, resulting in an estimate of the radiation source's location.

[0008] Furthermore, a multi-UAV spin phase difference and time difference joint passive positioning model is established to determine the positioning equations and observations, as follows:

[0009] Assuming that at the current observation time, there are N drones flying in formation, the positions of the drones and the fixed ground radiation source are confirmed; the phase difference and time difference observations of the signal confirming the position of the radiation source reaching the N drones are obtained; the observations of the multi-drone spin phase difference and time difference passive positioning model consist of phase difference observations and time difference observations, and the observations represent the time difference of arrival between the nth drone and the 1st drone at the current observation time.

[0010] Furthermore, a cost function is constructed based on the maximum likelihood principle, as follows: First, the phase difference observation noise vector is calculated, and then the maximum likelihood function of the phase difference observation noise vector is calculated; then, the time difference observation noise vector is calculated, and then the maximum likelihood function of the time difference observation noise vector is calculated; the maximum likelihood function of the phase difference observation noise vector and the time difference observation noise vector corresponding to the observation is calculated, with the aim of finding the maximum value of the maximum likelihood function corresponding to the observation, and a cost function J is established.

[0011] Furthermore, a multi-level, multi-hypothesis extended Kalman filter (EDF) localization algorithm is employed to calculate the location of the radiation source. Specifically, the observation area is divided into multiple levels of grids with different levels of fineness. The center of each grid point is assumed to be the initial value for the EDF algorithm, and filtering is performed. Finally, the obtained location results are used to calculate the cost function value using the cost function J, and the location with the minimum cost function value is taken as the estimated location of the radiation source.

[0012] Furthermore, the observation area is divided into L-level grids, with the width of each level grid set as follows: the coordinates of the observation center at each level; the maximum and minimum observation values ​​for each level observation range; and the number of grids obtainable at each level. The number of grids is calculated by taking the difference between the maximum and minimum observation values ​​as the numerator and the grid width as the denominator, obtaining the result value, and then squaring the obtained result value to obtain the required number of grids.

[0013] Center of each grid at each level As the initial value for the extended Kalman filter algorithm; the l-th stage... A single extended Kalman filter process at each initial position includes:

[0014] predicting the position and the covariance matrix;

[0015] calculating the innovation, the joint Jacobian matrix of the phase difference and the time difference, and the joint Kalman gain of the phase difference and the time difference;

[0016] outputting the result position;

[0017] calculating the value of the cost function J by using the obtained position, taking the position with the minimum J as the observation center of the next grid, and taking the position with the minimum J of the last grid as the estimated position of the radiation source.

[0018] Further, the application also provides a multi-unmanned aerial vehicle spin phase difference and time difference joint passive positioning device, which is internally provided with the multi-unmanned aerial vehicle spin phase difference and time difference joint passive positioning method.

[0019] The application has the following advantages:

[0020] In view of the problems that the existing multi-station passive positioning system may face great implementation difficulty, poor positioning accuracy, high cost and system complexity, and the need for a suitable positioning algorithm when applied to the unmanned aerial vehicle platform in electronic reconnaissance, a multi-unmanned aerial vehicle spin phase difference and time difference joint passive positioning method is provided. The method has smaller implementation difficulty, lower cost and system complexity, and higher positioning accuracy, and can be well applied in electronic reconnaissance and other military and civilian fields. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 which is the overall flowchart of the application.

[0022] Figure 2 which is the flowchart of the MLMH-EKF algorithm.

[0023] Figure 3 which is the positioning scene diagram of the application.

[0024] Figure 4 which is the comparison diagram of the positioning error and the Cramer-Rao lower bound of the method of the application.

[0025] Figure 5 which is the GDOP diagram of the positioning scene.

[0026] Figure 6 which is the RMSE curve diagram of the positioning. DETAILED DESCRIPTION

[0027] The specific embodiments are described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the application, and cannot be used to limit the protection scope of the application.

[0028] The application provides a multi-unmanned aerial vehicle spin phase difference and time difference joint passive positioning method (seeFigures 1-5 ), comprising the following steps:

[0029] Step 1: establishing a multi-UAV spin phase difference time difference joint passive positioning model, determining a positioning equation and an observation;

[0030] Step 2: constructing a cost function based on a maximum likelihood principle;

[0031] Step 3: adopting a multi-level multi-hypothesis extended Kalman filter positioning algorithm to solve the position of the radiation source.

[0032] Further, step 1 specifically includes:

[0033] Suppose at the observation time , The positions of the N UAVs in formation flight are represented as , The position of the ground fixed radiation source is , wherein The frequency of the radiation source signal is f, the baseline length of the interferometer is d, and the signal propagation speed is c. Then the phase difference of the radiation source signal reaching the N UAVs is represented as:

[0034]

[0035] wherein represents the observation time The unit pointing vector of the interferometer on the nth UAV, and K is a parameter constant.

[0036] Since the actual observed phase difference is only between or , the phase difference observation of the N UAVs is represented as:

[0037]

[0038] wherein represents the phase difference measurement noise of the nth UAV at the time , and mod represents the modulus.

[0039] The time difference observation of the radiation source signal reaching the N UAVs is represented as:

[0040]

[0041] wherein , represents the time difference measurement noise of the nth UAV at the time m.

[0042] The positioning model equation for the multi-UAV spin phase difference time difference passive positioning system is:

[0043]

[0044] Observations are ,in , .

[0045] Let m represent the time difference between the nth drone and the first drone at time m.

[0046] Furthermore, step 2 above specifically includes:

[0047] Assumption The phase difference and time difference observation noise at each time point both follow a Gaussian distribution, with variances of respectively. and Furthermore, the two are independent of each other. The phase difference observation noise vector is:

[0048]

[0049] in, , for The true value of the phase difference observation of the nth UAV at time n. .but The maximum likelihood function is:

[0050]

[0051] Similarly, the time difference observation noise vector is:

[0052]

[0053] in, ,and for True value of the time difference observation for the nth UAV at time n:

[0054]

[0055] but The maximum likelihood function is:

[0056]

[0057] From equations (1.6) and (1.9), it can be seen that the observed quantity Maximum likelihood function of corresponding phase difference time difference joint observation noise vector Is:

[0058]

[0059] Solve the maximum value of The cost function J is established:

[0060]

[0061] When J takes the minimum value, Take the maximum value.

[0062] Further, in the above step 3, the MLMH-EKF positioning algorithm is specifically:

[0063] The observation area is divided into multiple levels of different grid fineness, and it is assumed that the center of each grid point is the initial value of the extended Kalman filter algorithm, and the filter is performed. Finally, the position result obtained is used to calculate the cost function value by formula (1.11), and the position with the minimum cost function value is taken as the estimated radiation source position.

[0064] Taking the positioning model of the application as an example, a total of L levels of grids are divided, and the width of each level of grid is The observation center coordinates of each level are , wherein The observation range of each level is The number of grids obtained by each level is:

[0065]

[0066] The center of each grid of each level As the initial value of the extended Kalman filter algorithm. The one-time extended Kalman filter process of the initial position of the lth level and the mth grid is as follows: The prediction equation is:

[0067]

[0068]

[0069]

[0070] The state update equation is:

[0071]

[0072] ​

[0073] The innovation is:

[0074]

[0075] wherein, and respectively represent the phase difference and the time difference true value at the position, that is:

[0076]

[0077]

[0078] The covariance matrix is:

[0079]

[0080] wherein , is a unit matrix of order.

[0081] The Jacobian matrix corresponding to the phase difference observation is:

[0082]

[0083] wherein, .

[0084] The Jacobian matrix corresponding to the time difference observation is:

[0085]

[0086] The joint Jacobian matrix is represented as:

[0087]

[0088] The Kalman gain after the combination of the phase difference and the time difference is:

[0089]

[0090] The result output is:

[0091]

[0092] The position obtained from formula (1.25) is substituted into formula (1.11) to calculate the cost function value, and the position with the minimum J is taken as the observation center of the next level grid, and the position with the minimum J in the last level is the estimated position of the radiation source.

[0093] Embodiment:

[0094] As shown in Figure 3 , a multi-UAV spin phase difference and time difference joint passive positioning model is established, and the positioning equation and observation are determined, specifically:

[0095] Suppose there are four UAVs flying in formation, flying parallel to the ground in the positive north direction, with a flight speed of m / s. The initial positions of the four UAVs are m, m, m, m, and m, respectively. The position of the ground fixed radiation source is km. The radiation source emits signals at a frequency of Hz, and the propagation speed is the speed of light. Each UAV is equipped with a long baseline interferometer that can rotate horizontally and has a length of m. The phase difference observation noise is , and the time difference observation noise is m. The total observation time is s, and an observation is made every 1 s. According to formulas (1.1)~(1.4), the positioning model of the multi-UAV spin phase difference and time difference passive positioning system is established, and the positioning equation and observation are determined. According to the positioning model, positioning equation and observation established in step 1, and combining the maximum likelihood principle, the cost function is constructed according to formulas (1.5)~(1.11).

[0096] The observation area is divided into three levels of grid

[0097] , the first level observation center is the coordinate origin, the observation range is km, and the grid width is m. The extended Kalman filter positioning is performed at each grid point to calculate the cost function in step 2. The position of the grid point with the minimum cost function is taken as the second level observation center, and so on. The second level observation range is m, and the grid width is m. The third level observation range is m, and the grid width is m. The position of the grid point with the minimum third level cost function is taken as the estimated value of the radiation source position, denoted as .

[0098] The positioning results are analyzed, specifically: ​

[0099] (1) Through simulation experiments, the positioning error of the present application is compared with the Cramer-Rao lower bound, and the results are shown in Figure 4 . In the figure, positioning error of 10 represents , m, and so on.

[0100] It can be seen that in the case of low and moderate noise levels, the positioning method of the present application can reach the Cramer-Rao lower bound, indicating that the positioning method of the present application has better positioning performance. When the positioning error is greater than 50, the positioning method of the present application deviates from the Cramer-Rao lower bound due to excessive error.

[0101] (2) Figure 5 is the GDOP graph in the positioning scenario of the present embodiment, which reflects the influence of the geometric configuration of the radiation source and the unmanned aerial vehicle on the positioning accuracy. It can be seen from Figure 5 that the farther the position is from the geometric center of the configuration (in this embodiment, the center of the configuration is m), the smaller the positioning accuracy is, and the points with the same positioning accuracy are distributed on an approximately square curve with the center of the configuration as the geometric center.

[0102] (3) Figure 6 is the positioning RMSE curve comparison graph of the present embodiment, which reflects the change trend of the positioning error of the present application method and the comparison method with the increase of the observation noise. In the figure, observation noise of 10 represents , m, and so on. It can be seen from Figure 6 that the grid search method is most sensitive to observation noise, and there is already a large positioning error when the noise level is low. The anti-noise performance of EKF is better than that of the grid search method, but slightly worse than that of the present application method. During the process of increasing the observation noise to 60, the change range of the positioning error of the present application method is small, indicating that the positioning algorithm of the present application has good anti-noise performance.

[0103] In summary, the multi-unmanned aerial vehicle spin phase difference time difference joint passive positioning method proposed by the present application has better positioning performance, higher positioning accuracy and better anti-noise performance, so it can achieve good positioning effect.

[0104] The above is only a preferred embodiment of the present application, and does not limit the present application in any way. Any simple modification, change and equivalent change made according to the technical essence of the present application to the above embodiment are still within the protection scope of the technical solution of the present application.

Claims

1. A multi-UAV spin phase difference time difference joint passive positioning method, characterized in that, A plurality of unmanned aerial vehicles are used to fly in formation, each unmanned aerial vehicle is provided with a horizontal rotating long baseline interferometer to measure the phase difference of arrival of the radiation source signal, and each unmanned aerial vehicle measures the time difference of arrival of the radiation source signal; a phase difference-time difference joint passive positioning model is established according to a positioning model, a positioning equation is determined, a multi-level multi-hypothesis extended Kalman filtering algorithm is used for solving, and a position estimation of the radiation source is obtained.

2. The multi-UAV self-rotation phase difference time difference joint passive positioning method according to claim 1, characterized in that, A multi-unmanned aerial vehicle self-rotation phase difference-time difference joint passive positioning model is established, and a positioning equation and an observation are determined, and the specific implementation is as follows: It is assumed that at the current observation time, N unmanned aerial vehicles fly in formation, the positions of the unmanned aerial vehicles and the positions of the ground fixed radiation sources are confirmed; the phase difference observation and the time difference observation of the signal arriving at the N unmanned aerial vehicles are confirmed; the observation of the multi-unmanned aerial vehicle self-rotation phase difference-time difference passive positioning model is composed of the phase difference observation and the time difference observation, and the observation represents the time difference of arrival between the nth unmanned aerial vehicle and the first unmanned aerial vehicle at the current observation time.

3. The multi-UAV self-rotation phase difference time difference joint passive positioning method according to claim 1, characterized in that, A cost function is constructed based on the maximum likelihood principle, and the specific implementation is as follows: first, the phase difference observation noise vector is calculated, and then the maximum likelihood function of the phase difference observation noise vector is calculated; then, the time difference observation noise vector is calculated, and then the maximum likelihood function of the time difference observation noise vector is calculated; the maximum likelihood function of the phase difference observation noise vector and the time difference observation noise vector corresponding to the observation is calculated, and the cost function J is established for the purpose of solving the maximum value of the maximum likelihood function corresponding to the observation.

4. The multi-UAV self-rotation phase difference time difference joint passive positioning method according to claim 3, characterized in that, A multi-level multi-hypothesis extended Kalman filtering positioning algorithm is used to solve the position of the radiation source, and the specific implementation is as follows: the observation area is divided into a plurality of grids with different levels of detail, it is assumed that the center of each grid point is the initial value of the extended Kalman filtering algorithm, and filtering is performed; finally, the position result obtained is used to calculate the cost function value of the cost function J, and the position with the minimum cost function value is taken as the estimated position of the radiation source.

5. The multi-UAV self-rotation phase difference time difference joint passive positioning method according to claim 4, characterized in that, The observation area is divided into L-level grids, the width of each level grid is set as, the center coordinates of each level observation are set as, the maximum and minimum values of the observation range of each level are set as, and the number of grids obtained by each level is calculated, wherein the number of grids is: the difference between the maximum value and the minimum value of the observation is taken as the numerator, and the grid width is taken as the denominator to obtain a result value, and then the square of the obtained result value is taken to obtain the required number of grids; The center of each grid of each level is calculated as follows: as the initial value of the extended Kalman filter algorithm; the first extended Kalman filter process of the initial position of the lth level includes: as the initial value of the extended Kalman filter algorithm; the first extended Kalman filter process of the initial position of the lth level includes: The position and the covariance matrix are predicted; The innovation, the phase difference-time difference joint Jacobian matrix, and the phase difference-time difference joint Kalman gain are calculated; The result position is outputted; The value of the cost function J is calculated by using the obtained position, the position with the minimum J is taken as the observation center of the next level grid, and the position with the minimum J of the last level is the estimated position of the radiation source.

6. A multi-UAV spin phase difference time difference joint passive location device, characterized in that, The device is provided with the method according to any one of claims 1-5.

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