A Multi-UAV Spin Phase Difference and Time Difference Joint Passive Positioning Method

Abstract

This invention discloses a multi-UAV spin-phase-difference and time-difference combined passive localization method. The method utilizes multiple UAVs flying in formation, each equipped with a horizontally rotating long-baseline interferometer to measure the arrival phase difference of a radiation source signal. Simultaneously, each UAV measures the arrival time difference of the radiation source signal. A phase-difference and time-difference combined passive model is established based on a localization model to determine the localization equation. A multi-level, multi-hypothesis extended Kalman filter algorithm is used to solve the equation, obtaining an estimate of the radiation source's location. This invention is relatively easy to implement, has low cost and system complexity, and achieves high localization accuracy, making it suitable for applications in electronic reconnaissance and other military and civilian fields.

Description

Technical Field

[0001] This invention relates to the field of passive positioning technology, specifically to a multi-UAV spin phase difference and time difference combined passive positioning method. Background Technology

[0002] Multi-station passive positioning technology, which determines the location of radiation sources by receiving signals from non-cooperative radiation sources through multiple observation stations, has significant application value in military and civilian fields such as reconnaissance, surveillance, early warning, and personnel search and rescue, and has received widespread attention and research.

[0003] In recent years, the application of platform technologies such as unmanned aerial vehicles (UAVs) has become increasingly widespread. These platforms are characterized by low cost and miniaturization, making multi-station passive positioning based on such miniaturized platform formations of significant research and application value. However, existing multi-station passive positioning systems may face drawbacks such as high implementation difficulty, poor positioning accuracy, high cost, and high system complexity when applied to these platforms. Therefore, researching new multi-station passive positioning systems is of great importance.

[0004] Methods for solving passive localization equations typically include closed-form analytical methods such as pseudo-linear least squares and two-step weighted least squares, optimization algorithms such as grid search and particle swarm optimization, and filtering recursive algorithms such as extended Kalman filter and particle filter. Under different localization systems, the localization results achieved by different localization algorithms vary. Therefore, researching localization algorithms suitable for specific localization systems has significant theoretical and engineering application value. Summary of the Invention

[0005] To address the aforementioned problems, this invention proposes a multi-UAV spin-phase-difference-time-difference joint passive localization method, comprising a novel multi-UAV spin-phase-difference-time-difference joint localization architecture and a novel multi-level multi-hypothesis extended Kalman filter (MLMH-EKF) algorithm. Multiple UAVs fly in formation (i.e., the UAVs are relatively stationary, and the UAV swarm flies at a certain altitude). Each UAV is equipped with a horizontally rotating long baseline interferometer to measure the phase difference of arrival (PDOA) of the radiation source signal. Simultaneously, each UAV measures the time difference of arrival (TDOA) of the radiation source signal. A phase-difference-time-difference joint localization equation is established based on the localization model, and the multi-level multi-hypothesis extended Kalman filter algorithm is used to solve it, obtaining an estimate of the radiation source's location.

[0006] The technical solution of this invention is as follows:

[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] Predict location and covariance matrix;

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

[0016] Output the result location;

[0017] The cost function J is calculated using the obtained location. The location with the minimum J is taken as the observation center of the next level grid. The location with the minimum J in the last level is the estimated location of the radiation source.

[0018] Furthermore, the present invention also provides a multi-UAV spin phase difference time difference combined passive positioning device, which incorporates a multi-UAV spin phase difference time difference combined passive positioning method.

[0019] The beneficial effects of this invention are as follows:

[0020] To address the challenges of implementing existing multi-station passive positioning systems for electronic reconnaissance on UAV platforms, including high implementation difficulty, poor positioning accuracy, high cost and system complexity, and the need for suitable positioning algorithms, this paper proposes a multi-UAV spin phase difference and time difference joint passive positioning method. This method is relatively easy to implement, has lower cost and system complexity, and achieves higher positioning accuracy, making it suitable for applications in electronic reconnaissance and other military and civilian fields. Attached Figure Description

[0021] Figure 1 This is the overall flowchart of the present invention.

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

[0023] Figure 3 This is a positioning scene diagram for the present invention.

[0024] Figure 4 This is a comparison chart of the positioning error of the method of the present invention and the lower bound of Cramérault.

[0025] Figure 5 GDOP diagram for locating the scene.

[0026] Figure 6 To locate the RMSE curve. Detailed Implementation

[0027] Specific embodiments are given below with reference to the accompanying drawings. These embodiments are only used to more clearly illustrate the technical solutions of the present invention and should not be construed as limiting the scope of protection of the present invention.

[0028] This invention proposes a multi-UAV spin phase difference and time difference joint passive positioning method (see [link]). Figures 1-5 ), including the following steps:

[0029] Step 1: Establish a multi-UAV spin phase difference and time difference joint passive positioning model, and determine the positioning equation and observations;

[0030] Step 2: Construct the cost function based on the maximum likelihood principle;

[0031] Step 3: Use the multi-level, multi-hypothesis extended Kalman filter localization algorithm to calculate the location of the radiation source.

[0032] Furthermore, step 1 above specifically includes:

[0033] Assuming at the observation time , The drones fly in formation, and the positions of the drones are indicated as follows: , The location of the ground-based fixed radiation source is ,in The radiation source emits a signal at frequency f, the interferometer baseline length is d, and the signal propagation speed is c. The phase difference between the radiation source signal reaching N UAVs is expressed as:

[0034]

[0035] in, Indicates the observation time The unit pointing vector of the interferometer on the nth UAV, where K is a parameter constant.

[0036] Because the phase difference obtained from actual observation is only in or Therefore, the phase difference observation of N drones is expressed as:

[0037]

[0038] in, Indicates in The phase difference measurement noise of the nth UAV at time t, where mod represents modulo.

[0039] The time difference observation of the radiation source signal arriving at N UAVs is expressed as follows:

[0040]

[0041] in, , This represents the time difference measurement noise of the nth UAV at 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 The maximum likelihood function of the corresponding phase difference and time difference joint observation noise vector for:

[0058]

[0059] To solve To maximize the value, we establish the cost function J:

[0060]

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

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

[0063] The observation area is divided into multiple grids of varying fineness. Each grid point is assumed to have its center as the initial value for the extended Kalman filter algorithm. The resulting location is then used to calculate the cost function value using equation (1.11), and the location with the minimum cost function value is taken as the estimated radiation source location.

[0064] Taking the positioning model of this invention as an example, it is divided into L levels of grids, with each level having a grid width of [missing information]. The coordinates of each observation center are: ,in The observation range for each level is... The number of grid cells obtainable at each level is:

[0065]

[0066] Center of each grid at each level As the initial values ​​for the extended Kalman filter algorithm. (Level l, ...) The first extended Kalman filter process at each initial position is shown below:

[0067] The prediction equation is:

[0068]

[0069]

[0070] The state update equation is:

[0071]

[0072]

[0073] The new information is:

[0074]

[0075] in, and They represent The true values ​​of phase difference and time difference at the location, i.e.:

[0076]

[0077]

[0078] The covariance matrix is:

[0079]

[0080] in , yes An identity matrix of order 1.

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

[0082]

[0083] in, .

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

[0085]

[0086] The joint Jacobian matrix is ​​then expressed as:

[0087]

[0088] The Kalman gain after combining phase difference and time difference is:

[0089]

[0090] Output results:

[0091]

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

[0093] Example:

[0094] like Figure 3 As shown, a multi-UAV spin phase difference and time difference joint passive positioning model is established to determine the positioning equations and observations, specifically:

[0095] Four The drones, flying in formation, are parallel to the ground in a north-south direction, with a speed of [missing information]. m / s. Initial time The positions are respectively m, m, m, m. The location of the fixed ground radiation source is km. Frequency of the radiation source's emitted signal. Hz, with a propagation speed of light. Each drone carries a horizontally rotating device with a length of... A long-baseline interferometer with a length of m. Phase difference observation noise. Time difference observation noise m. Total observation time s, an observation is made every 1s. Based on formulas (1.1) to (1.4), a positioning model for the multi-UAV spin phase difference time difference passive positioning system is established, and the positioning equation and observations are determined.

[0096] Based on the positioning model, positioning equation and observations established in step 1, and combined with the maximum likelihood principle, the cost function is constructed according to formulas (1.5) to (1.11).

[0097] The observation area was divided into three levels of grids. The first-level observation center is the origin of the coordinate system, and the observation range is... km, grid width m, perform extended Kalman filtering for localization at each grid point, and calculate the cost function from step 2. The grid point with the minimum cost function is designated as the second-level observation center, and so on. The second-level observation range is... m, grid width m. The third-level observation range is... m, grid width m. The location of the grid point with the minimum third-level cost function is taken as the estimated location of the radiation source, denoted as m. .

[0098] The analysis and positioning results are as follows:

[0099] (1) The positioning error of the present invention was compared with the Cramer-Rao boundary through simulation experiments, and the results are as follows: Figure 4 As shown in the figure. A positioning error of 10 indicates... , m, and so on.

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

[0101] (2) Figure 5 This is the GDOP diagram for the positioning scenario in this embodiment, demonstrating the impact of the radiation source and the UAV's geometry on positioning accuracy. From Figure 5 It can be seen that the distance from the center of the multi-unmanned structure (in this embodiment, it is...) The farther the location (m), the smaller the positioning accuracy, and points with the same positioning accuracy are distributed on a curve that is approximately square with the configuration center as the geometric center.

[0102] (3) Figure 6 This is a comparison chart of the positioning RMSE curves in this embodiment, illustrating the trend of positioning error changes with increasing observation noise in the proposed method and the comparison method. In the chart, observation noise is represented by 10. , m, and so on. Figure 6 It can be seen that the grid search method is most sensitive to observation noise, exhibiting significant positioning errors even at low noise levels. The EKF method demonstrates better noise resistance than the grid search method, but slightly worse than the method of this invention. As the observation noise increases to 60, the positioning error of the method of this invention shows relatively small changes, indicating that the positioning algorithm of this invention has good noise resistance.

[0103] In summary, the multi-UAV spin phase difference time difference combined passive positioning method proposed in this invention has superior positioning performance, high positioning accuracy, and good noise resistance, thus achieving good positioning results.

[0104] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any way. Any simple modifications, alterations, and equivalent changes made to the above embodiments based on the inventive essence shall still fall within the protection scope of the present invention.

Claims

1. A multi-UAV spin phase difference time difference joint passive positioning method, characterized in that, The multi-UAV formation flight is used, each UAV is installed with a horizontal rotating long baseline interferometer to measure the arrival phase difference of the radiation source signal, and each UAV measures the arrival time difference of the radiation source signal; a phase difference-time difference joint passive 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; The multi-level multi-hypothesis extended Kalman filtering positioning algorithm is used to solve the position of the radiation source, and the implementation is as follows: the observation area is divided into multiple levels of grids with different levels of detail, the center of each grid point is assumed as 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 J, and the position with the minimum cost function value is taken as the estimated position of the radiation source; The observation area is divided into multiple levels of grids with different levels of detail, and the implementation is as follows: the observation area is divided into L levels of grids, the width of each level of grid is set as, the center coordinates of each level of observation are, the maximum and minimum observation values of each level of observation range are set, the number of grids obtained by each level is calculated, wherein the grid number is: the difference between the maximum observation value and the minimum observation value 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 grid number; 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 of grid, and the position with the minimum J of the last level is the estimated position of the radiation source. 2.The multi-UAV self-rotation phase difference time difference joint passive positioning method according to claim 1, characterized in that, A multi-UAV spin phase difference-time difference joint passive positioning model is established, and the positioning equation and the observation are determined, and the implementation is as follows: It is assumed that there are N UAVs in formation flight at the current observation time, the positions of the UAVs and the position of the ground fixed radiation source are confirmed; the phase difference observation and the time difference observation of the signal arriving at the N UAVs from the radiation source position are confirmed; the observation of the multi-UAV spin phase difference-time difference passive positioning model is composed of the phase difference observation and the time difference observation, and the observation represents the arrival time difference between the nth UAV and the first UAV 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 implementation is as follows: the phase difference observation noise vector is calculated first, 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 to solve the maximum value of the maximum likelihood function corresponding to the observation.

4. A multi-UAV spin phase difference time difference joint passive location device, characterized in that, The device is internally provided with the method of any one of claims 1-3.

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