Cross positioning method and device of mobile radiation source

Abstract

The invention relates to a cross positioning method and device for a mobile radiation source, belongs to the technical field of target tracking, and solves the problems that the existing single-station direction finding result is insufficient to reflect the position of the radiation source and the like. The method comprises the following steps: performing cross positioning by using a least square method based on known positions of two observation stations and angles from a radiation source to the two observation stations to obtain an initial position of the radiation source; performing static modeling on the target position of the radiation source and the measurement value thereof according to the initial position; multiple times of iterative estimation are carried out on the state of the target to generate a predicted value, dynamic information and measurement data are fused through steady-state Kalman filtering in each time of iterative estimation, and the change of the motion mode of the radiation source target and the uncertainty in the dynamic environment are processed; and when the error between the observed predicted value and the real measured value is smaller than a given threshold value, iteration is ended, and the accurate estimated position of the mobile radiation source target is obtained. Kalman filtering fuses dynamic information and measurement data, and deals with target motion mode change and uncertainty in a dynamic environment.

Description

Technical Field

[0001] The present invention relates to the technical field of target tracking, and particularly to a method and device for cross-locating a mobile radiation source. Background Art

[0002] The spatial positioning and tracking of mobile radiation sources involve the accurate positioning and tracking of mobile radiation sources in space. This field is of great significance in many practical applications, including military, civilian, scientific research and other fields. In the military field, accurately tracking and positioning mobile radiation sources includes tracking enemy aircraft, missiles, radars, etc., to ensure timely adoption of necessary defense measures. In the civilian field, the positioning and tracking of mobile radiation sources can be used in fields such as aviation, aerospace, meteorological monitoring, and emergency rescue. For example, the monitoring and control of unmanned aerial vehicles, the navigation of aircraft, weather forecasting, etc. In the scientific research field, for research in astronomy, geophysics, etc., the accurate positioning of mobile radiation sources is also crucial. For example, the observation of celestial objects, the monitoring of the earth's magnetic field, etc.

[0003] The positioning of mobile radiation sources usually involves multiple sensors, such as radars, GPS, inertial measurement units, etc. The algorithm needs to effectively fuse the information of these sensors to improve the positioning accuracy. Mobile radiation sources may move in a dynamic environment, such as an aircraft or unmanned aerial vehicle flying at high speed. The algorithm needs to consider the positions of the target at different time and space points and be able to adapt to the changes in the dynamic environment. In many applications, especially military applications, the positioning of mobile radiation sources needs to have high real-time performance to ensure timely decision-making and response.

[0004] The target positioning and tracking technology based on wireless sensor networks has become a current research hotspot. The background of the spatial positioning and tracking of mobile radiation sources involves multiple fields, and the key lies in developing algorithms that can accurately and real-time locate and track mobile radiation sources to meet the needs of different application fields.

[0005] However, in the actual environment, the electromagnetic environment is complex and there are many radiation sources. It is quite challenging for wireless sensor networks to achieve accurate positioning and tracking of a large number of radiation sources simultaneously. In the tracking of mobile targets, especially in the case of high-speed movement, the system needs to have sufficient adaptability to ensure the accuracy of positioning. This includes the rapid response to the target movement pattern and the research of adaptive algorithms. At the same time, effectively fusing information from different sensors to improve the positioning accuracy and robustness is still a challenging problem. Technical problems in aspects such as sensor data synchronization and data fusion algorithms need to be solved. In addition, many application scenarios have high requirements for the real-time performance of target positioning, such as military applications and emergency rescue. Therefore, it is necessary to study algorithms and system architectures with strong real-time performance to ensure the provision of accurate target position information in a short time.

[0006] In the aspect of the positioning and tracking of radiation sources, most methods have limitations in practical applications and are difficult to comprehensively and thoroughly solve the problem of multi-radiation source positioning. Summary of the Invention

[0007] In view of the above analysis, embodiments of the present invention aim to provide a cross-positioning method and device for mobile radiation sources to solve the problems that the existing single-station direction finding results are not sufficient to accurately reflect the spatial position of the radiation source and a single sensor may face problems such as signal occlusion and noise interference.

[0008] On the one hand, embodiments of the present invention provide a cross-positioning method for mobile radiation sources, including: performing cross-positioning using the least squares method based on the known position information of two observation stations and the angle information of the mobile radiation source obtained by direction finding to obtain the initial position of the mobile radiation source; statically modeling the target position and its measurement value of the mobile radiation source according to the initial position of the mobile radiation source to obtain the state equation and measurement equation of the mobile radiation source target; performing multiple iterative estimations on the state of the mobile radiation source target to generate observation prediction values, where each iterative estimation uses steady-state Kalman filtering to fuse dynamic information and measurement data to handle the changes in the motion mode of the mobile radiation source target and the uncertainties in the dynamic environment; and when the error between the observation prediction value and the true measurement value is less than a given threshold, ending the iteration and obtaining the accurate estimated position of the mobile radiation source target.

[0009] The beneficial effects of the above technical solutions are as follows: The least squares method is used for cross-positioning to obtain the initial spatial position estimation of the UAV, which helps to reduce the initial error of the target tracking system and thus improve the overall accuracy; by using the least squares initial value solution, a relatively good initial estimation can be provided, which helps to reduce the dependence on the filter. This is particularly important when the target is just being tracked. The steady-state Kalman filter can handle the changes in the target motion mode and the uncertainties in the dynamic environment by fusing dynamic information and measurement data, has good adaptability to handle the dynamic environment and sensor noise, and helps to improve the stability, robustness, and tracking accuracy of the system.

[0010] Based on a further improvement of the above method, the signals of the mobile radiation source are monitored and collected through a wireless sensor network, the angle of arrival and time of arrival of the mobile radiation source signals are observed, and the target position of the mobile radiation source is located and tracked, where the wireless sensor network includes sensors on ground stations, satellites, and airplanes.

[0011] Based on further improvements to the above method, the mobile radiation source includes a radar, an aircraft, or a drone. When the mobile radiation source is a radar, distributed target detection and multi-agent collaborative work are carried out through the wireless sensor network; when the mobile radiation source is an aircraft, the position of the aircraft is monitored through the wireless sensor network and navigation is provided for the aircraft; or when the mobile radiation source is a drone, the position, status, and environmental information of the drone are monitored in real time through the wireless sensor network to achieve autonomous navigation and obstacle avoidance.

[0012] Based on further improvements to the above method, cross-location is performed using the least squares method based on the known position information of two observation stations and the angle information of the mobile radiation source obtained by direction finding to the two observation stations, and the initial position of the mobile radiation source is obtained: The position (x, y, z) of the mobile radiation source is determined by the following formula:

[0013]

[0014]

[0015]

[0016]

[0017] It is deduced from the above formula that:

[0018]

[0019] where, (x 1 , y 1 , z 1 ) and (x 2 , y 2 , z 2 ) are the known positions of the two observation stations respectively, (α 1 , β 1 ), (α 2 , β 2 ) are the measured angles of the mobile radiation source to the two observation stations respectively, R 1 and R 2 are the straight-line distances from the mobile radiation source to the two observation stations respectively; The measured value Y of the mobile radiation source target is represented by the following formula:

[0020] Y = HX;

[0021] where, H is the measurement matrix, where

[0022]

[0023] X is the position vector to be estimated:

[0024]

[0025] The estimated value X of the target position at the initial moment is obtained by using the matrix least - squares formula 0 :

[0026] X 0 =(H T H) -1 H T Y.

[0027] Based on the further improvement of the above - mentioned method, static modeling of the target position and its measurement value of the mobile radiation source is carried out according to the initial position of the mobile radiation source to obtain the state equation and measurement equation of the mobile radiation source target, including: under the condition that the target position of the mobile radiation source remains static, static target modeling is carried out on the target position X k in the k - th iteration:

[0028] X k =X k-1 ;

[0029] The measurement value Y of the mobile radiation source target in the k - th iteration is calculated according to Y = HX k :

[0030] Y k =H k X k .

[0031] Based on the further improvement of the above - mentioned method, each iteration estimate uses the steady - state Kalman filter to fuse dynamic information and measurement data to handle the changes in the motion mode of the mobile radiation source target and the uncertainties in the dynamic environment, including: the steady - state Kalman filter is represented by the following formula

[0032]

[0033]

[0034]

[0035]

[0036] where is the state prediction value in the k - th iteration, is the state estimate value in the (k - 1) - th iteration, X 0 is the initial state at the first iteration; Y k is the measurement value in the k - th iteration, equal to the original measurement value Y; is the observation prediction value for the k - th iteration inversely derived based on the estimated in the (k - 1) - th iteration, is the steady-state Kalman filter gain, and W is the measurement covariance matrix, defined as W = diag(w 1 ,, .., w n ), Δi 2 is the i-th measurement variance.

[0037] Based on the further improvement of the above method, when the following formula is satisfied, the iteration ends, and the accurate estimated position of the moving radiation source target is obtained.

[0038]

[0039] where γ is a given threshold.

[0040] On the other hand, the embodiment of the present invention provides a cross-location device for a moving radiation source, including: a cross-location module, configured to perform cross-location using the least squares method based on the known position information of two observation stations and the angle information of the moving radiation source obtained by direction finding to the two observation stations, so as to obtain the initial position of the moving radiation source; a static model construction module, configured to perform static modeling on the target position of the moving radiation source and its measurement value according to the initial position of the moving radiation source to obtain the state equation and measurement equation of the moving radiation source target; a prediction module, configured to perform multiple iterative estimations on the state of the moving radiation source target to generate an observation prediction value, where each iterative estimation uses steady-state Kalman filtering to fuse dynamic information and measurement data to process the change of the motion mode of the moving radiation source target and the uncertainty in the dynamic environment; and a judgment module, configured to end the iteration and obtain the accurate estimated position of the moving radiation source target when the error between the observation prediction value and the true measurement value is less than a given threshold.

[0041] Based on the further improvement of the above device, the moving radiation source includes a radar, an aircraft or a drone, where the wireless sensor network is used for distributed target detection and multi-agent collaborative work in a radar system; for aircraft position monitoring and navigation; or for real-time monitoring of the position, state and environmental information of a drone to achieve autonomous navigation and obstacle avoidance.

[0042] Based on the further improvement of the above device, the cross-location module is configured to: determine the position (x, y, z) of the moving radiation source through the following formula:

[0043]

[0044]

[0045]

[0046]

[0047] It is derived from the above formula that:

[0048]

[0049] Wherein, (x 1 , y 1 , z 1 ) and (x 2 , y 2 , z 2 ) are the known positions of two observation stations respectively, (α 1 , β 1 ), (α 2 , β 2 ) are the measured angles from the mobile radiation source to the two observation stations respectively, R 1 and R 2 are the straight-line distances from the mobile radiation source to the two observation stations respectively;

[0050] The measured value Y of the mobile radiation source target is represented by the following formula:

[0051] Y = HX;

[0052] Wherein, H is the measurement matrix, wherein

[0053]

[0054] X is the position vector to be estimated:

[0055]

[0056] Using the matrix least squares formula to obtain the estimated value X 0 of the target position at the initial moment:

[0057] X 0 = (H r H) -1 H T Y.

[0058] Compared with the prior art, the present invention can at least achieve one of the following beneficial effects:

[0059] 1. Using the least squares method for cross-positioning to obtain the initial spatial position estimation of the UAV, which helps to reduce the initial error of the target tracking system and thus improve the overall accuracy;

[0060] 2. By using the least squares initial value solution, a relatively good initial estimation can be provided, which helps to reduce the dependence on the filter. This is particularly important for the situation when the target is just being tracked; and

[0061] 3. Steady-state Kalman filtering can process changes in target motion patterns and uncertainties in dynamic environments by fusing dynamic information and measurement data. It has good adaptability to handling dynamic environments and sensor noise, which helps improve the stability, robustness, and tracking accuracy of the system. At the same time, steady-state Kalman filtering has low computational complexity and is suitable for real-time processing. This is very important for application scenarios that require quick response (such as the navigation of aircraft or drones).

[0062] In the present invention, the above technical solutions can also be combined with each other to achieve more preferred combined solutions. Other features and advantages of the present invention will be described in the subsequent specification. Moreover, some advantages can be made obvious from the specification or understood by implementing the present invention. The objectives and other advantages of the present invention can be realized and obtained from the content specifically pointed out in the specification and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] The drawings are only for the purpose of showing specific embodiments and are not considered as a limitation to the present invention. Throughout the drawings, the same reference signs represent the same components.

[0064] Figure 1 is a flowchart of a cross-location method for a mobile radiation source according to an embodiment of the present invention;

[0065] Figure 2 is a schematic diagram of direction-finding cross-location of a cross-location method for a mobile radiation source according to an embodiment of the present invention;

[0066] Figure 3 is a comparison diagram of the estimated results of the UAV position by using the cross-location method for a mobile radiation source according to an embodiment of the present invention and the least squares method without filtering;

[0067] Figure 4 is a comparison diagram of the distance errors of the UAV position estimation by using the cross-location method for a mobile radiation source according to an embodiment of the present invention and the least squares method without filtering in 100 independent repeated experiments; and

[0068] Figure 5 is a block diagram of a cross-location device for a mobile radiation source according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0069] The following will specifically describe the preferred embodiments of the present invention with reference to the drawings. The drawings form a part of this application and are used together with the embodiments of the present invention to explain the principles of the present invention, rather than to limit the scope of the present invention.

[0070] Reference Figure 1, a specific embodiment of the present invention discloses a cross - location method for a mobile radiation source, including: in step S101, cross - location is performed using the least - squares method based on the known position information of two observation stations and the angular information of the mobile radiation source obtained by direction finding to obtain the initial position of the mobile radiation source; in step S102, static modeling is performed on the target position and its measurement values of the mobile radiation source according to the initial position of the mobile radiation source to obtain the state equation and measurement equation of the mobile radiation source target; in step S103, multiple iterative estimations are performed on the state of the mobile radiation source target to generate observation prediction values, where each iterative estimation uses steady - state Kalman filtering to fuse dynamic information and measurement data to handle changes in the motion pattern of the mobile radiation source target and uncertainties in a dynamic environment; and in step S104, when the error between the observation prediction value and the true measurement value is less than a given threshold, the iteration is ended and the accurate estimated position of the mobile radiation source target is obtained.

[0071] Compared with the prior art, the cross - location method for a mobile radiation source provided in this embodiment uses the least - squares method for cross - location to obtain an initial spatial position estimate of the unmanned aerial vehicle, which helps to reduce the initial error of the target tracking system and thus improve the overall accuracy; by using the least - squares initial value solution, a relatively good initial estimate can be provided, which helps to reduce the dependence on the filter. This is particularly important when the target is just being tracked. The steady - state Kalman filter can handle changes in the target motion pattern and uncertainties in a dynamic environment by fusing dynamic information and measurement data, has good adaptability to handle dynamic environments and sensor noise, and helps to improve the stability, robustness, and tracking accuracy of the system.

[0072] In the following, with reference to Figure 1 and Figure 2 , each step of the cross - location method for a mobile radiation source according to the embodiment of the present invention will be described in detail.

[0073] The mobile radiation source signal is monitored and collected through a wireless sensor network, the angle of arrival and time of arrival of the mobile radiation source signal are observed, and the target position of the mobile radiation source is located and tracked, where the wireless sensor network includes sensors on ground stations, satellites, and aircraft.

[0074] The mobile radiation source includes a radar, an aircraft, or an unmanned aerial vehicle. When the mobile radiation source is a radar, distributed target detection and multi - agent collaborative work are performed through a wireless sensor network; when the mobile radiation source is an aircraft, the position of the aircraft is monitored and navigation is provided for the aircraft through a wireless sensor network; or when the mobile radiation source is an unmanned aerial vehicle, the position, state, and environmental information of the unmanned aerial vehicle are monitored in real time through a wireless sensor network to achieve autonomous navigation and obstacle avoidance.

[0075] In step S101, based on the known position information of the two observation stations and the angle information of the mobile radiation source to the two observation stations obtained by direction finding, cross-location is performed using the least squares method to obtain the initial position of the mobile radiation source.

[0076] Based on the known position information of the two observation stations and the angle information of the mobile radiation source to the two observation stations obtained by direction finding, cross-location is performed using the least squares method to obtain the initial position of the mobile radiation source, including: determining the position (x, y, z) of the mobile radiation source through the following formula:

[0077]

[0078]

[0079]

[0080]

[0081] It is deduced from the above formula that:

[0082]

[0083] Among them, (x 1 , y 1 , z 1 ) and (x 2 , y 2 , z 2 ) are the known positions of the two observation stations respectively, (α 1 , β 1 ), (α 2 , β 2 ) are the measured angles of the mobile radiation source to the two observation stations respectively, R 1 and R 2 are the straight-line distances from the mobile radiation source to the two observation stations respectively;

[0084] The measured value Y of the mobile radiation source target is represented by the following formula:

[0085] Y = HX; Formula 6

[0086] Among them, H is the measurement matrix,

[0087]

[0088] X is the position vector to be estimated:

[0089]

[0090] Using the matrix least squares method formula, the estimated value X 0 of the target position at the initial moment is obtained as follows:

[0091] X 0 =(H T H) -1 H T Y Formula 8.

[0092] In step S102, static modeling is performed on the target position of the mobile radiation source and its measurement value according to the initial position of the mobile radiation source to obtain the state equation and measurement equation of the mobile radiation source target. Static modeling of the target position of the mobile radiation source and its measurement value according to the initial position of the mobile radiation source to obtain the state equation and measurement equation of the mobile radiation source target includes: under the condition that the target position of the mobile radiation source remains static, static target modeling is performed on the target position X k for the k-th iteration:

[0093] X k =X k-1 ; Formula 9

[0094] Calculate the measurement value Y of the mobile radiation source target for the k-th iteration according to Y = HX k :

[0095] Y k =H k X k Formula 10.

[0096] In step S103, multiple iterative estimations are performed on the state of the mobile radiation source target to generate observation prediction values. Among them, each iterative estimation uses steady-state Kalman filtering to fuse dynamic information and measurement data to handle the changes in the motion mode of the mobile radiation source target and the uncertainties in the dynamic environment. Each iterative estimation uses steady-state Kalman filtering to fuse dynamic information and measurement data to handle the changes in the motion mode of the mobile radiation source target and the uncertainties in the dynamic environment includes: representing steady-state Kalman filtering by the following formula:

[0097]

[0098]

[0099]

[0100]

[0101] where is the state prediction value for the k-th iteration, is the state estimation value for the (k - 1)-th iteration, X 0 is the initial state at the first iteration; Y k is the measurement value for the k-th iteration, equal to the original measurement value Y; is based on the estimation of the (k - 1)-th iteration The observed predicted value for the k-th iteration obtained by inversion, is the steady-state Kalman filter gain, W is the measurement covariance matrix, defined as W = diag(w 1 ,,,...., w n ), Δi 2 is the variance of the i-th measurement.

[0102] In step S104, when the error between the observed predicted value and the true measurement value is less than a given threshold, the iteration ends and the accurate estimated position of the moving radiation source target is obtained. When the following formula is satisfied, the iteration ends and the accurate estimated position of the moving radiation source target is obtained,

[0103]

[0104] where γ is the given threshold.

[0105] Reference Figure 5 , according to the cross-location device of the moving radiation source according to an embodiment of the present invention, includes: a cross-location module 501, a static model construction module 502, a prediction module 503, and a judgment module 504.

[0106] The cross-location module 501 is configured to perform cross-location using the least squares method based on the known position information of two observation stations and the angle information of the moving radiation source obtained by direction finding to the two observation stations, and obtain the initial position of the moving radiation source. The moving radiation source includes a radar, an aircraft, or a drone. Among them, the wireless sensor network is used for distributed target detection and multi-agent collaborative work in the radar system; for aircraft position monitoring and navigation; or for real-time monitoring of the position, status, and environmental information of the drone to achieve autonomous navigation and obstacle avoidance.

[0107] The cross-location module 501 is configured to determine the position (x, y, z) of the moving radiation source through the formulas 1 - 8 above and obtain the estimated value X of the target position at the initial moment as follows 0 .

[0108] The static model construction module 502 is configured to perform static modeling on the target position and its measurement value of the moving radiation source according to the initial position of the moving radiation source to obtain the state equation and measurement equation of the moving radiation source target; the prediction module 503 is configured to perform multiple iterative estimations on the state of the moving radiation source target to generate an observed predicted value. Among them, each iterative estimation uses the steady-state Kalman filter to fuse dynamic information and measurement data to handle the changes in the motion mode of the moving radiation source target and the uncertainties in the dynamic environment; and the judgment module 504 is configured to end the iteration and obtain the accurate estimated position of the moving radiation source target when the error between the observed predicted value and the true measurement value is less than a given threshold.

[0109] In the following, reference is made to Figures 2 to 4 a method for cross - locating a mobile radiation source according to an embodiment of the present invention is described in detail by way of specific examples.

[0110] A wireless sensor network is a brand - new platform for obtaining target situation information. It can locate and track the position of a radiation source target by monitoring and collecting radiation source signals and observing characteristic parameters such as the angle of arrival and time of arrival of the radiation source signal, and has broad application prospects. In a radar system, a wireless sensor network can be used for distributed target detection, multi - agent collaborative work, etc. By the collaborative work of multiple sensors, the flexibility and coverage of the radar system can be improved. A wireless sensor network can be used for the position monitoring and navigation of an aircraft. The sensor network can include ground stations, satellites, sensors on the aircraft, etc., which work together to provide accurate position information. In an unmanned aerial vehicle (UAV) system, a wireless sensor network can be used to monitor the position, state, and environmental information of the UAV in real time, so as to achieve autonomous navigation and obstacle avoidance.

[0111] The spatial position information of the radiation source is obtained by pairwise cross - location of multiple stations, effectively fusing information from different sensors. This multi - sensor fusion method helps to overcome problems that a single sensor may face, such as signal occlusion, noise interference, etc., to improve the accuracy and robustness of positioning and tracking. Steady - state Kalman filter. For this reason, this algorithm first uses the least - squares method for cross - location to obtain an initial spatial position estimate of the UAV, which helps to reduce the initial error of the target tracking system, thereby improving the overall accuracy. By using the least - squares initial value solution, a relatively good initial estimate can be provided, which helps to reduce the dependence on the filter. This is particularly important when the target is just starting to be tracked. In order to further optimize and obtain a more accurate positioning result, this algorithm models the target and its measurements as a static target, and on this basis, the target state is estimated iteratively multiple times using a steady - state Kalman filter until the error between the inverse measurement of the estimated target state and the true measurement is less than a given threshold, at which point the iteration ends and an accurate position estimate of the UAV is obtained. The steady - state Kalman filter can process changes in the target motion pattern and uncertainties in a dynamic environment by fusing dynamic information and measurement data, has good adaptability to dealing with a dynamic environment and sensor noise, helps to improve the stability, robustness, and tracking accuracy of the system. At the same time, the steady - state Kalman filter has low computational complexity and is suitable for real - time processing. This is very important for application scenarios that require quick response (such as the navigation of aircraft or UAVs).

[0112] To achieve the above object, the technical solution adopted by the present invention is: a UAV cross - location method based on the least - squares initial value solution and steady - state Kalman filter, comprising the following steps:

[0113] S1, through the known position information of the two observation stations and the angle results obtained by direction finding, the least squares method is used for cross positioning to obtain the initial spatial position estimate of the UAV target;

[0114] S2, combining the parameters obtained by cross-positioning of the two stations in step S1, static target modeling is performed for the target and its measurement, and the state equation and measurement equation of the target are written;

[0115] S3, based on the system model obtained in step S2, the target state is estimated multiple times iteratively, each estimation adopts the steady-state Kalman filter formula, wherein the initial value of the state is the estimated value obtained in step S1;

[0116] S4, based on the target state iteratively estimated in step S3, calculate the error between the inverted observation prediction value and the actual measurement. When this error is less than a given threshold, end the iteration and obtain the accurate estimated position of the UAV target.

[0117] As an improvement of the present invention, in step S1, the positions of the two observation stations are known, which are (x 1 ,y 1 , z 1 ) and (x 2 ,y 2 , z 2 ), the angles from the UAV to the two observation stations obtained by direction finding are (α 1 , β 1 )、(α 2 , β 2 ), according to the geometric relationship:

[0118]

[0119]

[0120]

[0121]

[0122] Among them, R 1 and R 2 are the straight-line distances from the drone to the two observation stations, and (x, y, z) is the position of the drone. Combining the above four equations, we can get:

[0123]

[0124] Let H be the measurement matrix, expressed as:

[0125]

[0126] Y is the observation vector, expressed as:

[0127]

[0128] X is the position vector to be estimated, expressed as:

[0129]

[0130] Then the above formula can be simplified to:

[0131] HX = Y,

[0132] Since the above formula is an overdetermined equation and there may not be an analytical solution, this method uses the matrix least squares formula to obtain the following solution:

[0133] X 0 =(H T H) -1 H T Y,

[0134] X 0 is the estimated value of the target position at the initial time;

[0135] As an improvement of the present invention, in step S2, a static target model is established for the target position X k at the k-th time, specifically:

[0136] X k = X k-1 ,

[0137] That is, the target position at the k-th time is the same as the previous time (k - 1), and the target maintains a static position unchanged;

[0138] The measurement Y k generated by the target at the k-th time, and the measurement generation of the target follows the equation HX = Y, that is:

[0139] Y k = H k X k ;

[0140] As an improvement of the present invention, in step S1, in step S3, based on step S2, the state of the target is iteratively estimated, and each estimation uses a steady-state Kalman filter, and the formula is as follows:

[0141]

[0142] where is the predicted value of the state at the k-th time, obtained from the estimated value at the (k - 1)-th time, and the formula is as follows:

[0143]

[0144] The initial state is X in step S1 0 ; Y k is the k-th observation, whose value does not change with the number of iterations and is equal to the original observed value Y; is estimated based on the (k - 1)-th iteration The observed predicted value for the k-th iteration obtained by inversion has:

[0145]

[0146] is the steady-state Kalman filter gain, and its calculation formula is:

[0147]

[0148] where W is the measurement covariance matrix, defined as W = diag(w 1 ,,,...., w n ), Δi 2 is the variance of the i-th measurement;

[0149] As an improvement of the present invention, in step S1 and step S4, calculate the error between the observed predicted value obtained by inverting the target state estimated by the iteration in step S3 and the true measurement. When this error is less than a given threshold, end the iteration, that is, when satisfying:

[0150]

[0151] end the iteration to obtain the accurate estimated position of the UAV target, where γ is the given threshold, and its value ranges from 0.4 to 0.8.

[0152] Compared with the prior art, the present invention has the following beneficial effects:

[0153] Compared with the least squares positioning method, the steady-state Kalman filter is innovatively used, and more accurate and reliable positioning results can be obtained for targets in three-dimensional space.

[0154] Embodiment 1

[0155] Taking the cross-positioning method based on the least squares initial value solution and the steady-state Kalman filter as an example, this method includes the following steps:

[0156] Step S1, first, the positions of two observation stations are known as (x 1 , y 1 , z 1 ) and (x 2 , y 2 , z 2 ), and the angles of the UAV to the two observation stations obtained by direction finding are (α1 , β 1 )、(α 2 , β 2 ), according to the geometric relationship, we can get:

[0157]

[0158]

[0159]

[0160]

[0161] Among them, R 1 and R 2 are the straight-line distances from the drone to the two observation stations, and (x, y, z) is the position of the drone. By combining the above four equations and sorting them out, we can get:

[0162]

[0163] Let H be the measurement matrix, expressed as:

[0164]

[0165] Y is the observation vector, expressed as:

[0166]

[0167] X is the position vector to be estimated, expressed as

[0168]

[0169] The above formula can be simplified to:

[0170] HX=Y,

[0171] Since the above equation is an overdetermined equation and does not necessarily have an analytical solution, this method uses the matrix least squares formula to obtain the following solution:

[0172] X 0 =(H T H) -1 H T Y,

[0173] X 0 That is the estimated value of the target position at the initial time;

[0174] Step S2: Next, the kth target position X k Do static target modeling, specifically:

[0175] X k =X k-1 ,

[0176] That is, the target position at the k-th time is the same as the previous time (k - 1), and the target remains static and unchanged all the time;

[0177] The measurement Y generated by the target at the k-th time k , follows the equation HX = Y obtained in step S1, that is:

[0178] Y k = H k X k ;

[0179] Step S3, to further optimize and obtain a more accurate positioning result, based on step S2, the state of the target is iteratively estimated, and each estimation uses a steady-state Kalman filter. The formula is as follows:

[0180]

[0181] Among them, is the predicted value of the state at the k-th time, obtained from the estimated value at the (k - 1)-th time. The formula is as follows:

[0182]

[0183] The initial state at the first iteration is X obtained in step S1 0 ; Y k is the k-th observation, and its value does not change with the number of iterations and is equal to the original observation value Y; is the observation prediction value of the k-th iteration inversely derived based on the (k - 1)-th iteration estimation. There is:

[0184]

[0185] is the steady-state Kalman filter gain, and the calculation formula is:

[0186]

[0187] Among them, W is the measurement covariance matrix, defined as W = diag(w 1 ,...., w n ), Δi 2 is the variance of the i-th measurement;

[0188] Step S4, according to the target state obtained by the iterative estimation in step S3, calculate the error between the inversely derived observation prediction value and the real measurement. When this error is less than a given threshold, end the iteration, that is, when it is satisfied, end the iteration, and this target estimated state is the accurate position of the UAV:

[0189]

[0190] Among them, γ is a given threshold, and its value ranges from 0.4 to 0.8.

[0191] Test case

[0192] Use the method proposed in this invention patent to accurately locate a single unmanned aerial vehicle (UAV).

[0193] Assume that the positions of two observation stations are (0, 0, 0) and (100, 0, 0) respectively, and the true angles of the UAV to the two observation stations are (30°, 60°) and (135°, 45°) respectively.

[0194] The angular measurement variances of the two observation stations are both 1°, and the given threshold of the error is set to 0.8.

[0195] Figure 2 It is a comparison graph of the estimated results of the UAV position by using the method of this invention patent and the least squares method without filtering. It can be seen that the target position estimated by the method of this invention patent is closer to the real UAV than the estimated result of the simple least squares method, and its positioning and tracking performance is better.

[0196] Figure 3 It is a comparison graph of the distance errors of the UAV position estimated by using the method of this invention patent and the least squares method without filtering under 100 independent repeated experiments. The calculation formula of this distance error is: It can be seen that the error between the target position estimated by the method of this invention patent and the real UAV position is very small; and its error is significantly smaller than the estimated error of the least squares method, indicating that the method of this invention patent can obtain a more accurate positioning result.

[0197] Those skilled in the art can understand that all or part of the processes of implementing the methods in the above embodiments can be completed by instructing relevant hardware through a computer program, and the program can be stored in a computer-readable storage medium. Among them, the computer-readable storage medium is a magnetic disk, an optical disk, a read-only memory or a random access memory, etc.

[0198] The above is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention should be covered by the protection scope of the present invention.

Claims

1. A cross - location method for a mobile radiation source, characterized in that, it includes: Based on the known position information of two observation stations and the angle information of the mobile radiation source obtained by direction finding, use the least - squares method for cross - location to obtain the initial position of the mobile radiation source; According to the initial position of the mobile radiation source, static modeling is performed on the target position and its measurement value of the mobile radiation source to obtain the state equation and measurement equation of the mobile radiation source target; Perform multiple iterative estimations on the state of the mobile radiation source target to generate observation prediction values. Among them, each iterative estimation uses a steady - state Kalman filter to fuse dynamic information and measurement data to handle the changes in the motion mode of the mobile radiation source target and the uncertainties in the dynamic environment; and When the error between the observation prediction value and the true measurement value is less than a given threshold, end the iteration and obtain the accurate estimated position of the mobile radiation source target.

2. The cross - location method for a mobile radiation source according to claim 1, characterized in that, Monitor and collect the mobile radiation source signal through a wireless sensor network, observe the angle of arrival and time of arrival of the mobile radiation source signal, and locate and track the target position of the mobile radiation source. Among them, the wireless sensor network includes sensors on ground stations, satellites and airplanes.

3. The cross - location method for a mobile radiation source according to claim 2, characterized in that, The mobile radiation source includes a radar, an airplane or a drone. Among them, When the mobile radiation source is a radar, perform distributed target detection and multi - agent collaborative work through the wireless sensor network; When the mobile radiation source is an airplane, monitor the position of the airplane and navigate the airplane through the wireless sensor network; or When the mobile radiation source is a drone, real - time monitor the position, state and environmental information of the drone through the wireless sensor network to achieve autonomous navigation and obstacle avoidance.

4. The cross - location method for a mobile radiation source according to claim 1, characterized in that, Based on the known position information of two observation stations and the angle information of the mobile radiation source obtained by direction finding, use the least - squares method for cross - location to obtain the initial position of the mobile radiation source: Determine the position (x, y, z) of the mobile radiation source through the following formula: Derived from the above formula: Among them, (x 1 , y 1 , z 1 ) and (x 2 , y 2 , z 2 ) are the known positions of two observation stations respectively, (α 1 , β 1 ), (α 2 , β 2 ) are the measured angles from the mobile radiation source to the two observation stations respectively, R 1 and R 2 are the straight-line distances from the mobile radiation source to the two observation stations respectively; Represent the measurement value Y of the mobile radiation source target through the following formula: Y = HX; where, H is the measurement matrix, where X is the position vector to be estimated: The estimated value X of the target position at the initial moment is obtained by using the matrix least squares formula 0 : X 0 = (H T H) -1 H T Y.

5. The cross - location method for a mobile radiation source according to claim 4, characterized in that, According to the initial position of the mobile radiation source, static modeling is performed on the target position and its measurement value of the mobile radiation source to obtain the state equation and measurement equation of the mobile radiation source target, including: Under the condition that the moving radiation source target remains static, model the target position X of the k-th iteration as a static target: k ​ X k = X k-1 ; Calculate the measured value Y of the mobile radiation source target at the k-th iteration according to Y = HX k : Y k = H k X k .

6. The cross - location method for a mobile radiation source according to claim 5, characterized in that, Each iterative estimation uses a steady - state Kalman filter to fuse dynamic information and measurement data to handle the changes in the motion mode of the mobile radiation source target and the uncertainties in the dynamic environment, including: Represent the steady - state Kalman filter through the following formula: Among them, is the state prediction value of the k-th iteration, is the state estimation value of the (k - 1)-th iteration, X 0 is the initial state at the first iteration; Y k is the measurement value of the k-th iteration, equal to the original measurement value Y; is based on the estimation of the (k - 1)-th iteration and the observed prediction value of the k-th iteration is inversely calculated, is the steady-state Kalman filter gain, W is the measurement covariance matrix, defined as Δi 2 is the i-th measurement variance.

7. The cross - location method for a mobile radiation source according to claim 6, It is characterized in that when the following formula is satisfied, the iteration is terminated and the accurate estimated position of the moving radiation source target is obtained, where γ is a given threshold.

8. An intersection positioning device for a moving radiation source, It is characterized in that comprising: An intersection positioning module, configured to perform intersection positioning using the least squares method based on the known position information of two observation stations and the angle information of the moving radiation source obtained by direction finding to the two observation stations, so as to obtain the initial position of the moving radiation source; A static model construction module, configured to perform static modeling on the moving radiation source target position and its measurement value according to the initial position of the moving radiation source to obtain the state equation and measurement equation of the moving radiation source target; A prediction module, configured to perform multiple iterative estimations on the state of the moving radiation source target to generate observation prediction values, wherein each iterative estimation uses steady-state Kalman filtering to fuse dynamic information and measurement data to handle the changes in the motion mode of the moving radiation source target and the uncertainties in the dynamic environment; and A judgment module, configured to terminate the iteration and obtain the accurate estimated position of the moving radiation source target when the error between the observation prediction value and the true measurement value is less than a given threshold.

9. The intersection positioning method for a moving radiation source according to claim 8, It is characterized in that the moving radiation source includes a radar, an aircraft or a drone, wherein the wireless sensor network is used for distributed target detection and multi-agent collaborative work in a radar system; for aircraft position monitoring and navigation; or for real-time monitoring of the position, state and environmental information of a drone to achieve autonomous navigation and obstacle avoidance.

10. The intersection positioning device for a moving radiation source according to claim 8, wherein the intersection positioning module is configured to: determine the position (x, y, z) of the moving radiation source through the following formula: Derived from the above formula: where (x 1 , y 1 , z 1 ) and (x 2 , y 2 , z 2 ) are the known positions of two observation stations respectively, (α 1 , β 1 ), (α 2 , β 2 ) are the measured angles from the mobile radiation source to the two observation stations respectively, R 1 and R 2 are the straight-line distances from the mobile radiation source to the two observation stations respectively; the measurement value Y of the moving radiation source target is represented by the following formula: Y = HX; where H is a measurement matrix, where X is the position vector to be estimated: The estimated value X of the target position at the initial moment is obtained by using the matrix least squares formula 0 : X 0 = (H T H) -1 H T Y.

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