Fixed station and maneuvering station cooperative passive positioning method based on pure angle measurement

Abstract

The invention discloses a fixed station and maneuvering station cooperative passive positioning method based on pure angle measurement, and belongs to the technical field of passive positioning. The method comprises the following steps: S1, judging whether a target appears or not, and when the target appears, positioning the target by a foundation observation station and an air-based observation station by using a double-station cooperative passive positioning algorithm to obtain the optimal estimation of the state of the target; s2, judging whether a target can be observed by the foundation observation station or not, if the target can be observed, positioning the target by the foundation observation station and the air-based observation station by using a double-station cooperative passive positioning algorithm, and obtaining the optimal estimation of the state of the target; if the target cannot be observed, the air-based observation station uses a single-station passive positioning algorithm to position the target, and the optimal estimation of the target state is obtained; s3, after the optimal estimation of the target state is obtained, the air-based observation station adjusts the flight state according to the target state, and it is ensured that the target can be observed all the time. According to the invention, based on pure angle measurement, high-precision positioning of the target is realized. The single-station passive positioning algorithm provided by the invention is small in algorithm limitation and convenient for practical application.

Description

Technical Field

[0001] The present invention belongs to the technical field of passive positioning, and particularly relates to a cooperative passive positioning method for a fixed station and a mobile station based on pure angle measurement. Background Art

[0002] As an important detection means, passive positioning technology has broad application prospects in many fields such as military and civilian. Compared with traditional active positioning technology, passive positioning technology does not actively emit signals and has advantages such as strong concealment and strong anti-interference ability. After years of research by scholars from various countries, passive positioning technology has made remarkable progress in algorithms, signal sources, positioning accuracy, equipment development, etc., but still faces many challenges.

[0003] There are various algorithms for passive positioning technology, mainly including methods based on angle of arrival (AOA), time difference of arrival (TDOA), frequency difference of arrival (FDOA), etc. and hybrid algorithms of various algorithm mechanisms. Each of the various algorithms has its own advantages and disadvantages, but the passive positioning algorithm based on angle of arrival is still the earliest studied, most mature and most stable passive positioning algorithm. It should be noted that the above all use multi-station cooperation to achieve positioning. The single-station passive positioning system has higher flexibility due to its simple system structure. However, the fatal disadvantage of the single-station positioning algorithm is the incomplete observability of the observation equation, and it is necessary to provide constraints through methods such as obtaining prior information of the target and maneuver planning to achieve positioning. But these assumptions are often difficult to obtain in practical applications, so the development of single-station passive positioning technology is greatly limited.

[0004] In terms of equipment, the ground-based passive positioning system has high positioning accuracy itself, the signal is less affected by the environment, and it is easier to perform high-precision positioning. However, due to terrain occlusion and fixed deployment, the flexibility and line-of-sight of the system are severely limited. The outstanding feature of the space-based passive positioning system is its flexibility and wide coverage, but due to its own state being easily interfered, the positioning accuracy is low. Summary of the Invention

[0005] In order to solve the above problems, the present invention further provides a cooperative passive positioning method for a fixed station and a mobile station based on pure angle measurement;

[0006] The technical solution adopted by the present invention is as follows:

[0007] A cooperative passive positioning method for a fixed station and a mobile station based on pure angle measurement, comprising the following steps:

[0008] S1. Determine whether the target appears. When the target appears, the ground-based observation station and the space-based observation station use the dual-station cooperative passive positioning algorithm to locate the target and obtain the optimal estimate of the target state;

[0009] S2. Determine whether the ground-based observation station can observe the target. If it can, the ground-based observation station and the space-based observation station use the dual-station cooperative passive positioning algorithm to locate the target and obtain the optimal estimate of the target state. If it cannot, the space-based observation station uses the single-station passive positioning algorithm to locate the target and obtain the optimal estimate of the target state.

[0010] S3. After obtaining the optimal estimate of the target state, the space-based observation station adjusts its flight state according to the target state to ensure that it can always observe the target.

[0011] The present invention has the following beneficial effects compared with the prior art:

[0012] The present invention is based on pure angle measurement to achieve high-precision positioning of the target. The present invention has the following remarkable advantages:

[0013] 1. Achieve positioning based on pure angle measurement. In a complex strong electromagnetic interference environment, the line-of-sight angle parameter is still the easiest signal to obtain and the most stable, and strict time synchronization and frame rate uniformity are not required.

[0014] 2. Through the cooperation of the ground-based observation station and the space-based observation station, comprehensively improve the positioning accuracy, maneuverability and regional coverage ability of the system.

[0015] 3. When both the ground-based observation station and the space-based observation station can observe the target, high-precision positioning of the target is achieved based on the dual-station cooperative positioning algorithm. When the fixed station (ground-based observation station) cannot observe the target, the mobile station (space-based observation station) can adjust its own state and, based on the determined target information, still continuously achieve high-precision positioning of the target based on the single-station passive positioning algorithm proposed by the present invention.

[0016] 4. Currently, the research on the single-station passive positioning algorithm mostly focuses on the theoretical level, with many algorithm limitations and inconvenience in implementation. The single-station passive positioning algorithm proposed by the present invention has few algorithm limitations and is convenient for practical application. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 is the northeast celestial right-angle coordinate system;

[0018] Figure 2 is the schematic diagram of the line-of-sight angle of the present invention;

[0019] Figure 3 is the flow chart of the cooperative passive positioning algorithm of the fixed station and the mobile station of the present invention;

[0020] Figure 4 is the three-dimensional view of the dual-station cooperative positioning scenario simulation;

[0021] Figure 5 is the top view of the dual-station cooperative positioning scenario simulation;

[0022] Figure 6 It is a three - dimensional view of the single - station passive positioning scenario simulation;

[0023] Figure 7 It is a top - view of the single - station passive positioning scenario simulation;

[0024] Figure 8 It is a three - dimensional view of the scenario simulation;

[0025] Figure 9 It is a top - view of the scenario simulation;

[0026] Figure 10 It is a three - dimensional view of the true trajectory and the filtered trajectory;

[0027] Figure 11 It is a top - view of the true trajectory and the filtered trajectory;

[0028] Figure 12 It is the absolute coordinate error of the target;

[0029] Figure 13 It is the absolute velocity error of the target;

[0030] Figure 14 It is the absolute position error of the target;

[0031] Figure 15 It is the percentage of the absolute distance error of the target. Specific implementation manners

[0032] To better understand the purpose, structure and function of the present invention, the following further detailed description of the present invention will be made with reference to the accompanying drawings.

[0033] Implementation scheme

[0034] (1) Define the coordinate system;

[0035] In the present invention, for the convenience of accurately analyzing and describing the observed quantities and the target motion state, the northeast - sky coordinate system is uniformly adopted as the research benchmark. As Figure 1 This coordinate system is a kind of Cartesian rectangular coordinate system. Its three coordinate axes respectively point to the geographical east, north and sky directions, are perpendicular to each other in pairs and intersect at the origin, forming a standard rectangular coordinate system. Specifically, the positive direction of the X - axis points to the east direction in the geographical coordinate system, the positive direction of the Y - axis points to the north direction in the geographical coordinate system, and the positive direction of the Z - axis points to the sky, that is, the sky direction of the geographical coordinate system, perpendicular to the earth's surface and upward.

[0036] (2) Define the line - of - sight angle

[0037] Taking the line - of - sight angle of the ground - based observation station to the UAV as an example, as Figure 2As shown in the figure, let the coordinates of the ground-based observation station be the origin O of the coordinate system, and the coordinates of the UAV in the three-dimensional space be U. The projection of U on the xoy plane is U'. Define the yaw angle θ as the angle between OU' and the x-axis, and define the pitch angle as the angle between OU and the OU' axis.

[0038] (3) Abbreviation and Symbol Explanation

[0039]

[0040]

[0041] (4) Implementation Process

[0042] The cooperative passive positioning system of the fixed station and the mobile station consists of a ground-based observation station D and an airborne observation station U, and the target is T. When the target T can be observed by both the ground-based observation station D and the airborne observation station U at the same time, precise positioning is achieved using the dual-aircraft cooperative positioning algorithm; when due to occlusion or beyond the line of sight, etc., the target T cannot be observed by the ground-based observation station D, then the airborne observation station U uses the single-aircraft passive positioning algorithm to achieve positioning, and the ground-based observation station D continues to search the key area based on the positioning result of the target T by the airborne observation station U; when the target T can be observed by both the ground-based observation station D and the airborne observation station U again, precise positioning is continued using the dual-aircraft cooperative positioning algorithm.

[0043] The flow chart of the cooperative passive positioning algorithm for the fixed station and the mobile station is as Figure 3 shown, and the specific process is described as follows:

[0044] 1. First, judge whether the target T appears. When the target T appears, the ground-based observation station D and the airborne observation station U use the dual-station cooperative passive positioning algorithm to locate the target T and obtain the optimal estimate of the state of the target T, as Figure 4 、 Figure 5 shown.

[0045] 2. During the continuous positioning and tracking of the target T, judge whether the ground-based observation station D can observe the target T. If it can be observed, the ground-based observation station D and the airborne observation station U use the dual-station cooperative passive positioning algorithm to locate the target T and obtain the optimal estimate of the state of the target T; if it cannot be observed, the airborne observation station U uses the single-station passive positioning algorithm to locate the target T and obtain the optimal estimate of the state of the target T, as Figure 6 、 Figure 7 shown.

[0046] 3. After obtaining the optimal estimate of the state of the target T, the airborne observation station U adjusts its flight state according to the state of the target T to ensure that it can always observe the target T.

[0047] (5) Algorithm description. Both the bistatic passive localization algorithm and the monostatic passive localization algorithm are passive localization algorithms based on pure angle measurement. The filtering algorithms relied on by the bistatic passive localization are shown in Table 1, and different filtering algorithms can be replaced according to needs to meet the requirements. Among them, the EKF technology is mature and most widely used. Moreover, in the application scenario of passive localization, the target is not aware that it is being locked and located. Therefore, it can be assumed that the target motion state is basically stable, and within a very short time interval of one sampling period, the target motion mode can be approximated by a single motion model. Therefore, the bistatic passive localization filtering algorithm of the present invention takes the EKF as an example to implement. The monostatic passive localization algorithm of the present invention uses the monostatic passive localization algorithm based on pure angle measurement proposed by the present invention, and the detailed steps of the algorithm will be introduced later.

[0048] Table 1 Technical characteristics and usage scenarios of different filtering algorithms

[0049]

[0050] The labels of the ground-based observation station D and the space-based observation station U are known, and the coordinates of the ground-based observation station D are (x D , y D , z D ). At time k, the coordinates of the space-based observation station U are The line-of-sight angles of the ground-based observation station D and the space-based observation station U to the target T are respectively Calculate the optimal estimated coordinates (x k , y k , z k ) of T at time k through the bistatic cooperative localization algorithm based on EKF.

[0051] Establish a mathematical model

[0052] 1. Principle of bistatic cooperative passive localization based on pure angle measurement

[0053] Define the coordinates of the ground-based observation station as D = [x D , y D , z D T ,

[0054] The coordinates of the space-based observation station are U = [x U , y U , z U T ,

[0055] The line-of-sight angles of the ground-based observation station and the space-based observation station to the target are respectively The coordinates of the target are T = [x, y, z] T .

[0056] ​​According to the definition of the line-of-sight angle in subsection (2), the relationship between the line-of-sight angle and the coordinates is expressed as follows:

[0057]

[0058] In the above system of equations, for the coordinates [x, y, z] of the target T, since the system of equations is an overdetermined system and has a unique solution, the coordinates [x, y, z] of the target T can be determined.

[0059] 2. Single-Station Passive Location Principle Based on Pure Angle Measurement

[0060] When the ground-based observation station D cannot observe the target, only the space-based observation station U can be used to locate the target. At this time, the coordinates of the space-based observation station U are U = [x U , y U , z U T , and the line-of-sight angles to the target T are

[0061] The coordinates of the target are T = [x, y, z] T . According to the definition of the line-of-sight angle in subsection (2), the relationship between the line-of-sight angle and the coordinates is expressed as follows:

[0062]

[0063] In the above system of equations, for the coordinates [x, y, z] of the target T, since the system of equations is an underdetermined system, the coordinates [x, y, z] of T cannot be uniquely determined. The detailed algorithm will be introduced later.

[0064] 3. Motion Model

[0065] Assume that the sampling period of the system is dt, and the state of the moving object (target T) at time k is Within one sampling period, approximate the motion model of the moving object as uniform motion, then the state of the moving object at time k + 1, X k+1 can be expressed as:

[0066]

[0067] 4. Flow of Passive Location Algorithm Based on EKF

[0068] (1) Prediction Step

[0069]

[0070] Among them, F is the state transition matrix, P is the state covariance matrix, and Q is the covariance matrix of the process noise.

[0071] (2) Update Step

[0072] Calculate the observation residual: ​

[0073]

[0074] Calculate the Kalman gain:

[0075]

[0076] Update the state and covariance:

[0077]

[0078] where h(X) is the observation function, which is a non-linear function of X, and H k is the Jacobian matrix of h(X) at time k, and R is the measurement error covariance matrix.

[0079] 5. Bistatic collaborative positioning algorithm

[0080] Ground-based observation station: The position is known, which is D = [x1, y1, z1] t ;

[0081] Space-based observation station: The position is known, and at time k, U = [x 2,k , y 2,k , z 2,k T ;

[0082] Target: The motion state is unknown. Assume that the state of the target at time k is X k = [x k , y k , z k , v x,k , v y,k , v z,k T ,

[0083] The observed values of the target by the ground-based observation station and the space-based fixed station at time k are:

[0084] Locate the target T:

[0085] The state transition matrix of the target T is:

[0086] X k = FX k-1 + w k (10)

[0087] where, according to formula (3), w k is the process noise, and its covariance matrix is Q;

[0088] According to formula (1), the observation equation is:

[0089] ​​

[0090] wherein, v k is the measurement noise, and its covariance matrix is R; in the formula, h(X k ) is a system of nonlinear equations. After linearizing h(X k ), the obtained Jacobian matrix can be expressed as:

[0091]

[0092] wherein,

[0093] Then, according to formulas (4)-(9), the state X k of T at time k is obtained.

[0094] Single-station passive positioning algorithm, space-based observation station: the motion state is known. At time k, U = [x 2,k , y 2,k , z 2,k T ;

[0095] Target: the motion state is unknown. Assume that the state of the target at time k is X k = [x k , y k , z k , v x,k , v y,k , v z,k T , and the measurement of the target by the space-based fixed station at time k is: Positioning target T:

[0096] The state transition matrix of target T is:

[0097] X k = FX k-1 + w k (13)

[0098] wherein, according to formula (3), w k is the process noise, and its covariance matrix is Q;

[0099] According to formula (2), the observation equation is:

[0100]

[0101] wherein, v k is the measurement noise, and its covariance matrix is R; in the formula, h(X k ) is a system of nonlinear equations. After linearizing h(X k ), the obtained Jacobian matrix can be expressed as:​​

[0102]

[0103] Among them,

[0104]

[0105] (1) Prediction step

[0106]

[0107] (2) Update step

[0108] 1. Keep it unchanged, let

[0109]

[0110] Calculate the observation residual:

[0111]

[0112] Calculate the Kalman gain:

[0113]

[0114] Update the state and covariance:

[0115]

[0116] Update

[0117]

[0118] 2. Keep it unchanged, let

[0119]

[0120] Calculate the observation residual:

[0121]

[0122] Calculate the Kalman gain:

[0123]

[0124] Update the state and covariance:

[0125]

[0126] Update

[0127]

[0128] 3. Remain unchanged, let

[0129]

[0130] Calculate the observation residual:

[0131]

[0132] Calculate the Kalman gain:

[0133]

[0134] Update the state and covariance:

[0135]

[0136] Update

[0137]

[0138] 4. Update

[0139]

[0140] where h(X) is the observation function, a non-linear function of X, and H k is the Jacobian matrix of h(X) at time k, and R is the measurement error covariance matrix.

[0141]

[0142]

[0143]

[0144] Simulation results

[0145] Simulation scenario settings: Set the simulation duration to 100 s and the sampling period to dt = 0.1 s;

[0146] Ground-based observation station: D = [100, 100, 0] T ;

[0147] Space-based observation station: Initial coordinates X 1,0 = [2000, 1000, 500] T and initial velocity

[0148] V 1,0 = [50 / s, 0 / s, 0 / s]. The simulation starts timing from detecting the target, simulates detecting the target, and it may be blocked by obstacles. Initial pitch angle Azimuth angle θ k = 0.06°k, at time k

[0149]

[0150] Target: Initial coordinate X T,0 = [0, 6000, 1000] T , Initial velocity V 2,0 = [90 / s, 20 / s, 10 / s], at time k

[0151]

[0152] Note: The aerial vehicle is subject to interference, and its trajectory cannot be a smooth curve. Adding random numbers is to simulate a situation closer to the actual flight of the aerial vehicle in the air.

[0153] The simulation trajectory is as Figures 10 to 15 shown.

[0154] It can be understood that the present invention is described by means of some embodiments. Those skilled in the art know that, without departing from the spirit and scope of the present invention, various changes or equivalent substitutions can be made to these features and embodiments. Additionally, under the teaching of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application belong to the scope protected by the present invention.

Claims

1. A cooperative passive positioning method for a fixed station and a mobile station based on pure angle measurement, characterized in that: It includes the following steps: S1. Determine whether the target appears. When the target appears, the ground-based observation station and the space-based observation station use the dual-station cooperative passive positioning algorithm to locate the target and obtain the optimal estimate of the target state; S2. Determine whether the ground-based observation station can observe the target. If it can observe, the ground-based observation station and the space-based observation station use the dual-station cooperative passive positioning algorithm to locate the target and obtain the optimal estimate of the target state; if not, the space-based observation station uses the single-station passive positioning algorithm to locate the target and obtain the optimal estimate of the target state; S3. After obtaining the optimal estimate of the target state, the space-based observation station adjusts its flight state according to the target state to ensure that it can always observe the target.

2. The collaborative passive positioning method for a fixed station and a mobile station based on pure angle measurement according to claim 1, characterized in that: The system used in the passive positioning method consists of a ground-based observation station D and a space-based observation station U.

3. A method for collaborative passive positioning of a fixed station and a mobile station based on pure angle measurement according to claim 2, characterized in that: The implementation basis of the dual-station cooperative passive positioning algorithm and the single-station passive positioning algorithm is as follows: a. Define the coordinate system with the northeast celestial coordinate system as the reference; b. Define the line-of-sight angle of the ground-based observation station to the unmanned aerial vehicle; c. Establish the mathematical model of the passive positioning method.

4. A cooperative passive positioning method for a fixed station and a mobile station based on pure angle measurement according to claim 3, characterized in that: The line-of-sight angle is: Let the coordinates of the ground-based observation station be the origin O of the coordinate system, and the coordinates of the UAV in the three-dimensional space be U. The projection of U on the xoy plane is U'. Define the yaw angle θ as the angle between OU' and the x-axis, and define the pitch angle as the angle between OU and the OU' axis.

5. A cooperative passive positioning method for a fixed station and a mobile station based on pure angle measurement according to claim 4, characterized in that: The established mathematical model is: a. Dual-station cooperative passive positioning principle based on pure angle measurement Define the coordinates of the ground observation station as D = [x D , y D , z D T ,​ The coordinates of the space-based observation station are U = [x U , y U , z U T ,​ The line-of-sight angles of the ground-based observation station and the space-based observation station to the target are respectively The coordinates of the target are T = [x, y, z] T ; According to the definition of the line-of-sight angle, the relationship between the line-of-sight angle and the coordinates is expressed as follows: In the above equations, the coordinates of the target T are [x, y, z]. The equations are overdetermined equations and have a unique solution, so the coordinates [x, y, z] of the target T can be determined; b. Single-station passive positioning principle based on pure angle measurement When the ground-based observation station cannot observe the target, the coordinates of the space-based observation station U are U = [x U , y U , z U T , and the line-of-sight angle to the target T is The coordinates of the target T are T = [x, y, z] T , and according to the definition of the line-of-sight angle, the relationship between the line-of-sight angle and the coordinates is expressed as follows:​ In the above equations, the coordinates of the target T are [x, y, z]. The equations are underdetermined equations and cannot uniquely determine the coordinates [x, y, z] of the target T; c. Motion model Let the sampling period of the system be dt, and the state of the moving object at time k be Within one sampling period, approximate the motion model of the moving object as uniform motion. Then the state of the moving object at time k+1 is X k+1 It is expressed as: d. Passive positioning algorithm process based on EKF (1) Prediction step where F is the state transition matrix, P is the state covariance matrix, and Q is the covariance matrix of the process noise; (2) Update step Calculate the observation residual: Calculate the Kalman gain: Update the state and covariance: Among them, h(X) is the observation function, which is a non-linear function of X, and H k is the Jacobian matrix of h(X) at time k, and r is the measurement error covariance matrix.

6. The collaborative passive positioning method for a fixed station and a mobile station based on pure angle measurement according to claim 5, wherein: The dual-station cooperative passive positioning algorithm in S1 is: Ground-based observation station: The position is known, which is D = [x1, y1, z1] T ; Space-based observation station: Location is known, at time k, U = [x 2,k , y 2,k , z 2,k T ;​ Objective: The motion state is unknown. Assume that the state of the target at time k is X k =[[x k ,[[y k ,[[z k ,[[v x,k ,[[v y,k ,[[v z,k T ,​ The observed quantities of the target by the ground-based observation station and the space-based fixed station at time k are as follows: Locate the target T: The state transition matrix of the target T is: X k = FX k-1 + w k (10) where, according to formula (3), w k is the process noise, and its covariance matrix is Q; According to formula (1), the observation equation is: where, v k is the measurement noise, and its covariance matrix is R; in the formula, h(X k ) is a system of nonlinear equations. After linearizing h(X k ), the obtained Jacobian matrix is expressed as: Among them, i ∈ (1, 2); Then, according to formulas (4)-(9), obtain the state X of T at time k k .

7. A method for cooperative passive positioning of a fixed station and a mobile station based on pure angle measurement according to claim 6, characterized in that: In S2, the single-station passive positioning algorithm is: Space-based observation station: the motion state is known, and at time k, U = [x 2,k , y 2,k , z 2,k T ;​ Objective: The motion state is unknown. Assume the state of the target at time k is X k = [x k , y k , z k , v x,k , v y,k , v z,k T ,​ The observation of the target by the space-based fixed station at time k is as follows: Locate the target T: The state transition matrix of the target T is: X k = FX k-1 + w k (13) where, according to Equation (3), w k is the process noise, and its covariance matrix is Q; According to formula (2), the observation equation is: where, v k is the measurement noise, and its covariance matrix is R; in the formula, h(X k ) is a system of nonlinear equations. After linearizing h(X k ), the obtained Jacobian matrix is expressed as: Among them, (1) Prediction step (2) Update step 1. Remain unchanged, let Calculate the observation residual: Calculate the Kalman gain: Update the state and covariance: Update 2. Remain unchanged, let Calculate the observation residual: Calculate the Kalman gain: Update the state and covariance: Update 3. Remain unchanged, let Calculate the observation residual: Calculate the Kalman gain: Update the state and covariance: Update 4. Update Among them, h(X) is the observation function, which is a non-linear function of X, and H k is the Jacobian matrix of h(X) at time k, and r is the measurement error covariance matrix.

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