阅读说明：本技术 一种基于广义二阶时延差的水下目标高精度定位方法 (High-precision underwater target positioning method based on generalized second-order time delay difference ) 是由 孙思博 梁国龙 明瑞和 曲龙 张光普 王燕 王逸林 付进 齐滨 邹男 于 2020-12-14 设计创作，主要内容包括：本发明公开一种基于广义二阶时延差的水下目标高精度定位方法。步骤1：等周期间隔选取解算位置,对水下目标的位置进行粗略解算；步骤2：计算目标的水平精度因子HDOP,同时优化定位周期号,最终得到最佳定位周期号；步骤3：根据选取的最佳周期号相应的位置基于广义二阶时延差信息进行定位解算。本发明降低了航行器航路和航行速度对定位精度的影响,进一步提升了定位解算精度,更加适应实际情况下的解算条件。(The invention discloses a high-precision positioning method for an underwater target based on generalized second-order time delay difference. Step 1: selecting resolving positions at intervals of equal period, and roughly resolving the position of the underwater target; step 2: calculating a horizontal precision factor HDOP of a target, and optimizing a positioning period number to finally obtain an optimal positioning period number; and step 3: and performing positioning calculation based on the generalized second-order delay difference information according to the corresponding position of the selected optimal cycle number. The method reduces the influence of the navigation path and the navigation speed of the aircraft on the positioning precision, further improves the positioning calculation precision, and is more suitable for the calculation conditions under the actual condition.)

1. A high-precision positioning method of an underwater target based on generalized second-order time delay difference is characterized by comprising the following steps,

step 1: selecting resolving positions at intervals of equal period, and roughly resolving the position of the underwater target; determining the distance between two positioning points according to the route of the underwater vehicle, and selecting the number of positioning cycles at equal intervals according to the distance; according to the position corresponding to the selected positioning period, establishing a resolving equation by using second-order delay difference information, and roughly resolving the position of the target;

step 2: calculating a horizontal precision factor HDOP of a target, and optimizing a positioning period number to finally obtain an optimal positioning period number; calculating a horizontal precision factor HDOP according to the result of the rough calculation and various existing measurement errors, optimizing a positioning period number by taking the minimized horizontal precision factor HDOP as a target, and obtaining an optimal positioning period number through an iterative algorithm;

and step 3: positioning and resolving are carried out on the basis of generalized second-order delay difference information according to the corresponding position of the selected optimal cycle number; and establishing a positioning calculation equation set according to the generalized second-order time delay difference information, wherein the positioning calculation equation is a nonlinear equation set, and the equation set is solved by adopting a Newton iterative algorithm to obtain the position coordinates of the target.

2. The method for high-precision positioning of the underwater target based on the generalized second-order time delay difference as recited in claim 1, wherein the step 1 specifically comprises: the position of the acoustic beacon is resolved by combining the signal arrival time information of the measuring platform and the beacon with the position coordinate of the maneuvering platform; the signal transmitted by the beacon is a periodic pulse signal, and the first periodic signal is assumed to be transmitted at the time t₀+t_sThen the arrival time of the signal with period number m is expressed as:

in the formula: c is the speed of sound in water,/_mMeasuring the distances from different measuring points of the maneuvering platform to the target;

the generalized second-order delay difference is defined as:

the arrival time information of the signal in the equation (2) is:

the arrival time samples of the four signals for coarse positioning are taken, the cycle numbers of the samples need to be equally spaced, and then the formula (2) is changed into:

c(t_m3-t_m2)-c(t_m2-t_m1)＝(l₃-l₂)-(l₂-l₁) ⑷

wherein the unknowns t have been eliminated in equation (4)₀And t_sAssuming that the horizontal coordinate of the acoustic beacon to be solved is [ x ]_s,y_s]With a depth known as z_s(ii) a The horizontal coordinate of the aircraft at different measurement points is given by the navigation system as [ x ]_m,y_m]Depth is given by the pressure sensor as z_m(ii) a The distance of the measurement point to the acoustic beacon is then expressed as:furthermore, a positioning resolving equation established by using the second-order delay difference information is as follows:

and (5) solving the equation set of the formula (5) to obtain a coarse positioning result of the target.

3. The method for high-precision positioning of the underwater target based on the generalized second-order time delay difference as recited in claim 1, wherein the step 2 specifically comprises: calculating a horizontal precision factor HDOP by using a result of the coarse positioning, and finding out an optimal cycle number corresponding to four optimal solution point positions by taking the minimum horizontal precision factor HDOP as a target; the horizontal precision factor HDOP is defined as:

in the above expression, E () represents expectation, [ x [ ]_s,y_s]Representing the true position of the underwater target,representing the solved estimate of the underwater target position; HDOP is calculated using a covariance matrix and is expressed as:

covariance matrix D_xExpressed as:

wherein D_x，D_t，D_insRespectively covariance matrix of target coordinate error, covariance matrix of arrival time error, covariance matrix of solution point coordinate error, M_x，M_t，M_insRespectively, are partial derivative matrices corresponding to the variables.

4. The method for high-precision positioning of the underwater target based on the generalized second-order time delay difference as claimed in claim 3, wherein the step 2 of calculating the position of the four optimal solution points comprises the following steps:

step 2.1: fixing the optimal solution point position m by taking the coarse positioning result and the period number in the step 1 as initial values₁Optimum calculated point position m₂Optimum calculated point position m₃And change the optimum solution point position m₄(ii) a Calculating the horizontal precision factor HDOP with m₄To find locally optimizedMinimize the average horizontal precision factor HDOP and then update m with the locally optimized value₄；

Step 2.2: fixed m₁、m₂、m₄And change m₃(ii) a Calculating HDOP as m₃To find locally optimizedMinimize average HDOP, update m with locally optimized value₃；

Step 2.3: fixed m₁、m₃、m₄And change m₂(ii) a Calculating HDOP as m₂To find locally optimizedMinimize average HDOP, update m with locally optimized value₂；

Step 2.4: fixed m₂、m₃、m₄And change m₁(ii) a Calculating HDOP as m₁To find locally optimizedMinimize average HDOP, update m with locally optimized value₁；

Step 2.5: repeating the steps 2 to 4; stopping the iteration once HDOP reaches a minimum value; setting of the selected number of cyclesIs m₁、m₂、m₃And m₄。

5. The method according to claim 4, wherein the step 3 is specifically to use the optimal resolving period number m obtained in the step 2 as the m₁、m₂、m₃、m₄Establishing a positioning resolving equation by utilizing generalized second-order delay difference information;

in the formula: c is the speed of sound in water,/₁、l₂、l₃、l₄For different measuring point distances to the target, i.e.t_m1、t_m2、t_m3、t_m4Respectively the signal arrival time of each measuring point;

equation (9) is a nonlinear equation set, and if a newton iteration method is used to solve the nonlinear equation set, X is ═ X for two equations in equation (9)_s,y_s]^T，F＝[f(_GSTDOA,1),f(_GSTDOA,2)]^TThen the system of equations is written as:

F(X)＝0 ⑽

the Newton iteration method of the single equation is directly used for solving the linear equation system, and a Newton iteration formula for solving the nonlinear equation system is obtained by the formula (10):

X_n+1＝X_n-F′(X_n)^-1F(X_n)(n＝0,1,2,…) ⑾

wherein, F' (X)^-1The inverse matrix of the jacobian matrix of the nonlinear equation system is recorded as:

X_n+1-X_n＝ΔX_n ⑿

the Jacobian matrix is:

first, the linear equation set F' (X) is solved_n)ΔX_n＝-F(X_n) Finding the vector DeltaX_nAnd then order:

X_n+1＝ΔX_n+X_n ⒁

if the solved result does not accord with the iteration precision requirement, the cyclic solution is repeatedly carried out until the solved precision requirement is met.

Technical Field

The invention relates to the technical field of underwater target positioning, in particular to a high-precision underwater target positioning method based on generalized second-order time delay difference.

Background

A high-precision underwater target positioning method based on generalized second-order time delay difference refers to a technology for solving the position of a target by calculating the difference value of arrival time delay differences of signals at different moments under the condition that the emission time and the period of the signals are unknown. The scene situation diagram is shown in fig. 1, and the underwater acoustic beacon position is mainly determined by receiving periodic signals emitted by acoustic beacons at different positions by a single maneuvering aircraft. In the figure, the aircraft runs along a preset airway, the acoustic beacon emits acoustic pulse signals at a certain period, and the aircraft respectively runs at t_m1、t_m2、t_m3、t_m4The ping signal is received at a time. The underwater target high-precision positioning method based on the generalized second-order time delay difference has wide application prospect, and can be applied to the aspects of searching and rescuing crash airplanes, ships and underwater submergence vehicles, and searching and positioning airborne and shipborne black boxes, acoustic beacons and the like;

in the field of underwater positioning research, the method is divided into a positioning method based on arrival time delay and a positioning method based on arrival time delay difference according to whether the initial transmitting time of a target transmitting signal is known or not. However, the traditional time delay positioning method is difficult to solve the problem that the signal emission period cannot be accurately known, and in order to solve the problem, a positioning calculation method based on second-order arrival time delay difference can be used. However, the positioning calculation method of the second-order arrival time delay difference is easily affected by the route and the navigation speed of the aircraft to cause the reduction of the positioning accuracy, so that the requirements on the preset route and the navigation speed are higher.

Disclosure of Invention

The invention provides a high-precision underwater target positioning method based on generalized second-order time delay difference, which reduces the influence of an aircraft route and navigation speed, further improves positioning resolving precision, and is more suitable for resolving conditions under actual conditions.

The invention is realized by the following technical scheme:

as shown in fig. 1-2, a method for high-precision positioning of an underwater target based on generalized second-order time delay difference comprises the following steps,

step 1: selecting resolving positions at intervals of equal period, and roughly resolving the position of the underwater target; determining the distance between two positioning points according to the route of the underwater vehicle, and selecting the number of positioning cycles at equal intervals according to the distance; according to the position corresponding to the selected positioning period, establishing a resolving equation by using second-order delay difference information, and roughly resolving the position of the target;

step 2: calculating a horizontal precision factor HDOP of a target, and optimizing a positioning period number to finally obtain an optimal positioning period number; calculating a horizontal precision factor HDOP according to the result of the rough calculation and various existing measurement errors, optimizing a positioning period number by taking the minimized horizontal precision factor HDOP as a target, and obtaining an optimal positioning period number through an iterative algorithm;

and step 3: positioning and resolving are carried out on the basis of generalized second-order delay difference information according to the corresponding position of the selected optimal cycle number; and establishing a positioning calculation equation set according to the generalized second-order time delay difference information, wherein the positioning calculation equation is a nonlinear equation set, and the equation set is solved by adopting a Newton iterative algorithm to obtain the position coordinates of the target.

Further, the step 1 specifically comprises: the position of the acoustic beacon is resolved by combining the signal arrival time information of the measuring platform and the beacon with the position coordinate of the maneuvering platform; the signal transmitted by the beacon is a periodic pulse signal, and the first periodic signal is assumed to be transmitted at the time t₀+t_sThen the arrival time of the signal with period number m is expressed as:

in the formula: c is the speed of sound in water,/_mMeasuring the distances from different measuring points of the maneuvering platform to the target;

the generalized second-order delay difference is defined as:

the arrival time information of the signal in the equation (2) is:

the arrival time samples of the four signals for coarse positioning are taken, the cycle numbers of the samples need to be equally spaced, and then the formula (2) is changed into:

c(t_m3-t_m2)-c(t_m2-t_m1)＝(l₃-l₂)-(l₂-l₁) ⑷

wherein the unknowns t have been eliminated in equation (4)₀And t_sAssuming that the horizontal coordinate of the acoustic beacon to be solved is [ x ]_s,y_s]With a depth known as z_s(ii) a The horizontal coordinate of the aircraft at different measurement points is given by the navigation system as [ x ]_m,y_m]Depth is given by the pressure sensor as z_m(ii) a The distance of the measurement point to the acoustic beacon is then expressed as:furthermore, a positioning resolving equation established by using the second-order delay difference information is as follows:

and (5) solving the equation set of the formula (5) to obtain a coarse positioning result of the target.

Further, the step 2 specifically comprises: calculating a horizontal precision factor HDOP by using a result of the coarse positioning, and finding out an optimal cycle number corresponding to four optimal solution point positions by taking the minimum horizontal precision factor HDOP as a target; the horizontal precision factor HDOP is defined as:

in the above expression, E () represents expectation, [ x [ ]_s,y_s]Representing the true position of the underwater target,representing the solved estimate of the underwater target position; HDOP is calculated using a covariance matrix and is expressed as:

covariance matrix D_xExpressed as:

wherein D_x，D_t，D_insRespectively covariance matrix of target coordinate error, covariance matrix of arrival time error, covariance matrix of solution point coordinate error, M_x，M_t，M_insRespectively, are partial derivative matrices corresponding to the variables.

Further, the calculation of the four optimal solution point positions in step 2 includes the following steps:

step 2.1: fixing the optimal solution point position m by taking the coarse positioning result and the period number in the step 1 as initial values₁Optimum calculated point position m₂Optimum calculated point position m₃And change the optimum solution point position m₄(ii) a Calculating the horizontal precision factor HDOP with m₄To find locally optimizedMinimize the average horizontal precision factor HDOP and then update m with the locally optimized value₄；

Step 2.2: fixed m₁、m₂、m₄And change m₃(ii) a Calculating HDOP as m₃To find locally optimizedMinimize average HDOP, update m with locally optimized value₃；

Step 2.3: fixed m₁、m₃、m₄And change m₂(ii) a Calculating HDOP as m₂To find locally optimizedMinimize average HDOP, update m with locally optimized value₂；

Step 2.4: fixed m₂、m₃、m₄And change m₁(ii) a Calculating HDOP as m₁To find locally optimizedMinimize average HDOP, update m with locally optimized value₁；

Step 2.5: repeating the steps 2 to 4; stopping the iteration once HDOP reaches a minimum value; the selected number of cycles is set to m₁、m₂、m₃And m₄。

Further, the step 3 specifically includes that the optimal resolving period number obtained in the step 2 is used as m₁、m₂、m₃、m₄Establishing a positioning resolving equation by utilizing generalized second-order delay difference information;

in the formula: c is the speed of sound in water,/₁、l₂、l₃、l₄For different measuring point distances to the target, i.e.t_m1、t_m2、t_m3、t_m4Respectively the signal arrival time of each measuring point;

equation (9) is a nonlinear equation set, and if a newton iteration method is used to solve the nonlinear equation set, X is ═ X for two equations in equation (9)_s,y_s]^T，F＝[f(_GSTDOA,1),f(_GSTDOA,2)]^TThen the system of equations is written as:

F(X)＝0 ⑽

the Newton iteration method of the single equation is directly used for solving the linear equation system, and a Newton iteration formula for solving the nonlinear equation system is obtained by the formula (10):

X_n+1＝X_n-F′(X_n)^-1F(X_n)(n＝0,1,2,…) ⑾

wherein, F' (X)^-1The inverse matrix of the jacobian matrix of the nonlinear equation system is recorded as:

X_n+1-X_n＝ΔX_n ⑿

the Jacobian matrix is:

first, the linear equation set F' (X) is solved_n)ΔX_n＝-F(X_n) Finding the vector DeltaX_nAnd then order:

X_n+1＝ΔX_n+X_n ⒁

if the solved result does not accord with the iteration precision requirement, the cyclic solution is repeatedly carried out until the solved precision requirement is met.

The invention has the beneficial effects that:

when the method is used for positioning the unknown periodic acoustic beacon, the positioning navigation track of the aircraft can be better adapted, the optimal resolving position can be found, and the positioning accuracy is better compared with other methods.

Drawings

FIG. 1 is a schematic view of the scene situation of the present invention.

FIG. 2 is a schematic flow chart of the method of the present invention.

FIG. 3 is a diagram illustrating positioning results according to an embodiment of the present invention.

FIG. 4 is a schematic diagram of an embodiment of the present invention.

Detailed Description

The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

Example 1

As shown in fig. 1-2, a method for positioning underwater targets with high precision based on generalized second-order time delay difference includes the following steps,

step 1: selecting resolving positions at intervals of equal period, and roughly resolving the position of the underwater target; determining the distance between two positioning points according to the route of the underwater vehicle, and selecting the number of positioning cycles at equal intervals according to the distance; according to the position corresponding to the selected positioning period, establishing a resolving equation by using second-order delay difference information, and roughly resolving the position of the target;

step 2: calculating a horizontal precision factor HDOP of a target, and optimizing a positioning period number to finally obtain an optimal positioning period number; calculating a horizontal precision factor HDOP according to the result of the rough calculation and various existing measurement errors, optimizing a positioning period number by taking the minimized horizontal precision factor HDOP as a target, and obtaining an optimal positioning period number through an iterative algorithm;

and step 3: positioning and resolving are carried out on the basis of generalized second-order delay difference information according to the corresponding position of the selected optimal cycle number; and establishing a positioning calculation equation set according to the generalized second-order time delay difference information, wherein the positioning calculation equation is a nonlinear equation set, and the equation set is solved by adopting a Newton iterative algorithm to obtain the position coordinates of the target.

Further, the step 1 specifically comprises: the position of the acoustic beacon is resolved by combining the signal arrival time information of the measuring platform and the beacon with the position coordinate of the maneuvering platform; the signal transmitted by the beacon is a periodic pulse signal, and the first periodic signal is assumed to be transmitted at the time t₀+t_sThen the arrival time of the signal with period number m is expressed as:

in the formula: c is the speed of sound in water,/_mMeasuring the distances from different measuring points of the maneuvering platform to the target;

for targets with unknown emission times and periods, t₀And t_sAs an unknown number, the distance l from different measuring points to the acoustic beacon cannot be directly calculated by the formula (1)_m(ii) a It is therefore necessary to calculate a generalized second order delay difference to cancel t₀And t_s；

The generalized second-order delay difference is defined as:

the arrival time information of the signal in the equation (2) is:

the positioning method stated in the invention needs to firstly carry out coarse positioning on the target, the arrival time samples of four signals for the coarse positioning are carried out, and the cycle numbers of the taken samples need to be equally spaced (namely, m is satisfied)₁+m₃-2m₂0); at this time, equation (2) becomes:

c(t_m3-t_m2)-c(t_m2-t_m1)＝(l₃-l₂)-(l₂-l₁) ⑷

wherein the unknowns t have been eliminated in equation (4)₀And t_sAssuming that the horizontal coordinate of the acoustic beacon to be solved is [ x ]_s,y_s]With a depth known as z_s(ii) a The horizontal coordinate of the aircraft at different measurement points is given by the navigation system as [ x ]_m,y_m]Depth is given by the pressure sensor as z_m(ii) a The distance of the measurement point to the acoustic beacon is then expressed as:furthermore, a positioning resolving equation established by using the second-order delay difference information is as follows:

and (5) solving the equation set of the formula (5) to obtain a coarse positioning result of the target.

Further, the step 2 specifically comprises: the positioning result in step 1 is influenced by the actual track and the movement speed of the maneuvering positioning platform, and the positioning accuracy may be greatly influenced, so that the positioning is called coarse positioning. In fact, four cycle numbers are taken for positioning one acoustic beacon, and the optimal cycle number exists so that the positioning precision of the target is the highest; calculating a horizontal precision factor HDOP by using a result of the coarse positioning, and finding out an optimal cycle number corresponding to four optimal solution point positions by taking the minimum horizontal precision factor HDOP as a target; the horizontal precision factor HDOP is defined as:

in the above expression, E () represents expectation, [ x [ ]_s,y_s]Representing the true position of the underwater target,showing the resolved underwater eyeAn estimate of the target position; HDOP is calculated using a covariance matrix and is expressed as:

covariance matrix D_xExpressed as:

wherein D_x，D_t，D_insRespectively covariance matrix of target coordinate error, covariance matrix of arrival time error, covariance matrix of solution point coordinate error, M_x，M_t，M_insRespectively, are partial derivative matrices corresponding to the variables.

Further, the calculation of the four optimal solution point positions in step 2 includes the following steps:

step 2.1: fixing the optimal solution point position m by taking the coarse positioning result and the period number in the step 1 as initial values₁Optimum calculated point position m₂Optimum calculated point position m₃And change the optimum solution point position m₄(ii) a Calculating the horizontal precision factor HDOP with m₄To find locally optimizedMinimize the average horizontal precision factor HDOP and then update m with the locally optimized value₄；

Step 2.2: fixed m₁、m₂、m₄And change m₃(ii) a Calculating HDOP as m₃To find locally optimizedMinimize average HDOP, update m with locally optimized value₃；

Step 2.3: fixed m₁、m₃、m₄And change m₂(ii) a Calculating HDOP as m₂To find locally optimizedMinimize average HDOP, update m with locally optimized value₂；

Step 2.4: fixed m₂、m₃、m₄And change m₁(ii) a Calculating HDOP as m₁To find locally optimizedMinimize average HDOP, update m with locally optimized value₁；

Step 2.5: repeating the steps 2 to 4; stopping the iteration once HDOP reaches a minimum value; the selected number of cycles is set to m₁、m₂、m₃And m₄。

Further, the step 3 specifically includes that the optimal resolving period number obtained in the step 2 is used as m₁、m₂、m₃、m₄Establishing a positioning resolving equation by utilizing generalized second-order delay difference information;

in the formula: c is the speed of sound in water,/₁、l₂、l₃、l₄For different measuring point distances to the target, i.e.t_m1、t_m2、t_m3、t_m4Respectively the signal arrival time of each measuring point;

equation (9) is a nonlinear equation set, and if a newton iteration method is used to solve the nonlinear equation set, X is ═ X for two equations in equation (9)_s,y_s]^T，F＝[f(_GSTDOA,1),f(_GSTDOA,2)]^TThen the system of equations is written as:

F(X)＝0 ⑽

the Newton iteration method of the single equation is directly used for solving the linear equation system, and a Newton iteration formula for solving the nonlinear equation system is obtained by the formula (10):

X_n+1＝X_n-F′(X_n)^-1F(X_n)(n＝0,1,2,…) ⑾

wherein, F' (X)^-1The inverse matrix of the jacobian matrix of the nonlinear equation system is recorded as:

X_n+1-X_n＝ΔX_n ⑿

the Jacobian matrix is:

first, the linear equation set F' (X) is solved_n)ΔX_n＝-F(X_n) Finding the vector DeltaX_nAnd then order:

X_n+1＝ΔX_n+X_n ⒁

if the solved result does not accord with the iteration precision requirement, the cyclic solution is repeatedly carried out until the solved precision requirement is met.

Example 2

The following describes the implementation of the present invention by simulation. The simulation parameters are as follows: the track of the aircraft is positioned to be a circular track, the radius is 707m, the depth is 0m, the aircraft performs uniform acceleration motion, the initial speed is 5.56m/s, and the acceleration is 0.014m/s²(ii) a Unknown periodic acoustic beacon real coordinate is [100150]m, the depth is 100 m; the sound velocity is 1500 m/s; the estimation error of each input parameter is as follows: the sound velocity estimation error is 1.5m/s, the depth estimation error is 1m, the measurement error of the arrival time is 1ms, and the error of the position coordinate of the resolving point is 1.8 m; the acoustic beacon signal is in the form of a CW signal with a period of 1s and a period drift of 20 mus.

The positioning method of the invention is adopted to estimate the position of the acoustic beacon. The real-time calculation result is shown in fig. 3, the corresponding positioning error is shown in fig. 4, and the stabilized positioning error is 2.91 m. As can be seen from the figure, the positioning method can effectively estimate the position of the acoustic beacon, has higher positioning precision, effectively solves the problem of positioning the acoustic beacon with unknown signal period, and has higher precision and stronger adaptability than other methods under the same condition. .