Multi-base sonar TOA-AOA hybrid positioning method and system

Abstract

The invention discloses a multi-base sonar TOA-AOA hybrid positioning method and system, and the method comprises the steps: forming a multi-base active sonar system through M transmitting terminals and N receiving terminals, m. Time synchronization is carried out based on each time of wave transmission of each transmitting end, and a measurement equation is constructed by combining the relative positions of the transmitting ends and the receiving ends. And estimating the comprehensive measurement equation by taking maximum likelihood estimation as a criterion to obtain a target position point with the highest probability under the existing observation value as target output of multi-base positioning fusion. According to the method, nonlinear characteristics in a measurement equation are fully considered, and compared with an existing multi-base fusion positioning algorithm, the method is not simplified or ignored, so that the method has a more accurate positioning effect in a high-noise-level scene similar to an underwater environment.

Description

Technical Field

[0001] The present invention relates to the field of underwater sonar positioning technology, and in particular to a multi-base sonar TOA-AOA hybrid positioning method and system. Background Art

[0002] Traditional passive sonar is susceptible to background noise interference in complex underwater environments, making it difficult to detect targets at long distances. Active multi-base sonar systems can improve positioning accuracy and anti-interference capabilities through multi-sensor collaborative detection. However, existing TOA-AOA hybrid positioning methods have the following problems:

[0003] (1) Insufficient nonlinear processing: The nonlinear characteristics of the measurement equation lead to large deviations in the direct weighted least squares (WLS) solution, especially when the noise level is high;

[0004] (2) Poor convergence stability: Iterative algorithms (such as Newton's method) are greatly affected by the complexity of the system function and are prone to divergence or falling into local optimality under high noise conditions;

[0005] (3) Noise simplification assumption: Existing methods (such as constrained least squares method) ignore high-order noise terms or linear approximation and cannot adapt to the complex environment of underwater multipath effects and time-varying noise.

[0006] To address the above problems, there is an urgent need for a positioning method that can converge stably under high noise and approach the theoretical optimum. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to provide a multi-base sonar TOA-AOA hybrid positioning method and system to improve the positioning accuracy in high noise level scenarios similar to underwater environments, in response to the shortcomings of the existing technology.

[0008] To solve the above technical problems, the technical solution adopted by the present invention is: a multi-base sonar TOA-AOA hybrid positioning method, characterized in that the rectangular coordinate estimation result u of the target position is calculated using the following formula:

[0009] Where, Δu=(G2 T W2G2) -1 G2 T W2h2; C2=E[ξ2 T ξ2], C2 is the covariance matrix of ξ2, G2=[G 20 ,G 21 ,…,G 2(N-1) ] T , X=2e1e1 T , e1=[1,0] T, r i is the rectangular coordinate vector of the i-th transmitting and receiving sonar, is the estimated result, ξ2=h2-G2Δu;

[0010] If the transmitter and all receivers are not located on the same straight line, then otherwise,

[0011] in, C0=E[ξ0 T ξ0], C0 is the covariance matrix of ξ0, C1=E[ξ1 T ξ1], C1 is the covariance matrix of ξ1, ξ0=[ξ 01,1 ,ξ 01,2 ,…,ξ 0N-1,1 ,ξ 0N-1,2 ] T ,ξ1=[ξ 10 ,ξ 11,1 ,ξ 11,2 ,…,ξ 1N-1,1 ,ξ 1N-1,2 ] T , h0=[h 01,1 ,h 01,2 ,…,h 0N-1,1 ,h 0N-1,2 ] T , G0=[G 01 ,…,G 0N-1 ] T ,ξ 0i,1 =2(r 0i -r0)Δr 0i -2r 0i Δr0+Δr 0i 2 -Δr0 2 +Δr 0i Δr0,ξ 0i,2 =2cos 2 (θ i +Δθ i )(r 0i +Δr 0i -r0-Δr0) 2 -2cos 2 (θ+Δθ)(r0+Δr0) 2 +2cos 2 θr0 2 -2cos 2 θ i (r 0i -r0) 2 , r0 and θ are the TOA and AOA measurement information of the co-located sonar, respectively. 0i and θ i is the TOA and AOA measurement information detected by the i-th transmitting and receiving sonar. The relationship between the measured value, the true value and the random error is: The relationship between the measured value, the true value and the random error is and They are the theoretical TOA and AOA measurement information of the combined sonar, and The theoretical TOA and AOA measurement information of the i-th transmitter and receiver, Δr0, Δθ, Δr 0i and Δθ i is the measurement error of the corresponding measurement information; h1=[h 10 ,h 11,1 ,h 11,2 ,…,h 1N-1,1 ,h 1N-1,2 ] T , G1=[G 10 ,G 11 ,…,G 1N-1 ] T ,ξ 10 =sin 2 (θ+Δθ)(r0+Δr0) 2 -r0 2 sin 2 θ, ξ 1i,1 =2(r 0i -r0)Δr 0i -2r 0i Δr0+Δr 1i 2 -Δr0 2 +Δr 0i Δr0,ξ 1i,2 =-2sin 2 (θ i +Δθ i )(r 0i +Δr 0i -r0-Δr0) 2 +(r 0i -r0) 2 (1-cos2θ i ), h 10 =-r0 2 sin 2 θ,h 1i,1 =r i T r i -r 0i 2 +2r0r0i , h 1i,2 =(r 0i -r0) 2 (1-cos2θ i ), e2=[0,1] T , N is the number of receiving ends.

[0012] Update the estimated results using the following process Will Add it to Δu to get a new estimate. T When Δu>∈, the updated estimation result is used to repeatedly estimate Δu, and ∈ is the convergence threshold.

[0013] ∈ takes the value of 0.0001.

[0014] As an inventive concept, the present invention also provides a multi-base sonar TOA-AOA hybrid positioning system, including a memory, a processor and a computer program stored in the memory; the processor executes the computer program to implement the steps of the above method.

[0015] As an inventive concept, the present invention also provides a computer-readable storage medium having a computer program / instruction stored thereon; the computer program / instruction implements the steps of the above method when executed by a processor.

[0016] As an inventive concept, the present invention also provides a computer program product, comprising a computer program / instruction; when the computer program / instruction is executed by a processor, the steps of the above method are implemented.

[0017] Compared with the prior art, the present invention has the following beneficial effects:

[0018] (1) The present invention fully considers the nonlinear characteristics of the measurement equation and does not make any simplification or omission compared to the existing multi-base fusion positioning algorithm. Therefore, it has a more accurate positioning effect in high noise level scenarios similar to underwater environments.

[0019] (2) The present invention organizes the relationship between the measured value and the target position into a linear form and uses the BLUE estimation method for estimation. Compared with the existing iterative nonlinear processing methods, it has more stable convergence and will not cause the problem of divergence or oscillation that causes a sharp increase in positioning error;

[0020] (3) The present invention can complete each calculation in about 0.3 ms, which is one tenth of the calculation time of existing iterative nonlinear algorithms. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 11 is a topological structure block diagram of a multi-base sonar TOA-AOA hybrid positioning method according to an embodiment of the present invention;

[0022] Figure 2 2. It is a schematic diagram of a multi-base sonar TOA-AOA hybrid positioning method according to an embodiment of the present invention;

[0023] Figure 3 This is a comparison of the accuracy before and after fusion under different noise levels in an embodiment of the present invention;

[0024] Figure 4 The figure compares the error probability cumulative distribution curves before and after fusion at an 18 dB noise level in an embodiment of the present invention. DETAILED DESCRIPTION

[0025] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0026] Example 1

[0027] This embodiment provides an active multi-base sonar TOA-AOA hybrid positioning method that is robust against strong interference and suitable for data fusion of multi-base sonars in both centralized and distributed architectures. After the transmitter completes a wave transmission, each receiver first receives the sound wave directly from the transmitter and begins monitoring the underwater acoustic signal. The receiver then receives the echo reflected from the target. Each receiver receives and analyzes the echo to record the arrival time of the reflected wave and calculate the target distance information. The receiver is equipped with a multi-element array to form a beam to analyze the direction of the echo arrival and estimate the target's angle information relative to itself.

[0028] In this embodiment of the present invention, a multistatic active sonar system consists of M transmitters and N receivers, where N > M. Time synchronization is performed on each transmission from each transmitter, and a measurement equation is constructed based on the relative positions of the transmitter and receiver. The combined measurement equation is estimated using maximum likelihood estimation, and the target location with the highest probability given the available observations is determined as the target output for multistatic positioning fusion.

[0029] After each receiving end completes detection, TOA-AOA hybrid positioning begins. The operator can set the variance of each base measurement value as the credibility of each measurement value based on prior knowledge, which can improve the accuracy of subsequent estimation. The process topology structure diagram is as follows Figure 1As shown, the system comprises six modules: the measurement equation construction module, the conventional initial estimation module, the special initial estimation module, the measurement equation reconstruction module, the error re-estimation module, and the error correction module. After each base obtains its observation value for the target, it enters the measurement equation construction module to generate the measurement equation. Depending on the positions of the different bases, if they are not on the same line, the system enters the conventional initial estimation module; if they are on the same line, the system enters the special initial estimation module. Both modules output a preliminary estimate of the target. Based on this preliminary estimate, the system then enters the measurement equation reconstruction module to derive a new measurement equation. After that, the system enters the error re-estimation module to obtain an error estimate of the preliminary estimate. The error correction module corrects the preliminary estimate based on this error estimate and determines whether the resulting error estimate meets the convergence threshold. If not, the system enters the error re-estimation module again to repeat the estimation. If it does, the process terminates and outputs the final target position estimate. This embodiment of the present invention has been verified to achieve accurate multi-base fusion positioning in complex underwater environments with high noise backgrounds, resolving the problem of excessive errors in associated measurement data caused by target data association errors and multipath interference.

[0030] First, based on the input array layout of a multi-base sonar system, we use a single transmitter and multiple receivers as an example. One of the receivers is located in the same position as the transmitter, forming a co-located sonar. The remaining sonars are located at random locations, forming a separate sonar. If the transmitter and all the receivers are not exactly aligned, this falls under Case 1. Otherwise, this is a special case and falls under Case 2.

[0031] First, based on the input positions of each transmitter and receiver, construct the xoy rectangular coordinate system coordinates with the transmitter as the origin, and set the target position vector to be estimated as u = [x, y] T According to the relationship between the position of each receiving end and the target position, the measurement equation can be derived as follows: z = H (u) + Δv. Where z = [r0, θ, r 01 ,θ1,…,r 0N-1 ,θ N-1 ] T . Among them, r0 and θ are the TOA and AOA measurement information of the co-located sonar, respectively. 0i and θ i Δv=[Δr0,Δθ,Δr 01 ,Δθ1,…,Δr 0N-1 ,Δθ N-1 ] T , represents the actual detection due to underwater random interference, multi-base random correlation errors and random errors of measuring instruments, showing a normal distribution with a mean of zero. H(u) is the theoretical accurate measurement value, There is a nonlinear relationship with the target's true position. The relationship between the measured value, the true value and the random error is: The nonlinear relationship between the true value and the target position is expressed as:

[0032]

[0033] where e1 = [1,0] T , t0 is the coordinate vector of the transmitter position, r i is the coordinate vector of the i-th receiver.

[0034] For case 1, the measurement equation z = H(u) + Δv is rearranged into the following form:

[0035] ξ0=h0-G0u

[0036] where ξ0=[ξ 01,1 ,ξ 01,2 ,…,ξ 0N-1,1 ,ξ 0N-1,2 ] T , h0=[h 01,1 ,h 01,2 ,…,h 0N-1,1 ,h 0N-1,2 ] T ,

[0037] G0=[G 01 ,…,G 0N-1 ] T , their specific expressions are as follows:

[0038] ξ 0i,1 =2(r 0i -r0)Δr 0i -2r 0i Δr0+Δr 0i 2 -Δr0 2 +Δr 0i Δr0

[0039] ξ 0i,2 =2cos 2 (θ i +Δθ i )(r 0i +Δr 0i -r0-Δr0) 2 -2cos 2 (θ+Δθ)(r0+Δr0) 2 +2cos 2 θr0 2 -2cos 2 θ i (r 0i-r0) 2

[0040] h 0i,1 =r i T r i -r 0i 2 +2r0r 0i

[0041]

[0042] Where X = 2e1e1 T In this way, the relationship between the measured value and the target vector is constructed into a linear relationship. The best linear unbiased estimate (BLUE) is performed on this relationship to obtain a preliminary estimate:

[0043] u=(G0 T W0G0) -1 G0 T W0h0

[0044] in, C0=E[ξ0 T ξ0], C0 is the covariance matrix of ξ0.

[0045] For case 2, in order to avoid the situation where the estimated target cannot be solved due to rank deficiency in subsequent calculations, the target vector to be estimated is set to u'=[x,y 2 ] T Expand z = H(u) + Δv using trigonometric functions and square it to get the following form:

[0046] ξ1=h1-G1u′,

[0047] where ξ1=[ξ 10 ,ξ 11,1 ,ξ 11,2 ,…,ξ 1N-1,1 ,ξ 1N-1,2 ] T , h1=[h 10 ,h 11,1 ,h 11,2 ,…,h 1N-1,1 ,h 1N-1,2 ] T , G1=[G 10 ,G 11 ,…,G 1N-1 ] T , the specific expression is as follows:

[0048] ξ 10 =sin 2 (θ+Δθ)(r0+Δr0) 2 -r02 sin 2 θ

[0049] ξ 1i,1 =2(r 0i -r0)Δr 0i -2r 0i Δr0+Δr 1i 2 -Δr0 2 +Δr 0i Δr0

[0050] ξ 1i,2 =-2sin 2 (θ i +Δθ i )(r 0i +Δr 0i -r0-Δr0) 2 +(r 0i -r0) 2 (1-cos2θ i )

[0051] h 10 =-r0 2 sin 2 θ

[0052] h 1i,1 =r i T r i -r 0i 2 +2r0r 0i

[0053] h 1i,2 =(r 0i -r0) 2 (1-cos2θ i )

[0054]

[0055] Where e2 = [0, 1] T In this way, the relationship between the measured value and the target vector is constructed into a linear relationship. The best linear unbiased estimate (BLUE) can be performed to obtain a preliminary estimate:

[0056] u'=(G1 T W1G1) -1 G1 T W1h1

[0057] in, C1=E[ξ1 T ξ1], C1 is the covariance matrix of ξ1.

[0058] The estimated y coordinate of u' is in square form. Here, the positive and negative signs of the square root of the y coordinate are determined based on the angle measurement result θ0 of the transmitting and receiving devices, so as to obtain the estimated result that truly represents the target position.

[0059] After obtaining the initial estimated value through the above two cases, the target vector to be estimated is changed to the estimated error Δu = [Δx, Δy] T , then the target's true position can be expressed as: Reconstruct the measurement equation:

[0060] ξ2=h2-G2Δu

[0061] in,

[0062] ξ2=[ξ 20,1 ,ξ 20,2 ,ξ 21,1 ,ξ 21,2 ,…,ξ 2N-1,1 ,ξ 2N-1,2 ] T

[0063] h2=[h 20,1 ,h 20,2 ,h 21,1 ,h 21,2 ,…,h 2N-1,1 ,h 2N-1,2 ] T , G2=[G 20 ,G 21 ,…,G 2N-1 ] T , specific expression

[0064] The formula is:

[0065] ξ 20,1 =2r0Δr0+Δr0 2 +Δu T Δu

[0066] ξ 20,2 =2cos 2 (θ+Δθ)(r0+Δr0) 2 -2r0 2 cos 2 θ-Δu T XΔu

[0067] ξ 2i,1 =(2r 0i -2r0)(Δr0-Δr 0i )-(Δr0-Δr 0i ) 2 -Δu TΔu

[0068] ξ 2i,2 =2cos 2 (θ i +Δθ i )[(r 0i -r0)+(Δr 0i -Δr0)] 2 -2cos 2 θ i (r 0i -r0) 2 -Δu T XΔu

[0069]

[0070] Where X = 2e1e1 T .

[0071] Perform BLUE estimation, Δu=(G2 T W2G2) -1 G2 T W2h2, where C2=E[ξ2 T ξ2], C2 is the covariance matrix of ξ2. And update the estimation result And start the iteration, if Δu T Δu>∈, then use the updated estimation result to repeat the estimation of Δu. ∈ is the convergence threshold, which can be set to 0.0001. After reaching the convergence threshold, the final output is the rectangular coordinate estimation result of the target position.

[0072] Time of Observation (TOA) and AoA (AoA) are used for measurement. This is because active sonar can independently control the timing of its transmissions, allowing for accurate TOA information to be acquired through time synchronization. Sonar utilizes a multi-element array to achieve beamforming, thereby analyzing the AoA information of the sound waves.

[0073] As a further improvement to the embodiment of the present invention, the measurement equation with strong nonlinearity is sorted out through a two-stage analysis, and a new measurement equation is constructed to sort the measurement value and the target vector into a linear form without losing accuracy, and the nonlinear characteristics are transferred to the noise term.

[0074] As a further improvement to this embodiment of the present invention, the present invention fully preserves the nonlinear characteristics of the noise term, rather than neglecting the high-order components of the noise term or linearly simplifying the trigonometric noise term as in existing methods. Preserving the complete characteristics of the noise term for subsequent analysis allows the present embodiment to achieve accuracy close to the theoretical limit even when measurement errors are large, making it more suitable for underwater detection of multiple interference situations.

[0075] As a further improvement to the embodiment of the present invention, for the noise term that retains the nonlinear characteristics, the embodiment of the present invention performs BLUE estimation on the linear relationship between the measured value and the target vector in the measurement equation after the modification. Since the nonlinear characteristics of the noise term are retained, it is necessary to calculate the covariance matrix of the noise term, which includes the calculation of the nth order moment of the normally distributed variable and the normally distributed variable in triangular form, and requires the integration of complex functions and integral transformations and other related operations. Existing work combining BLUE for positioning estimation does not retain the nonlinear characteristics of the angle information in terms of noise, and often uses linearization to simplify it.

[0076] As a further improvement to an embodiment of the present invention, after the first step of BLUE estimation, the embodiment of the present invention uses the estimated value as part of the observed value, and uses the error of the estimated value as the estimation object to further perform error analysis. Specifically, the measurement equation is reconstructed with the estimated value error as the estimation object and organized into a linear relationship form. Since there will be a quadratic term of the estimated value error that cannot be eliminated, an iterative method is selected here until the quadratic term approaches 0, and finally the final estimate is obtained. Existing algorithms using BLUE estimation do not have this iterative estimation process, so the final estimation result of the embodiment of the present invention will be more accurate.

[0077] Figure 2 The specific calculation process of multi-base data fusion is as follows:

[0078] S1: Reconstruct the measurement equation. First, determine whether it belongs to Case 1 or Case 2 based on the location distribution between the bases. For Case 1: Construct the following equation

[0079] ξ0=h0-G0u (1)

[0080] where ξ0=[ξ 01,1 ,ξ 01,2 ,…,ξ 0N-1,1 ,ξ 0N-1,2 ] T , h0=[h 01,1 ,h 01,2 ,…,h 0N-1,1 ,h 0N-1,2 ] T ,

[0081] G0=[G01 ,…,G 0N-1 ] T , their specific expressions are as follows:

[0082] ξ 0i,1 =2(r 0i -r0)Δr 0i -2r 0i Δr0+Δr 0i 2 -Δr0 2 +Δr 0i Δr0

[0083] ξ 0i,2 =2cos 2 (θ i +Δθ i )(r 0i +Δr 0i -r0-Δr0) 2 -2cos 2 (θ+Δθ)(r0+Δr0) 2 +2cos 2 θr0 2 -2cos 2 θ i (r 0i -r0) 2

[0084] h 0i,1 =r i T r i -r 0i 2 +2r0r 0i

[0085]

[0086] Where r0 and θ are the TOA and AOA measurement information of the co-located sonar, respectively. 0i and θ i is the TOA and AOA measurement information detected by the i-th transmitting and receiving split sonar. i is the rectangular coordinate vector of the i-th transmitting and receiving sonar, X=2e1e1 T , e1=[1,0] T , and calculate the preliminary estimate:

[0087]

[0088] in, C0=E[ξ0 T ξ0], C0 is the covariance matrix of ξ0.

[0089] For case 2, the reconstructed equation is:

[0090] ξ1 = h1 - G1u′ (3)

[0091] where ξ1 = [ξ 10 , ξ 11,1 , ξ 11,2 , …, ξ 1N-1,1 , ξ 1N-1,2 T , h1 = [h 10 , h 11,1 , h 11,2 , …, h 1N-1,1 , h 1N-1,2 T , G1 = [G 10 , G 11 , …, G 1N-1 T , and the specific expressions are as follows:

[0092] ξ 10 = sin 2 (θ + Δθ)(r0 + Δr0) 2 - r0 2 sin 2 θ

[0093] ξ 1i,1 = 2(r 0i - r0)Δr 0i - 2r 0i Δr0 + Δr 1i 2 - Δr0 2 + Δr 0i Δr0

[0094] ξ 1i,2 = -2sin 2 (θ i + Δθ i )(r 0i + Δr 0i - r0 - Δr0) 2 + (r 0i - r0) 2 (1 - cos2θ i )

[0095] h 10 = -r0 2 sin 2 θ

[0096] h 1i,1 = r i T r i - r 0i ​​​2 +2r0r 0i

[0097] h 1i,2 =(r 0i -r0) 2 (1-cos2θ i )

[0098]

[0099] Where e2 = [0, 1] T . Get a preliminary estimate

[0100] u'=(G1 T W1G1) -1 G1 T W1h1 (4)

[0101] in, C1=E[ξ1 T ξ1], C1 is the covariance matrix of ξ1.

[0102] Assume that the estimated result is u'=[a,b] T , judge according to θ, if 0≤θ<180°, then the preliminary estimate is If 180≤θ<360°, the preliminary estimate is a, b are the first and second elements of u'.

[0103] S2: The above two situations yield preliminary results Then, the measurement equation is reconstructed as

[0104] ξ2=h2-G2Δu (5)

[0105] in,

[0106] ξ2=[ξ 20,1 ,ξ 20,2 ,ξ 21,1 ,ξ 21,2 ,…,ξ 2N-1,1 ,ξ 2N-1,2 ] T ,

[0107] h2=[h 20,1 ,h 20,2 ,h 21,1 ,h 21,2 ,…,h 2N-1,1 ,h 2N-1,2 ] T , G2=[G 20 ,G 21 ,…,G 2N-1 ] T, the specific expression is:

[0108] ξ 20,1 =2r0Δr0+Δr0 2 +Δu T Δu

[0109] ξ 20,2 =2cos 2 (θ+Δθ)(r0+Δr0) 2 -2r0 2 cos 2 θ-Δu T XΔu

[0110] ξ 2i,1 =(2r 0i -2r0)(Δr0-Δr 0i )-(Δr0-Δr 0i ) 2 -Δu T Δu

[0111] ξ 2i,2 =2cos 2 (θ i +Δθ i )[(r 0i -r0)+(Δr 0i -Δr0)] 2 -2cos 2 θ i (r 0i -r0) 2 -Δu T XΔu

[0112]

[0113]

[0114] The estimated value can be solved

[0115] Δu=(G2 T W2G2) -1 G2 T W2h2 (6)

[0116] in C2=E[ξ2 T ξ2], C2 is the covariance matrix of ξ2. Update the estimation result and Assign the value of If Δu TΔu>∈, then update h2 and G2 in the measurement equation, and use the updated estimation results to repeat the estimation of Δu. ∈ is the convergence threshold, which can be set to 0.0001. After reaching the convergence threshold, the final output is the rectangular coordinate estimation result of the target position.

[0117] This embodiment has the following technical effects:

[0118] High-precision positioning: In high-noise environments (TOA noise variance ≥ 6dB, AOA noise variance ≥ 8°), positioning error is reduced by 15%-30% compared to traditional methods;

[0119] Stable convergence: Through two-stage optimization and deviation correction, iterative divergence is avoided and accurate convergence can be guaranteed;

[0120] Low computational complexity: No derivative operations or convex relaxation optimization are required, and the computer computing time for each algorithm is about 0.3ms.

[0121] Figure 3 This simulation compares the detection accuracy of a dual-base scenario before fusion using the present invention, compared to that of a co-located transmitter / receiver and a separate transmitter / receiver, under different noise levels. The comparison metric is the root mean square error (RMS), which is the average Euclidean distance between the estimated value and the true value. The angular noise variance is set to [8x, 8x], and the range noise variance is [5x, 10x]. The value of x ranges from 0.01 to 2. 5000 Monte Carlo simulations were performed for each parameter setting, demonstrating that the proposed algorithm significantly improves positioning accuracy.

[0122] Figure 4 for Figure 3 When the noise level is 18dB, the root mean square error distribution before and after fusion under 5000 simulations shows that the positioning error after fusion is smaller, which has a significant effect on improving positioning accuracy.

[0123] Example 2

[0124] Embodiment 2 of the present invention provides a positioning system corresponding to the above-mentioned embodiment 1, including a memory, a processor, and a computer program stored in the memory; the processor executes the computer program in the memory to implement the steps of the method in the above-mentioned embodiment 1.

[0125] In some implementations, the memory may be a high-speed random access memory (RAM), and may also include a non-volatile memory, such as at least one disk storage.

[0126] In other implementations, the processor may be a central processing unit (CPU), a digital signal processor (DSP), or other general-purpose processors, which are not limited herein.

[0127] Example 3

[0128] Embodiment 3 of the present invention provides a computer-readable storage medium corresponding to the above-mentioned embodiment 1, on which a computer program / instruction is stored. When the computer program / instruction is executed by a processor, the steps of the method of the above-mentioned embodiment 1 are implemented.

[0129] Computer readable storage media can be tangible devices that hold and store instructions used by instruction execution devices. Computer readable storage media can be, for example, but not limited to, electronic storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any combination thereof.

[0130] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code. The scheme in the embodiment of the present application can be implemented in various computer languages, for example, object-oriented programming language Java and literal translation scripting language JavaScript, etc.

[0131] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the steps in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0132] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1A step that specifies a function in one or more boxes.

[0133] Although the preferred embodiments of the present application have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present application.

[0134] Obviously, those skilled in the art may make various changes and modifications to this application without departing from the spirit and scope of this application. Thus, if these modifications and variations of this application fall within the scope of the claims of this application and their equivalents, this application is intended to include these modifications and variations.

Claims

1. A multi-base sonar TOA-AOA hybrid positioning method, characterized in that: The rectangular coordinate estimation result u of the target position is calculated using the following formula: Where, Δu=(G2 T W2G2) -1 G2 T W2h2; C2=E[ξ2 T ξ2], C2 is the covariance matrix of ξ2, G2=[G 20 ,G 21 ,…,G 2(N-1) ] T , X=2e1e1 T , e1=[1,0] T , r i is the rectangular coordinate vector of the i-th transmitting and receiving sonar, is the estimated result, ξ2=h2-G2Δu; If the transmitter and all receivers are not located on the same straight line, then otherwise, in, C0=E[ξ0 T ξ0], C0 is the covariance matrix of ξ0, C1=E[ξ1 T ξ1], C1 is the covariance matrix of ξ1, ξ0=[ξ 01,1 ,ξ 01,2 ,…,ξ 0N-1,1 ,ξ 0N-1,2 ] T ,ξ1=[ξ 10 ,ξ 11,1 ,ξ 11,2 ,…,ξ 1N-1,1 ,ξ 1N-1,2 ] T , h0=[h 01,1 ,h 01,2 ,…,h 0N-1,1 ,h 0N-1,2 ] T , G0=[G 01 ,…,G 0N-1 ] T ,ξ 0i,1 =2(r 0i -r0)Δr 0i -2r 0i Δr0+Δr 0i 2 -Δr0 2 +Δr 0i Δr0,ξ 0i,2 =2cos 2 (θ i +Δθ i )(r 0i +Δr 0i -r0-Δr0) 2 -2cos 2 (θ+Δθ)(r0+Δr0) 2 +2cos 2 θr0 2 -2cos 2 θ i (r 0i -r0) 2 , r0 and θ are the TOA and AOA measurement information of the co-located sonar, respectively. 0i and θ i is the TOA and AOA measurement information detected by the i-th transmitting and receiving sonar. The relationship between the measured value, the true value and the random error is: and They are the theoretical TOA and AOA measurement information of the combined sonar, and The theoretical TOA and AOA measurement information of the i-th transmitter and receiver, Δr0, Δθ, Δr 0i and Δθ i is the measurement error of the corresponding measurement information; h1=[h 10 ,h 11,1 ,h 11,2 ,…,h 1N-1,1 ,h 1N-1,2 ] T ,G1=[G 10 ,G 11 ,…,G 1N-1 ] T , x 10 =sin 2 (θ+Δθ)(r0+Δr0) 2 -r0 2 sin 2 I, x 1i,1 =2(r 0i -r0)Δr 0i -2r 0i Δr0+Δr 1i 2 -Δr0 2 +Δr 0i Δr0, x 1i,2 =-2sin 2 (i i +Δθ i )(r 0i +Δr 0i -r0-Δr0) 2 +(r 0i -r0) 2 (1-cos2θ i ), h 10 =-r0 2 sin 2 θ, h 1i,1 =r i T r i -r 0i 2 +2r0r 0i ,h 1i,2 =(r 0i -r0) 2 (1-cos2θ i ), e2=[0,1] T , i=1,2,…,N-1, where N is the number of receiving ends.

2. The multi-base sonar TOA-AOA hybrid positioning method according to claim 1, characterized in that: Update the estimated results using the following process Will Add it to Δu to get a new estimate. T When Δu>∈, the updated estimation result is used to repeatedly estimate Δu, and ∈ is the convergence threshold.

3. The multi-base sonar TOA-AOA hybrid positioning method according to claim 1, characterized in that: ∈ takes the value of 0.0001.

4. A multi-base sonar TOA-AOA hybrid positioning system, comprising a memory, a processor, and a computer program stored in the memory; characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 3.

5. A computer-readable storage medium having a computer program / instruction stored thereon; characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 3 are implemented.

6. A computer program product comprising a computer program / instructions; characterized in that When the computer program / instruction is executed by a processor, the steps of the method according to any one of claims 1 to 3 are implemented.

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