TDOA-DOA underwater target passive positioning method and system under sensor position prior observation error

Abstract

The present invention belongs to the field of target position estimation technology, and particularly relates to a method and system for passive positioning of underwater targets based on TDOA-DOA under a priori observation error of sensor position. First, multiple sensors are used to obtain the TDOA and DOA observations of the target, and a TDOA-DOA positioning model is constructed using the relationship between distance and angle observations, and the target position is preliminarily estimated by the least squares method; then a joint estimation equation of the target positioning error and the sensor position is constructed, and the target positioning error and the sensor position are jointly estimated by the weighted least squares method; finally, the preliminarily estimated target position is corrected by the positioning error. The present invention can effectively improve the positioning accuracy of the target, and further verify through simulation experimental data that the target position estimation performance of the scheme in this case is more excellent, which is convenient for application in actual scenarios.

Description

Technical Field

[0001] The present invention belongs to the technical field of target position estimation, and in particular relates to a method and system for passive positioning of underwater targets based on TDOA-DOA under a priori observation error of sensor position. Background Art

[0002] Passive positioning of underwater sound sources has important application value in underwater target reconnaissance. At present, it mainly includes matching field positioning and target positioning based on underwater wireless sensor networks (UWSNs). The accuracy of matching field positioning depends on the modeling of underwater acoustic channels. If the modeling of underwater acoustic channels is mismatched, it will cause large errors. Underwater wireless sensor networks are sensor node network systems dispersedly deployed in vast waters. Target positioning based on underwater wireless sensor networks does not require channel prior information. Its methods mainly include TDOA positioning based on hyperbolic equations and DOA positioning based on azimuth intersection. Among them, TDOA uses the time difference between the arrival of the wave signal to different sensors for target positioning. The system can obtain higher positioning accuracy, but there is positioning ambiguity in some cases; DOA only needs two sensors for target positioning, but the positioning error is large. Combining multiple positioning parameters can significantly improve the positioning performance of the algorithm and enhance the stability of the system. Therefore, underwater target positioning based on TDOA-DOA has attracted widespread attention.

[0003] Due to underwater current movement and the inability of underwater sensors to use satellites for self-positioning, the position of the sensor itself cannot be accurately known. The sensor's own position error will greatly reduce the target positioning accuracy. Therefore, when designing a target positioning algorithm, the sensor position error cannot be ignored. Summary of the invention

[0004] To this end, the present invention provides a TDOA-DOA underwater target passive positioning method and system under a priori observation error of sensor position, so as to improve the estimation accuracy and performance of underwater target.

[0005] According to the design scheme provided by the present invention, a TDOA-DOA underwater target passive positioning method under a priori observation error of sensor position includes the following contents:

[0006] The TDOA-DOA positioning model is constructed using the relationship between the angle and distance between the target and the sensor, and the target position is preliminarily estimated using the least squares method.

[0007] Construct a joint equation between the target positioning error and the sensor position, and use the weighted least squares method to jointly estimate the target positioning error and the sensor position;

[0008] The initial estimated target position is corrected by the positioning error.

[0009] Furthermore, the present invention also provides a TDOA-DOA underwater target passive positioning system under sensor position error, comprising: a preliminary estimation module and a position correction module, wherein:

[0010] The preliminary estimation module is used to construct a TDOA-DOA positioning model using the relationship between the angle and distance between the target and the sensor, and to preliminarily estimate the target position using the least squares method;

[0011] The position correction module is used to construct a joint equation between the target positioning error and the sensor position, and use the weighted least squares method to jointly estimate the target positioning error and the sensor position, and correct the initially estimated target position through the positioning error.

[0012] Beneficial effects of the present invention:

[0013] The present invention aims at the problem of low positioning accuracy caused by sensor position error in passive positioning of underwater targets. By constructing an idealized error-free TDOA-DOA model and using the least squares algorithm to roughly estimate the target position, the joint equation of target positioning error and sensor position is constructed by considering the measurement error and sensor position error and solved by weighted least squares. Finally, the rough estimate of the target position is corrected by using the target positioning error to obtain a more accurate positioning result. Further simulation experiments show that the algorithm in this case can jointly estimate the target position and sensor position. Compared with existing algorithms, it has higher positioning accuracy and is more suitable for underwater target positioning in the case of prior observation errors in the sensor position, and has good application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 The flowchart of the TDOA-DOA underwater target passive positioning method under the sensor position error in the embodiment is shown;

[0015] Figure 2 It is a schematic diagram of the underwater TDOA-DOA passive positioning scenario in the embodiment;

[0016] Figure 3 Schematic diagram of the target and receiving sensor position distribution in the embodiment;

[0017] Figure 4 In the embodiment, the RMSE of target position estimation varies with σ s The change curve is shown in figure;

[0018] Figure 5 is the RMSE of sensor position estimation in the embodiment as σ s The change curve is shown in figure;

[0019] Figure 6In the embodiment, the RMSE of target position estimation varies with σ doa The change curve is shown in figure;

[0020] Figure 7 is the RMSE of sensor position estimation in the embodiment as σ doa Variations of the song;

[0021] Figure 8 In the embodiment, the RMSE of target position estimation varies with σ tdoa The change curve is shown in figure;

[0022] Fig. 9 is the RMSE of sensor position estimation in the embodiment as σ tdoa The change curve is shown. DETAILED DESCRIPTION

[0023] In order to make the purpose, technical solutions and advantages of the present invention clearer and more understandable, the present invention is further described in detail below in conjunction with the accompanying drawings and technical solutions.

[0024] In view of the problem that the accuracy of passive positioning of underwater targets is affected by the position error of sensors, an embodiment of the present invention provides a TDOA-DOA underwater target passive positioning method under sensor position error, see Figure 1 As shown, it contains the following contents:

[0025] S101, constructing a TDOA-DOA positioning model by using the pseudo-linear relationship between the angle and distance between the target and the sensor, and preliminarily estimating the target position by using the least squares method;

[0026] S102, constructing a joint equation between the target positioning error and the sensor position, and jointly estimating the target positioning error and the sensor position using a weighted least squares method;

[0027] S103: Correct the initially estimated target position by using the positioning error to obtain a more accurate target position.

[0028] An idealized error-free TDOA-DOA model is constructed, and the target position is roughly estimated using the least squares algorithm. The measurement error and sensor position error are taken into account, and the joint equation of target positioning error and sensor position is constructed and solved using weighted least squares. Finally, the target positioning error is used to correct the rough estimate of the target position to obtain a more accurate positioning result.

[0029] like Figure 2 As shown, the underwater non-cooperative target position coordinates are u = [x, y, z] T , M sensors are randomly distributed in the nearby waters to estimate the azimuth and elevation of the target, where the position coordinates of the i-th sensor are s i =[xi ,y i ,z i ] T (1≤i≤M). i represents the distance between the target and the i-th sensor, θ i and β i are the azimuth and elevation of the target with respect to the i-th sensor.

[0030] Depend on Figure 2 As shown, the distance r from the target to the i-th sensor i for:

[0031]

[0032] ||·|| is the l2 norm. The first sensor is used as the reference sensor, r i,1 It represents the difference between the distance between the target and the ith sensor and the distance between the target and the reference sensor. Its expression is shown in formula (2). c is the speed of sound propagation in water, which is usually 1500 m / s. t i,1 is the TDOA measurement value.

[0033] r i,1 =r i -r1=||us i ||-||u-s2||=ct i,1 (2)

[0034] By shifting the terms in the above equation and squaring it, we can get:

[0035]

[0036] [·] T The left side of equation (3) contains not only the target position u to be estimated, but also the unknown distance r1 between the target and the reference sensor. Therefore, the equation of formula (3) can be directly pseudo-linearized:

[0037]

[0038] According to the azimuth angle θ i and elevation angle β i The geometric relationship can be obtained:

[0039]

[0040]

[0041] Expanding equation (5) and equation (6) yields:

[0042] x sinθ i -y cosθi =x i sinθ i -y i cosθ i (7)

[0043] (x cosθ i +y sinθ i )sinβ i -z cosβ i =(x i cosθ i +y i sinθ i )sinβ i -z i cosβ i (8)

[0044] Since the precise value of the sensor position may not be available, only the sensor position observation value containing errors can be obtained. And because of the existence of measurement errors, only TDOA and DOA observations containing errors can be obtained. As shown in formula (9), Δs i , Δr i,1 , Δθ i , Δβ i represents the observation error, and Δs i =[Δx i ,Δy i ,Δz i ] T .

[0045]

[0046] For ease of expression, the observations and errors are vectorized:

[0047]

[0048] In formula (10), represents the sensor position observation vector, ε s is the corresponding sensor position error vector, represents the observation vector of TDOA and DOA, ε γ is the corresponding error vector. For convenience, assume that ε s and ε γ All obey a Gaussian distribution with zero mean and constant variance, Q s and Q γ are their covariance matrices respectively.

[0049] Q s =E[εs (ε s ) T ] (11)

[0050] Q γ =E[ε γ (ε γ ) T ] (12)

[0051] In the embodiment of this case, the situation where TDOA-DOA measurement error and receiving sensor position error coexist is comprehensively considered, and it is divided into two steps. The first step is to obtain a rough estimate of the target position using the least squares algorithm under an ideal model without considering the error; the second step is to construct a joint estimation equation of the target positioning error and the sensor position on the basis of the coexistence of the measurement error and the sensor position error, and solve it based on the weighted least squares. Finally, the obtained target positioning error estimate is used to correct the rough estimate of the target position in the first step to obtain a more accurate target position estimate.

[0052] In the first step of rough estimation of target positioning, the TDOA-DOA measurement error and the receiving sensor position error are not considered. An idealized TDOA-DOA positioning model is constructed, and equations (4), (7) and (8) are combined and written in matrix form.

[0053]

[0054] in,

[0055]

[0056]

[0057] Based on the least squares principle, a rough estimate of the target position can be obtained. for:

[0058]

[0059] (·) -1 Find the inverse of a matrix.

[0060] The first step is to construct an idealized TDOA-DOA positioning equation without considering the actual TDOA-DOA measurement error and sensor position error. There is a large gap between the actual target position u and the target position u, so the second step is used to further Correct the positioning error to make it closer to the true value.

[0061] In the second step of target positioning correction, based on the existence of TDOA-DOA measurement error and the position error of the sensor itself, a joint estimation equation of target positioning error and sensor position is constructed based on the idea of ​​joint estimation, and solved using weighted least squares. Finally, the obtained target positioning error is used to correct the rough estimate of the target position in the first step.

[0062] Let the target positioning error be Δu=[Δx,Δy,Δz] T , so

[0063]

[0064] Substituting the above equation into equations (4), (7) and (8) yields:

[0065]

[0066]

[0067]

[0068] Considering the actual TDOA-DOA measurement error and sensor position error, equations (18), (19) and (20) are and Taking the first-order Taylor expansion and ignoring the second-order error term, we can get:

[0069]

[0070]

[0071]

[0072] Arranging equations (21), (22) and (23), we can obtain:

[0073]

[0074] in,

[0075]

[0076]

[0077] Ω γ ∈R (3M-1)×(3M-1) ,Ω s ∈R (3M-1)×3M , the elements in the matrix are as follows,

[0078]

[0079]

[0080] Construct the joint estimation equation of target positioning error Δu and sensor position s:

[0081]

[0082] Let Q2 be the error covariance matrix of the new equation (29), which is expressed as follows.

[0083]

[0084] The criterion function for the weighted least squares problem is:

[0085]

[0086] I 3M is a 3M×3M unit matrix. By minimizing equation (31), the parameter vector can be estimated as:

[0087]

[0088] According to formula (30), the weighted matrix The calculation of is related to the target position error vector Δu, but Δu is an unknown quantity to be determined. Set it as the unit matrix, so as to obtain and The initial estimate is then recalculated to update And again get and After repeating 3-5 times, the estimated value of the target position can reach a convergence state, so the final target position estimate is:

[0089]

[0090] The implementation steps of the proposed algorithm can be designed as follows:

[0091] Step 1: Establish an error-free idealized underwater TDOA-DOA joint positioning equation (13), and obtain a rough estimate of the target position through equation (16):

[0092] Step 2: Considering the TDOA-DOA measurement error and sensor position error, establish the joint estimation equation of the target positioning error Δu and the sensor position s (29);

[0093] Step 3: Initialize the weight matrix Using formula (32) we can obtain and

[0094] Step 4: and Substitute into formula (30) to update, and use formula (32) to obtain a more accurate and An estimated value of

[0095] Step 5: Repeat step 4 3-5 times to get the final estimate Based on formula (34), the final estimated value of the target position is obtained

[0096] Further, based on the above method, an embodiment of the present invention also provides a TDOA-DOA underwater target passive positioning system under sensor position error, comprising: a preliminary estimation module and a position correction module, wherein:

[0097] The preliminary estimation module is used to construct a TDOA-DOA positioning model by using the pseudo-linear relationship between the angle and distance between the target and the sensor, and to preliminarily estimate the target position by the least square method;

[0098] The position correction module is used to construct a joint equation between the target positioning error and the sensor position, and use the weighted least squares method to jointly estimate the target positioning error and the sensor position, and correct the initially estimated target position through the positioning error.

[0099] In order to verify the effectiveness of this solution, the following is a further explanation based on simulation test data:

[0100] The Cramer-Rao lower bound CRB is the best estimation performance that a minimum variance unbiased estimator can achieve. Let η = [us] T , Then the joint probability density function of the observed quantity χ under the determined quantity η is p(χ;η), where τ is a constant.

[0101]

[0102] Taking the logarithm of the above formula and finding the second-order derivative gives the CRB expression:

[0103]

[0104] in,

[0105]

[0106]

[0107] in,

[0108]

[0109] and

[0110]

[0111] in,

[0112]

[0113]

[0114]

[0115]

[0116] Wherein, blkdiag{·} is a block diagonal operation.

[0117] Assume the coordinate position of the unknown target in the water is u=[1550,950,87] T , and 6 receiving sensors are placed around, their positions are s1 = [1000, 1500, 67] T s2 = [2000, 1200, 51] T s3 = [-3000, -800, 61] T s4 = [2500, 2000, 55] T s5 = [-1000,-1200,50] T s6 = [2000, -3000, 60] T ,like Figure 3 Assume that the measurement errors of TDOA and DOA are independent zero-mean Gaussian distributions, and their standard deviations are σ tdoa and σ doa , so ε γ It has a mean of zero and a covariance matrix of Gaussian distribution, where 1 4×4 is a 4×4 matrix with all 1s; at the same time, the sensor position error ε s It has zero mean and the covariance matrix is Gaussian distribution, ε γ and ε s Statistical independence.

[0118] The root mean square error (RMSE) can be used to measure the positioning performance of the algorithm. The definition is shown in formula (44), where represents the estimated value of the target position in the kth experiment, and M = 1000 Monte Carlo experiments can be set. In order to objectively compare the performance of the algorithms, the algorithm in this case, the two-step least squares positioning algorithm without considering the sensor position error (referred to as algorithm A), and the one-step least squares algorithm considering the sensor position error (referred to as algorithm B) are compared under different TDOA measurement error standard deviations σ tdoa , DOA measurement error standard deviation σ doa and the sensor position error standard deviation σs The following is a comparison.

[0119]

[0120] Figure 4 and Figure 5 is tdoa =10 -3 s,σ doa =0.1°, different σ s The following are the target position estimation RMSE and sensor position estimation RMSE curves of the three algorithms. It can be seen that the target position estimation CRB and sensor position estimation CRB both increase with the increase of the sensor position observation error. Figure 4 It can be seen that when σ tdoa and σ doa When the sensor position error exists, the positioning model of algorithm A does not take the sensor position error into consideration, so the performance is seriously degraded. However, both algorithm B and the algorithm in this case construct the positioning equation based on the existence of measurement error and sensor position error. Therefore, σ s The increase of does not have much impact on the target position estimation. The algorithm in this case jointly estimates the target positioning error and the sensor position, and uses the obtained and Weighted Matrix Update to obtain a more accurate target positioning error estimate Finally, we get a target position estimate that is closer to the true value. Therefore, under the same simulation conditions, the target positioning RMSE of the algorithm in this case is closer to the CRB curve than that of the B algorithm. At the same time, since the algorithm in this case estimates the sensor position at the same time, the sensor position is corrected. Figure 5 It can be seen that the RMSE for sensor position estimation can also reach the corresponding CRB, while algorithm A and algorithm B only estimate the target position but not the sensor position.

[0121] Figure 6 and Figure 7 is s =10m,σ tdoa =10 -3 s, different σ doa The target position estimation RMSE and sensor position estimation RMSE curves of the following three algorithms are shown. It can be clearly seen that the target position estimation of the algorithm in this case is significantly better than that of the B algorithm, while the A algorithm does not consider the sensor position error. Therefore, under the current simulation conditions, its target positioning performance is far inferior to that of the algorithm in this case and the B algorithm. Similarly, the algorithm in this case also estimates the sensor position. doa When it is small, the sensor position estimation RMSE can reach CRB.

[0122] Figure 8 and Fig. 9 is s =10m,σ doa =0.1°, different σ tdoa The target position estimation RMSE and sensor position estimation RMSE curves of the following three algorithms are shown. It can be seen that under the current simulation conditions, the target positioning performance of this algorithm and algorithm B is not much different, but it is obviously better than algorithm A. At the same time, the algorithm in this paper corrects the sensor position.

[0123] In summary, for the passive positioning model of underwater targets based on TDOA-DOA, the embodiment of this case simultaneously considers the TDOA-DOA measurement error and the underwater sensor position error, estimates the target position and the sensor position, and its target position estimation performance is significantly better than the case where the sensor position error is not considered. Compared with the B positioning algorithm that also targets the sensor position error, the algorithm of this case can estimate the sensor position at the same time, and the target position estimation performance of this case is better.

[0124] Unless otherwise specifically stated, the relative steps, numerical expressions and values ​​of the components and steps set forth in these embodiments do not limit the scope of the present invention.

[0125] Based on the above method and / or system, an embodiment of the present invention also provides a server, including: one or more processors; a storage device for storing one or more programs, when the one or more programs are executed by the one or more processors, the one or more processors implement the above method.

[0126] Based on the above method and / or system, an embodiment of the present invention further provides a computer-readable medium having a computer program stored thereon, wherein the above method is implemented when the program is executed by a processor.

[0127] In all examples shown and described herein, any specific values ​​should be interpreted as merely exemplary and not as limiting, and thus other examples of the exemplary embodiments may have different values.

[0128] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0129] Finally, it should be noted that the above-described embodiments are only specific implementations of the present invention, which are used to illustrate the technical solutions of the present invention, rather than to limit them. The protection scope of the present invention is not limited thereto. Although the present invention is described in detail with reference to the above-described embodiments, ordinary technicians in the field should understand that any technician familiar with the technical field can still modify the technical solutions recorded in the above-described embodiments within the technical scope disclosed by the present invention, or can easily think of changes, or make equivalent replacements for some of the technical features therein; and these modifications, changes or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A TDOA-DOA underwater target passive positioning method under sensor position prior observation error, characterized in that: Contains the following: The TDOA-DOA positioning model is constructed by using the relationship between the angle and distance difference between the target and the sensor and the target position and the sensor position, and the target position is preliminarily estimated by the least squares method. In this model, the first sensor is set as the reference sensor, r i represents the distance parameter between the target and the i-th sensor, θ i and β i are the azimuth and elevation parameters of the target for the i-th sensor, respectively. The TDOA-DOA positioning model is constructed using the distance difference between the target and the i-th sensor and the distance between the target and the reference sensor, as well as the azimuth and elevation angles of the target and the i-th sensor. The geometric relationship between the distance difference and the azimuth and elevation angles is expressed as: xsinθ i -ycosθ i =x i sinθ i -y i cosθ i , (xcosθ i +ysinθ i )sinβ i -zcosβ i =(x i cosθ i +y i sinθ i )sinβ i -z i cosβ i , r i,1 is the distance difference, and r i,1 =r i -r1=||us i ||-||u-s2||=ct i,1 t i,1 is the TDOA measurement value, the position coordinates of the i-th sensor s i Expressed as: s i =[x i ,y i ,z i ] T , 1≤i≤M, M is the number of sensors, and the target coordinate u is expressed as: u=[x,y,z] T , the TDOA-DOA positioning model is expressed as: represents the sensor position observation vector, represents the observation vector of TDOA and DOA, The joint equation between the target positioning error and the sensor position is constructed, and the target positioning error and the sensor position are jointly estimated using the weighted least squares method, where the target positioning error is set to be expressed as Δu = [Δx, Δy, Δz] T , then the joint estimation equation of the target positioning error Δu and the sensor position s is expressed as: ε s is the sensor position error vector, ε γ is the TDOA-DOA observation error vector, I 3M is a 3M×3M unit matrix, Ω γ ,Ω s Respectively represent the coefficient matrices of the sensor position error vector and the TDOA-DOA observation error vector, The initial estimated target position is corrected by the positioning error.

2. The TDOA-DOA underwater target passive positioning method under sensor position prior observation error according to claim 1 is characterized in that: Based on the least squares principle, the target position is preliminarily estimated It is expressed as:

3. The TDOA-DOA underwater target passive positioning method under sensor position prior observation error according to claim 1 is characterized in that: The weighted least squares method is used to jointly estimate the target positioning error and the sensor position, and the criterion function of the weighted least squares problem is established. The positioning error is obtained by iteratively solving the criterion function.

4. The TDOA-DOA underwater target passive positioning method under sensor position prior observation error according to claim 3 is characterized in that: In the iterative solution, first, the error covariance matrix in the joint positioning equation is initialized with the unit matrix to obtain the initial estimated values ​​of the target positioning error and the sensor position parameter vector; then, the error covariance matrix in the joint positioning equation is updated with the initial estimated values, and the estimated values ​​of the target positioning error and the sensor position parameter vector are obtained again. This is iterated N times until the convergence state of the joint positioning equation is met, and the final target positioning error is obtained.

5. The TDOA-DOA underwater target passive positioning method under sensor position prior observation error according to claim 1, 3 or 4, characterized in that: Using the positioning error Δu and the formula To get an estimate of the final target location 6. A TDOA-DOA underwater target passive positioning system under sensor position prior observation error, characterized in that: The method according to claim 1 is implemented, comprising: a preliminary estimation module and a position correction module, wherein: The preliminary estimation module is used to construct a TDOA-DOA positioning model by using the pseudo-linear relationship between the angle and distance between the target and the sensor, and to preliminarily estimate the target position by the least square method; The position correction module is used to construct a joint equation between the target positioning error and the sensor position, and use the weighted least squares method to jointly estimate the target positioning error and the sensor position, and correct the initially estimated target position through the positioning error.

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