Satellite radiation source-based air target TDOA iterative positioning method

Abstract

The application discloses a satellite radiation source-based aerial target TDOA iterative positioning method, which comprises the following steps: constructing a multi-station TDOA measurement model, wherein the multi-station TDOA measurement model is a relationship formula of measurement values of each positioning radar and a target position; constructing a TDOA four-station iterative positioning model and a TDOA three-station iterative positioning model based on the multi-station TDOA measurement model; and realizing four-station target positioning and three-station target positioning according to the TDOA four-station iterative positioning model and the TDOA three-station iterative positioning model respectively. The application reduces the requirement for the number of receiving stations on the basis of ensuring positioning accuracy, and has a good engineering application prospect.

Description

Technical Field

[0001] This invention belongs to the field of radar technology and relates to an iterative positioning method for aerial targets based on satellite radiation sources using TDOA (time difference of arrival), providing an efficient means for high-precision positioning of multi-station aerial targets. Background Technology

[0002] In the context of future information warfare, multi-station target precise localization provides a strong guarantee for effectively carrying out enemy intelligence gathering, electronic jamming, and even precision strikes, making it a key technology in battlefield reconnaissance and surveillance systems. Multi-station target localization typically employs either direct localization methods (directly estimating target parameters from target signals) or indirect localization methods (first extracting measurement information from target signals, then obtaining target parameters through localization calculations). While theoretically, direct localization methods can achieve higher accuracy, they are prone to model mismatch and require multi-dimensional search to estimate target positions, significantly impacting both the algorithm's estimation accuracy and runtime.

[0003] Existing multi-station target precise positioning methods do not take into account the limitation of the number of receiving observation stations. In a real-time battlefield environment, the number of receiving observation stations is a very valuable resource. We hope to achieve the given target positioning accuracy target with as few receiving observation stations as possible. However, existing two-step positioning methods require the introduction of an additional reference distance in the first-stage calculation, which increases the number of independent measurements to four, requiring at least five receiving observation stations to support the task. This is highly detrimental to the requirement of minimizing the number of receiving observation stations. Therefore, there is an urgent need to propose an iterative positioning method for airborne targets under the condition of fewer receiving observation stations, providing high-precision target positioning for fire control, reconnaissance, guidance, and other applications. Summary of the Invention

[0004] The purpose of this invention is to overcome the above-mentioned defects and provide an iterative positioning method for aerial targets based on satellite radiation sources (TDOA). This method solves the technical problem that traditional positioning methods cannot obtain as few receiving observation stations as possible. This invention reduces the requirement for the number of receiving stations while ensuring positioning accuracy, and has good prospects for engineering applications.

[0005] To achieve the above-mentioned objectives, the present invention provides the following technical solution:

[0006] An iterative TDOA localization method for aerial targets based on satellite radiation sources includes:

[0007] A multi-station TDOA measurement model is constructed, which is the relationship between the measurement values ​​of each positioning radar and the target position.

[0008] Based on the multi-station TDOA measurement model, a four-station iterative positioning model and a three-station iterative positioning model for TDOA are constructed. Based on the four-station iterative positioning model and the three-station iterative positioning model for TDOA, four-station target positioning and three-station target positioning are respectively realized.

[0009] The TDOA four-station iterative positioning model and the TDOA three-station iterative positioning model include the relationship between the distance estimation from the reference radar to the target and the target position estimation.

[0010] Furthermore, suppose the distributed multi-station radar system comprises M radars, where the first radar is a reference radar and the second to M radars are positioning radars; M ≥ 2, 2 ≤ i ≤ M;

[0011] The multi-station TDOA measurement model is as follows:

[0012]

[0013] Where, r i Let r be the distance from the target to the i-th positioning radar, r1 be the distance from the target to the reference radar, and r be the measurement value of the i-th positioning radar. i1 =r i -r1, s i Let s1 be the true position of the i-th positioning radar, s1 be the true position of the reference radar, and u be the target position.

[0014] Furthermore,

[0015] in, Let Δs be the navigation position of the i-th positioning radar. i Let be the position error of the i-th positioning radar;

[0016] r i =||us i ||2.

[0017] Furthermore, the TDOA four-station iterative positioning model includes:

[0018]

[0019]

[0020]

[0021]

[0022]

[0023] When n=1,

[0024] When n > 1

[0025]

[0026] Where n represents the nth iteration, n≥1, Let be the differential pseudorange of the i-th positioning radar. This is the distance estimate from the reference radar to the target used in the nth iteration. For the reference radar navigation position, The three-dimensional target position estimate obtained in the nth iteration, W1(n) is the weighting matrix for the nth iteration. This is the distance estimate for the i-th localization radar to reach the target during the n-th iteration. Q is the distance estimate from the reference radar to the target obtained in the nth iteration. t =c 2 E [ΔtΔt] T ], Q p =c 2 E[ΔsΔs T ], c represents the speed of light, Δt is the time error, and Δs is the position error of the drone.

[0027] Furthermore, the methods for achieving four-station target localization based on the TDOA four-station iterative localization model include:

[0028] S1.1 Acquisition

[0029] S1.2 According to We obtain h1(n), and from B1(n) and D1(n) we obtain W1(n). From h1(n), G1, and W1(n) we obtain...

[0030] S1.3 Based on the results obtained in the previous step get

[0031] S1.4 Determine if the preset number of iterations has been reached. If the preset number of iterations has been reached, output the current value. After completing the target localization at four stations, if the preset number of iterations has not been reached, return to step S1.2 and use... Proceed to the next iteration.

[0032] Furthermore, Where, r b For dual-station detection range, r t (n) represents the distance from the satellite to the target in the nth iteration;

[0033] In the first iteration, the distance r from the satellite to the target... t (1) That is, the distance from the satellite to the center of the ground beam.

[0034] Furthermore, the TDOA three-station iterative positioning model includes:

[0035]

[0036]

[0037]

[0038]

[0039]

[0040] Where n represents the nth iteration, n≥1, and ε1(n) is the error term of the nth iteration. Let be the differential pseudorange of the i-th positioning radar. For the two-dimensional target position estimate obtained in the nth iteration, (x i y i Let (x1, y1) be the two-dimensional position coordinates of the i-th positioning radar, and (x1, y1) be the two-dimensional position coordinates of the reference radar. This is the distance estimate from the reference radar to the target during the nth iteration. For the reference radar navigation position, The three-dimensional target position estimate obtained in the nth iteration Let x(n+1) and y(n+1) be the distance estimate from the reference radar to the target obtained in the nth iteration, and let x(n+1) and y(n+1) be the x and y coordinates of the two-dimensional target position estimate obtained in the nth iteration.

[0041] Furthermore, the methods for achieving four-station target localization based on the TDOA four-station iterative localization model include:

[0042] S2.1 Acquisition and This is the height estimate of the target during the first iteration;

[0043] S2.2 According to We obtain h1(n), based on ε1(n), h1(n), and get

[0044] S2.3 According to and get

[0045] S2.4 According to get

[0046] S2.5 Determines whether the preset number of iterations has been reached. If the preset number of iterations has been reached, outputs the current value. Complete the three-station target localization. If the preset number of iterations has not been reached, return to step S2.2 and use... Proceed to the next iteration.

[0047] Furthermore, Where, r b For dual-station detection range, r t (n) represents the distance from the satellite to the target in the nth iteration;

[0048] In the first iteration, the distance r from the satellite to the target... t (1) That is, the distance from the satellite to the center of the ground beam.

[0049] Furthermore, in step S2.2, when n > 1, based on the result obtained from the previous iteration... Solve

[0050]

[0051] Among them, s x s y s z The satellite's position coordinates,

[0052] Compared with the prior art, the present invention has at least one of the following advantages:

[0053] (1) This invention proposes a four-station iterative positioning method for aerial targets based on satellite radiation sources. It uses reference radar distance measurement estimation as the initial value for iteration. By decomposing the relationship between redundant parameters and the three-dimensional position of the target, and based on the weighted least squares algorithm, it obtains high-precision positioning results of aerial targets. This reduces the requirement for the number of receiving stations for the joint estimation of the target's three-dimensional position and reference measurement, and has good prospects for engineering applications.

[0054] (2) This invention proposes a three-station iterative positioning method for aerial targets based on satellite radiation sources. It uses reference radar distance measurement and target height prior information as initial values ​​for iteration. By decomposing the relationship between redundant parameters and the target's planar position, and based on the weighted least squares algorithm, it obtains high-precision positioning results for aerial targets. Based on the four-station iterative positioning, it further reduces the requirement for the number of receiving stations and has good engineering application prospects. Attached Figure Description

[0055] Figure 1 This is a flowchart of the TDOA iterative positioning method for aerial targets based on satellite radiation sources according to the present invention. Detailed Implementation

[0056] The features and advantages of the present invention will become clearer and more apparent from the following detailed description.

[0057] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments. Although various aspects of embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless specifically indicated otherwise.

[0058] This invention employs mainstream indirect positioning to study the problem of air target localization and proposes an iterative air target localization method based on specific application backgrounds. Specifically, this invention combines measurement information from single and multiple stations to fill the gaps in the identifiable conditions of parameter vectors, proposing an iterative air target localization method under conditions with fewer receiving observation stations, providing high-precision target localization for fire control, reconnaissance, guidance, and other applications.

[0059] The TDOA iterative localization method for airborne targets based on satellite radiation sources in this invention can be applied to the field of radar-based airborne target localization. First, radar prior information is used as the initial value for iteration. By decomposing the relationship between redundant parameters and the target position, and based on a weighted least squares algorithm, a high-precision localization result for the airborne target is obtained. This reduces the requirement for a certain number of receiving stations for joint estimation of the target's three-dimensional position and reference measurements, and has good engineering application prospects. Figure 1 The implementation steps are as follows:

[0060] Step 1: Multi-station TDOA measurement modeling. The specific method is as follows:

[0061] Assume a distributed multi-station radar system consists of M airborne radars, with the navigation position of the i-th radar located at... The actual location of this radar i and navigation location The relationship is In the formula Δs i This represents the radar's position error. The target to be detected in the scene is located at u = [x, y, z]. T The true distance from the target to the i-th radar can then be expressed as:

[0062] r i =||us i ||2

[0063] Furthermore, the distance r from the target to the i-th radar i The difference between the distance r1 and the distance to the reference radar can be written as

[0064] r i1 =r i -r1

[0065] The difference pseudo-moment can then be expressed as: Where c represents the speed of light, Δt i1 This represents the measurement delay error.

[0066] Rearranging the above expression into r i1 +r1=r i By squaring both sides, we can obtain

[0067]

[0068] In the formula

[0069] Step 2 includes two parallel schemes: TDOA four-station iterative positioning and TDOA three-station iterative positioning.

[0070] (1) TDOA four-station iterative positioning, the specific method is as follows:

[0071] Considering the limited number of receiving stations, an iterative approach is adopted to handle the estimation of target position and reference radar range. First, the range estimate from the reference radar to the target (i.e., single-station range estimate) is obtained. For the nth iteration, combine the measurements r of all radars. i1 achievable

[0072] ε1(n)=h1(n)-G1u(n+1)

[0073] In the formula

[0074]

[0075]

[0076] By minimizing The least squares estimate of u in the nth iteration can be obtained.

[0077]

[0078] In the formula, W1(n) represents the weighting matrix of the nth iteration.

[0079] The error term ε1(n) composed of error variables is:

[0080]

[0081] In the formula

[0082]

[0083] When n=1,

[0084] When n > 1

[0085] in This represents the single-base distance from the i-th radar to the target in the nth iteration. Since it can be obtained through single-station distance estimation, W1(n) can be expressed as:

[0086]

[0087] In the formula Q t =c 2 E [ΔtΔt] T ], Q p =c 2 E[ΔsΔs T ], where c represents the speed of light and E represents the related operations. Based on the estimated target position, the distance estimate for the (n+1)th iteration can be obtained.

[0088]

[0089] This leads to an iterative estimation method for the target's three-dimensional position and the range of a single reference radar station.

[0090] The total number of iterations is determined by the computational complexity of the algorithm and the target position error.

[0091] (2) TDOA three-station iterative positioning, the specific method is as follows:

[0092] For three-station TDOA target localization, the parameter identifiability condition is not met. An iterative approach is adopted. First, the distance and altitude (Z coordinate) from a single station (reference radar) to the target are estimated. Then, a system of linear equations is constructed, and weighted least squares are used to estimate the target's X and Y coordinates. This forms an iterative method for distance-target altitude and target XY coordinates. All coordinate systems in this invention are local coordinate systems (Northeast-Sky coordinate system). Specifically, first, the estimated distance from the reference radar to the target is obtained. and height estimation For the nth iteration, the modified system of linear equations is:

[0093]

[0094] In the formula

[0095]

[0096]

[0097] Based on the estimated target location, the distance estimate for the (n+1)th iteration can be obtained.

[0098]

[0099] In the formula Further combining single-station angle estimation yields... This leads to an iterative method for determining the distance, target height, and target XY coordinates.

[0100] The total number of iterations is determined by the computational complexity of the algorithm and the target position error.

[0101] The effects of the present invention will be further illustrated below using simulation data.

[0102] Assuming a satellite orbital altitude of 36,000 km and a satellite position error of 100 m, the positions of the four UAVs are [350e3, 100e3, 23e3] m, [400e3, 300e3, 22e3] m, [200e3, 100e3, 24e3] m, and [400e3, 300e3, 25e3] m, and the target position is [300e3, 200e3, 12e3] m, with a target signal-to-noise ratio set to 25 dB. Table 1 shows the target positioning accuracy for single-station, three-station, and four-station methods. It can be seen that, under the condition of a limited number of receiving stations, both the three-station and four-station TDOA iterative positioning methods can estimate the target's location with high accuracy.

[0103] Table 1 Comparison of target positioning accuracy at single, three, and four stations.

[0104] type Single station Three stations Four stations Positioning accuracy (m) 3800 1631 973

[0105] Simulation analysis conclusions: This invention addresses the air target localization problem with only four and three airborne receiving radars by employing an iterative approach to reduce the radar number requirement of the weighted least squares method, thus satisfying the identifiable conditions for air target localization. Even with radar position errors, it can still achieve target localization relatively well.

[0106] The present invention has been described in detail above with reference to specific embodiments and exemplary examples; however, these descriptions should not be construed as limiting the present invention. Those skilled in the art will understand that various equivalent substitutions, modifications, or improvements can be made to the technical solutions and embodiments of the present invention without departing from the spirit and scope of the invention, and all such modifications and improvements fall within the scope of the present invention. The scope of protection of the present invention is defined by the appended claims.

[0107] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A method for iterative TDOA localization of aerial targets based on satellite radiation sources, characterized in that, include: A multi-station TDOA measurement model is constructed, which is the relationship between the measurement values ​​of each positioning radar and the target position. Based on the multi-station TDOA measurement model, a four-station iterative positioning model and a three-station iterative positioning model for TDOA are constructed. Based on the four-station iterative positioning model and the three-station iterative positioning model for TDOA, four-station target positioning and three-station target positioning are respectively realized. The TDOA four-station iterative positioning model and the TDOA three-station iterative positioning model include the relationship between the distance estimation of the reference radar to the target and the target position estimation; The TDOA four-station iterative positioning model includes: ； ； ； ； when n When =1, ; when n When >1, ; ； in, n Representing the n iteration n ≥1, For the first i Differential pseudorange of the local positioning radar, For the first n The distance estimate from the reference radar to the target used in the next iteration. For the reference radar navigation position, No. n The three-dimensional target position estimate obtained in the second iteration. For the first The weighting matrix of the next iteration. For the first n During the nth iteration i The distance estimation for the radar to reach the target. For the first n The distance estimate from the reference radar to the target obtained in the next iteration. , c represents the speed of light. Due to time error, This refers to the positional error of the drone; The TDOA three-station iterative positioning model includes: ； ； ； ； ； in, n Representing the n iteration n ≥1, For the first n Error term of the next iteration For the first i Differential pseudorange of the local positioning radar, For the first n The two-dimensional target position estimate obtained in the second iteration, ( , ) is the first i The two-dimensional position coordinates of the positioning radar, , ( ) represents the two-dimensional position coordinates of the reference radar. For the first n In the next iteration, the distance estimate from the radar to the target is referenced. For the reference radar navigation position, No. n The three-dimensional target position estimate obtained in the second iteration. For the first n The distance estimate from the reference radar to the target obtained in the next iteration. For the first n The two-dimensional target position estimate obtained in the second iteration x and y coordinate.

2. The iterative TDOA positioning method for aerial targets based on satellite radiation sources according to claim 1, characterized in that, Assume a distributed multi-station radar system includes The radar consists of two radars, of which the first radar is a reference radar, and the second... The radar is a positioning radar; ≥2, ; The multi-station TDOA measurement model is as follows: ； in, To achieve the goal of i The distance of the positioning radar. For the distance from the target to the reference radar, the first i Measurements from the local positioning radar , , , For the first i The actual location of the radar. To reference the actual radar location, The target location.

3. The iterative positioning method for aerial targets based on satellite radiation sources according to claim 2, characterized in that, ； in, For the first i The navigation position of the positioning radar. For the first i Position error of the local positioning radar; 。 4. The iterative positioning method for aerial targets based on satellite radiation sources according to claim 1, characterized in that, The methods for achieving four-station target localization based on the TDOA four-station iterative localization model include: S1.1 Acquisition ; S1.2 According to get ,according to and get ,according to , and get ; S1.3 Based on the results obtained in the previous step get ; S1.4 Determine if the preset number of iterations has been reached. If the preset number of iterations has been reached, output the current value. Complete the four-station target localization. If the preset number of iterations has not been reached, return to step S1.2 and use... Proceed to the next iteration.

5. The iterative positioning method for aerial targets based on satellite radiation sources according to claim 4, characterized in that, In the TDOA four-station iterative positioning model, ;in, For dual-station detection range, For the first n The distance from the satellite to the target at the next iteration; In the first iteration, the distance from the satellite to the target... That is, the distance from the satellite to the center of the ground beam.

6. The iterative TDOA positioning method for aerial targets based on satellite radiation sources according to claim 1, characterized in that, The methods for achieving four-station target localization based on the TDOA four-station iterative localization model include: S2.1 Acquisition and , This is the height estimate of the target during the first iteration; S2.2 According to get ,according to , and get ; S2.3 According to and get ; S2.4 According to ,get ; S2.5 Determines whether the preset number of iterations has been reached. If the preset number of iterations has been reached, outputs the current value. Complete the three-station target localization. If the preset number of iterations has not been reached, return to step S2.2 and use... Proceed to the next iteration.

7. The TDOA iterative positioning method for aerial targets based on satellite radiation sources according to claim 1, characterized in that, In the TDOA three-station iterative positioning model, ;in, For dual-station detection range, For the first n The distance from the satellite to the target at the next iteration; In the first iteration, the distance from the satellite to the target... That is, the distance from the satellite to the center of the ground beam.

8. The iterative positioning method for aerial targets based on satellite radiation sources according to claim 7, characterized in that, In step S2.2, when When >1, based on the result of the previous iteration Solve : ； in, , , The satellite's position coordinates, , .

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