Target cooperative positioning method for air-ground integrated aircraft

Abstract

The embodiment of the invention provides a space-ground integrated aircraft target cooperative positioning method, which comprises the following steps: obtaining measurement element data of an aircraft target, the measurement element data comprising space-based measurement element data based on a space-based time difference positioning system and ground-based measurement element data based on a ground-based time difference positioning system; constructing a cooperative positioning measurement model; according to the measured metadata and the cooperative positioning measurement model, carrying out nonlinear iterative positioning calculation on the target position of the aircraft, and eliminating error sensitive features in the nonlinear iterative positioning calculation process; and determining the target trajectory of the aircraft target according to the positioning calculation result. According to the technical scheme, under the background of cooperative positioning of the space-based time difference positioning system and the ground-based time difference positioning system, the influence factors on the positioning precision in different feature dimensions are determined, a cooperative positioning algorithm based on error sensitive feature selection is provided, and the target track precision is remarkably improved.

Description

Technical Field

[0001] The present invention relates to the field of measurement and positioning technology, and in particular to an aircraft target positioning method, and more particularly to a ground-ground integrated aircraft target collaborative positioning method. Background Art

[0002] Tracking and monitoring long-range aircraft targets in the entire time domain to form unified, stable, and accurate target track information is an important basis for further identity recognition, track prediction, and intention analysis, and is a key requirement in the fields of national defense, aerospace, etc.

[0003] As a passive positioning method, passive positioning systems utilize multiple base stations to synchronously receive electromagnetic radiation signals from a target. They offer advantages such as long detection range, good concealment, and strong survivability. Currently, passive positioning systems primarily utilize measurement information including received signal strength (RSS), angle of arrival (AOA), time of arrival (TOA), and time difference of arrival (TDOA). While RSS offers advantages such as simple calculation and low equipment complexity, detecting the energy of the received signal can be challenging in long-range positioning. AOA is highly dependent on angle measurement accuracy, and the impact of angle measurement errors is exponentially magnified at long distances. TOA's positioning accuracy relies on clock synchronization between the station and the target radiation source, which cannot be achieved in some practical scenarios (such as non-cooperative target positioning). TDOA, on the other hand, utilizes the time difference between the radiation signal source reaching different stations. It requires less demanding measurement equipment, its accuracy is less affected by distance, and it does not require clock synchronization between the station and the target radiation source. Therefore, considering the actual application needs and application scenarios, long-distance space target positioning mainly relies on the passive time difference positioning system.

[0004] In a time-of-day positioning system, each TDOA forms a cluster of hyperbolas with its corresponding observation station, and positioning is achieved through hyperbolic intersection. Although some classic algorithms, such as the constrained weighted least squares algorithm, the CHAN algorithm, and the conjugate gradient algorithm, can be used to solve this problem, generating stable and accurate positioning results from a time-of-day positioning system remains a significant challenge. In fact, compared to spherical intersection, the unique structure of hyperbolic intersection makes positioning results more susceptible to factors such as atmospheric refraction error, random measurement error, and equipment system error, leading to problems such as low positioning accuracy, local interruptions, and discontinuous target tracks.

[0005] Refined data processing is an effective way to improve the stability and accuracy of positioning results. For example, if the noise is additive Gaussian, the Gauss-Markov estimator can achieve the Cramer-Rao lower bound. In addition, information fusion has been used to process positioning results from different positioning systems to further improve target positioning accuracy and generate a unified target track.

[0006] Despite extensive research on passive time-of-difference positioning systems, several practical needs remain to be addressed. Current tracking and positioning of aerial targets in the open ocean typically involves ballistic-level data fusion between space-based and ground-based passive time-of-difference positioning systems. This involves separately calculating the target track and then performing a weighted fusion to improve positioning accuracy and achieve target track enhancement. However, due to the varying quality of measurement data from space-based and ground-based passive positioning systems, significant discrepancies exist between the positioning results of the two systems. Furthermore, differences in system configurations lead to significant differences in positioning accuracy across different dimensions (latitude, longitude, and elevation), which are not accounted for by classic fusion methods. Therefore, while the two systems can operate independently, inconsistent results, unstable tracks, and substandard accuracy make it difficult to generate unified, stable, and accurate target track information.

[0007] Therefore, how to improve the fusion process of the space-based time difference positioning system and the ground-based time difference positioning system to obtain a unified, stable and accurate aircraft target track is a problem that needs to be solved. Summary of the Invention

[0008] The embodiment of the present invention provides a space-ground integrated aircraft target collaborative positioning method, which is used to improve the fusion process of a space-based time difference positioning system and a ground-based time difference positioning system to obtain a unified, stable and accurate aircraft target track.

[0009] To achieve the above-mentioned purpose, an embodiment of the present invention provides a space-ground integrated aircraft target collaborative positioning method, including: obtaining measurement data of the aircraft target, the measurement data including space-based measurement data based on a space-based time difference positioning system, and ground-based measurement data based on a ground-based time difference positioning system (the measurement data is directly obtained through measurement); enhancing the measurement data through a spline function to obtain enhanced measurement data, the enhancement processing refers to removing outliers in the measurement data and filling missing values ​​in the measurement data; constructing a collaborative positioning measurement model according to the measurement principle; performing nonlinear iterative positioning solution on the aircraft target position according to the enhanced measurement data and the collaborative positioning measurement model, and eliminating error-sensitive features in the nonlinear iterative positioning solution process; determining the target trajectory of the aircraft target according to the positioning solution result.

[0010] The above technical solution has the following beneficial effects:

[0011] In the context of collaborative positioning of space-based and ground-based passive time-of-day positioning systems, this application determines the influencing factors of different feature dimensions (latitude, longitude and altitude) on positioning accuracy, and proposes a collaborative positioning algorithm based on error-sensitive feature selection. The good solution performance of the collaborative algorithm is demonstrated through theoretical derivation and simulation experiments. When the target track is jointly solved with data methods such as spline smoothing-based measurement enhancement and spline constraint-based track modeling, the target track accuracy is significantly improved, which has great practical significance for target positioning solution in actual engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0013] Figure 1 This is a flow chart of a ground-ground integrated aircraft target collaborative positioning method according to an embodiment of the present invention;

[0014] Figure 2 Schematic diagram of integrated space-ground collaborative positioning in an embodiment of the present invention;

[0015] Figure 3 is a schematic diagram of the steps of the collaborative positioning algorithm in an embodiment of the present invention;

[0016] Figure 4 It is the enhanced result of the measurement data of the space-based time difference positioning system in the simulation experiment;

[0017] Figure 5 It is the enhanced result of the ground-based time difference positioning system measurement data in the simulation experiment;

[0018] Figure 6 It is the point-by-point positioning result under the original data in the simulation experiment;

[0019] Figure 7 It is the point-by-point positioning result after enhancing the data in the simulation experiment;

[0020] Figure 8 It is the integrated space-ground positioning result after enhancing the data in the simulation experiment;

[0021] Figure 9 This is the result of integrated space-ground positioning under spline constraints in the simulation experiment;

[0022] Figure 10It is the result of latitude calculation accuracy under different algorithms in the simulation experiment;

[0023] Figure 11 It is the calculation accuracy result of longitude under different algorithms in the simulation experiment;

[0024] Figure 12 It is the result of the elevation calculation accuracy under different algorithms in the simulation experiment;

[0025] Figure 13 is the overall positioning error under different algorithms in the simulation experiment;

[0026] Figure 14 is the positioning error bar under different positioning algorithms in the simulation experiment. DETAILED DESCRIPTION

[0027] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. 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 are within the scope of protection of the present invention.

[0028] like Figure 1 As shown, an embodiment of the present invention provides a ground-ground integrated aircraft target collaborative positioning method, comprising:

[0029] S101, obtaining measurement data of an aircraft target, wherein the measurement data includes space-based measurement data based on a space-based time difference positioning system and ground-based measurement data based on a ground-based time difference positioning system;

[0030] S102, performing enhancement processing on the measurement data using a spline function to obtain enhanced measurement data, wherein the enhancement processing refers to removing outliers in the measurement data and filling missing values ​​in the measurement data;

[0031] S103, constructing a collaborative positioning measurement model;

[0032] S104, performing nonlinear iterative positioning solution on the aircraft target position based on the enhanced measurement data and the collaborative positioning measurement model, and eliminating error-sensitive features during the nonlinear iterative positioning solution process;

[0033] S105: Determine the target trajectory of the aircraft target according to the positioning solution result.

[0034] Furthermore, the collaborative positioning measurement model determined in step S103 is in the form of:

[0035]

[0036] Among them, p represents the position of the aircraft target, Y s Y is the space-based measurement data, g is the ground-based measurement data, F s (p) is the measurement equation of the space-based time difference positioning system, specifically:

[0037]

[0038] F g (p) is the measurement equation of the ground-based time difference positioning system, specifically:

[0039]

[0040] Where, is the position of the i-th satellite, is the position of the satellite ground station corresponding to the i-th satellite, is the position of the i-th ground base station, and the positions of these satellites, satellite ground stations and ground base stations are all known quantities.

[0041] Λ s is the measurement noise covariance matrix corresponding to the space-based measurement data, Λ g is the measurement noise covariance matrix corresponding to the ground-based measurement data. Both noise covariance matrices are prior information and are known quantities.

[0042] Furthermore, before step S103, the method further includes:

[0043] The following method is used to eliminate the correlation between the enhanced post-test metadata:

[0044]

[0045] Where,

[0046]

[0047] Furthermore, in step S104, the following nonlinear iterative formula is used to perform nonlinear iterative positioning solution on the target position of the aircraft:

[0048]

[0049] Where p k+1 represents the target position of the aircraft at the k+1th iteration, p k represents the target position of the aircraft at the kth iteration;

[0050] Eliminating error-sensitive features during the nonlinear iterative positioning solution process described in step S104 specifically includes:

[0051] Construct the Jacobian matrix in the nonlinear iterative process, and perform singular value decomposition on the Jacobian matrix in the nonlinear iterative process to obtain a diagonal matrix Σ containing singular values s and the diagonal matrix Σ g , wherein the Jacobian matrix in the nonlinear iterative process includes F s (p) Jacobian matrix J with respect to position s , and F g (p) Jacobian matrix J with respect to position g ,

[0052]

[0053] Singular values ​​satisfy

[0054] Among them, U s ,U g ,V s ,V g All are obtained through singular value decomposition and are orthogonal matrices with corresponding dimensions;

[0055] The diagonal matrix Σ s The smallest singular value in the diagonal matrix Σ g The minimum singular value in is used as the error-sensitive feature, and the error-sensitive feature is replaced by 0 to eliminate the influence, and the updated diagonal matrix is ​​obtained. And the updated diagonal matrix

[0056]

[0057] Furthermore, in the aforementioned nonlinear iterative positioning solution process for the target position of the aircraft, the iteration stopping condition is:

[0058] ||p k+1 -p k ||<ε

[0059] Or k = k max ,

[0060] Where ε is the preset first convergence threshold, k max The first maximum number of iterations is preset.

[0061] Furthermore, the method for collaborative positioning of a ground-ground integrated aircraft target further includes: adding the following target trajectory constraint condition to the collaborative positioning measurement model (the purpose of introducing the constraint condition is to ensure that the target track is smooth and conforms to the constraints of the laws of physics):

[0062]

[0063] Where, T i For the time interval [t1,t n ] set up γ control nodes, and are the model parameters to be determined, the superscripts x, y, and z are the three-dimensional coordinates of the target position p of the aircraft in space, and ΔT i =T i+1 -T i is the node distance, B(·) is the cubic standard B-spline function, which is a non-negative function on the interval [-2,2], specifically:

[0064]

[0065] Furthermore, the model parameters to be determined and Determine according to the following process:

[0066] All the model parameters to be determined and Written in vector form as follows:

[0067] β=[b x ,b y ,b z ];

[0068] According to the collaborative positioning measurement model at time t, the Jacobian matrix J of the collaborative positioning measurement model with respect to the parameter β is constructed. t,β , specifically:

[0069]

[0070] Where, represents the Kronecker product, B γ =B(T γ ) is determined according to the cubic standard B-spline function;

[0071] Calculate all actual measurement times τ1,τ2,…,τ n , let t=τ1,τ2,…,τ n ,, then according to the Jacobian matrix J t,β Get the Jacobian matrix in the second nonlinear iterative process Specifically:

[0072]

[0073] According to the Jacobian matrix And the following nonlinear iterative formula is used to perform nonlinear iterative positioning solution on the vector β:

[0074]

[0075] Where,

[0076]

[0077] Afterwards, the model parameters to be determined are determined according to the solution results of the vector β. and

[0078] Furthermore, in the aforementioned nonlinear iterative positioning solution process for the vector β, the iteration stopping condition is:

[0079] or,

[0080] k=k 2max ;

[0081] Where ε2 is the preset second convergence threshold, k 2max The second maximum number of iterations.

[0082] The following is a detailed description of the above method:

[0083] 1. The time difference positioning system integrating the sky and the earth:

[0084] 1.1 Coordinate system conversion and unification:

[0085] The space-based time difference positioning system is composed of satellites and their ground stations, while the ground-based time difference positioning system is composed of multiple ground base stations. Usually, the coordinates of the satellite are given in the ECEF coordinate system. The ECEF coordinate system takes the center of the earth O as the origin, the OX axis points from the center of the earth to the intersection of the starting meridian and the equator, the OY axis points from the center of the earth to the intersection of the 90-degree longitude and the equator, and the OZ axis points from the center of the earth to the North Pole. The coordinates of the satellite ground station and the ground base station are usually given in the WGS-84 coordinate system, that is, the latitude, longitude and elevation of the point, referred to as "latitude, longitude and elevation". The conversion relationship between ECEF coordinates and WGS-84 coordinates is:

[0086]

[0087] Where [B, L, H] is the target's "latitude, longitude, and altitude" in the WGS-84 coordinate system, [x, y, z] is the target's corresponding coordinate in the ECEF coordinate system, a is the Earth's semi-major axis, and e is the Earth's eccentricity.

[0088] After unifying the coordinates, assuming that the target's "latitude, longitude, and altitude" in the WGS-84 coordinate system is [B, L, H], the corresponding coordinates in the ECEF coordinate system are p = [x, y, z] T , the ECEF coordinates of the i-th satellite are The ECEF coordinates of the satellite ground station corresponding to the i-th satellite are: The ECEF coordinates of the i-th ground base station are

[0089] 1.2. Measurement model of time difference positioning system:

[0090] The time difference positioning system uses multiple base stations to synchronously receive signals from the same radiation source (target) and estimates the position of the radiation source (target) based on the propagation delay difference of the signals.

[0091] like Figure 2 As shown in Figure 1, the space-based passive time difference positioning system (abbreviated as space-based time difference positioning system) uses high-orbit (or low-orbit) satellites to forward target signals to achieve beyond-horizon distant sea target positioning. Its positioning model is expressed as:

[0092]

[0093] Where c is the speed of light, ||·||2 represents the 2-norm of the vector, is the time difference measurement of the forwarding signal between the i-th satellite and the i+1-th satellite, is the transmission distance of the target signal forwarded by the i-th satellite to the corresponding ground station, r i s (p) is the distance from the target to the i-th satellite, is the distance between the i-th satellite and its corresponding satellite ground station, is the satellite measurement error, which usually satisfies

[0094] Similarly, the ground-based passive time difference positioning system (abbreviated as ground-based time difference positioning system) method uses ground base stations to locate aerial targets. The positioning model is expressed as:

[0095]

[0096] Where r i g (p) is the distance from the target to the i-th ground base station, is the ground station measurement error, satisfying

[0097] Of these two types of time-difference positioning systems, space-based passive positioning systems have the advantage of a larger monitoring area. However, due to the influence of constellation geometry and ephemeris deviations, in addition to observation errors, there may also be a certain degree of system parameter deviation, resulting in relatively low positioning accuracy. In contrast, ground-based passive positioning systems have the advantage of high positioning accuracy, as system parameters such as the site of the ground base station and processing delay can be precisely calibrated. However, due to the limited line-of-sight of the Earth's ellipsoid, the monitoring area is smaller.

[0098] Through the integrated space-ground collaborative positioning method, the measurement data (or observation results) of the two positioning methods are integrated to effectively improve the positioning accuracy of aerial targets and enhance the track of important targets.

[0099] 2. Positioning solution method and performance evaluation:

[0100] 2.1. Nonlinear point-by-point solution method:

[0101] In model (2), It is independent of the position of the target, so the notation is introduced in model (3) The measurement models of the space-based time difference positioning system and the ground-based time difference positioning system can be unified in form. In this case, the superscripts s and g in the model can be ignored, and the system model is unified as follows:

[0102]

[0103] Where,

[0104]

[0105] It is worth noting that there is a correlation between the measurements of the time difference positioning system, namely:

[0106]

[0107] Where, Λ i,j represents the element in row i and column j of the covariance matrix Λ. In particular, when σ1=σ2=…=σ m+1 =σ, the covariance matrix Λ has the following form:

[0108]

[0109] According to the Gauss-Newton iteration formula, the iterative process of the nonlinear generalized least squares estimation of the target position p is as follows:

[0110]

[0111] Where λ is the adjustable step size, which can usually be directly selected as λ = 1. is the Jacobian matrix, specifically:

[0112]

[0113] The termination condition of iterative formula (6) is usually set as:

[0114] ||p k+1 -p k ||<ε or k=k max (8)

[0115] Where ε is the preset convergence threshold, k max is the preset maximum number of iterations.

[0116] 2.2 Positioning solution accuracy assessment:

[0117] By iterating formula (6) and termination condition (8), the position estimation of the target in the ECEF coordinate system can be obtained: Since ECEF coordinates correspond to WGS-84 coordinates one by one, the estimated value of the target's "latitude and longitude height" can be uniquely determined according to the conversion relationship (1), which can be recorded as Then, the error transfer relationship between ECEF coordinates and WGS-84 coordinates is analyzed in detail, and the positioning solution accuracy under the two types of coordinate systems is given.

[0118] 2.2.1 ECEF coordinate accuracy assessment:

[0119] In a single measurement process, the ECEF coordinate positioning error caused by the observation error W is recorded as:

[0120]

[0121] Consider the first-order Taylor expansion of F(p), we have:

[0122]

[0123] Where, Represents a high-order epsilon of the ECEF coordinate error.

[0124] According to the iterative formula (6) and formula (10), the transfer equation from measurement error to positioning error can be obtained as follows:

[0125]

[0126] In the absence of unmodeled systematic errors, the positioning error Δp ​​is usually considered to be zero-mean, that is:

[0127]

[0128] At this time, ignore the high-order small quantities After that, the covariance matrix P of the positioning error Δp ​​can be obtained as:

[0129]

[0130] In engineering practice, the modulus of Δp is usually used to directly describe the positioning accuracy ACC (Accuracy). The relationship between this indicator and the covariance matrix P is as follows:

[0131]

[0132] Where Tr[·] represents the trace of the matrix. Subsequently, the relationship between the station configuration and positioning accuracy is determined.

[0133] Theorem 1: The error transfer matrix determined only by the configuration is defined as:

[0134]

[0135] Where, the superscript E represents the WGS-84 coordinate system. Then, the geometric dilution of precision (GDOP) of the space-ground time difference positioning system is:

[0136]

[0137] At this time, the positioning error of the system satisfies the following inequality:

[0138]

[0139] Where λ max is the maximum eigenvalue of the covariance matrix Λ.

[0140] In Theorem 1, the GDOP index established by Equation (16) is only related to the station configuration and has nothing to do with the observation error. In addition, inequality (17) gives the upper bound of the positioning accuracy of the time difference positioning system, which is determined by the GDOP index and the observation error. Therefore, the GDOP index can be used as a key indicator for evaluating system performance.

[0141] 2.2.2. WGS-84 coordinate accuracy assessment:

[0142] In engineering practice, the target positioning results also need to be given in the form of "latitude, longitude and height" in the WGS-84 coordinate system. Therefore, additional accuracy assessment is required for the WGS-84 coordinates.

[0143] It is worth noting that the WGS-84 coordinate solution error caused by the observation error W is:

[0144]

[0145] Since the accuracy evaluation results of ECEF coordinates have been given in the previous section, we only need to consider the total differential of the coordinate transformation relationship (1) to establish the transfer relationship between the ECEF coordinate solution error and the WGS-84 coordinate solution error.

[0146] In fact,

[0147]

[0148] where represents the high-order minima of the WGS-84 coordinate error; and:

[0149]

[0150] Where,

[0151] Similarly, ignoring high-order small quantities Then, combining formula (11) and formula (19), we can get:

[0152]

[0153] because It is naturally a reversible matrix, based on which the positioning error in the WGS-84 coordinate system can be obtained as [ΔB, ΔL, ΔH] T The covariance matrix of for:

[0154]

[0155] Where,

[0156]

[0157] Similar to Theorem 1, the influence of station configuration on positioning accuracy in the WGS-84 coordinate system can be obtained.

[0158] Theorem 2: In the WGS-84 coordinate system, the error transfer matrix determined only by the configuration is defined as:

[0159]

[0160] Where the superscript w represents the WGS-84 coordinate system. Then, the WGS-84 coordinate error satisfies the following inequality:

[0161]

[0162] Where, is the matrix G w The element at row i and column i.

[0163] It is worth noting that, unlike ECEF coordinates, the "latitude, longitude, and altitude" units in the WGS-84 coordinate system are inconsistent, so their accuracy assessments need to be performed separately.

[0164] 3. Track-enhanced collaborative positioning algorithm:

[0165] This section starts from the three levels of "data", "model" and "algorithm" to construct a collaborative positioning algorithm with track enhancement.

[0166] 3.1. Element enhancement based on spline smoothing:

[0167] In a space-ground integrated time-of-day positioning system, measurement data often contain missing values ​​and outliers, resulting in low measurement quality and severely impacting positioning accuracy. Therefore, this section employs spline smoothing for data enhancement, enabling the prediction of missing data and the detection of outliers.

[0168] Model (4) gives a single moment measurement model, however, when tracking a moving target, the measurement value is time-varying. Consider the time period [t1,t n ], if there is no ambiguity, we still use Y to represent the measurement data, then:

[0169]

[0170] Where, subscript t i (i=1,2,…,n) represents the time of measurement.

[0171] Since there are correlations between the measurement data, it is necessary to transform the measurement data Y to eliminate these correlations, that is, consider:

[0172]

[0173] After transformation, the matrix Each row of data is unrelated, so each row of data can be processed separately.

[0174] Let's remember the matrix The data in the i-th row is:

[0175]

[0176] Subsequently, spline smoothing is used for data augmentation, that is, considering the following loss function:

[0177]

[0178] Where λ is the preset smoothing parameter, is a natural spline function, which is expressed as:

[0179]

[0180] Where N j (t) is the basis function of the natural spline.

[0181] At this time, the loss function It can be expressed as follows:

[0182]

[0183] Where, the matrix N and Ω N The elements in row j and column k are:

[0184] {N} j,k =N j (t k )

[0185] {Ω N} j,k =∫N″ j (t)N″ k (t)dt

[0186] According to the generalized ridge regression, the estimate of the parameter θ is easily obtained as:

[0187]

[0188] Substituting formula (33) into the original function (31), we can obtain:

[0189]

[0190] Consider the measurement time t k The data reconstruction error at , then:

[0191]

[0192] According to the 3-Sigma principle, it can be detected whether it is an outlier, that is:

[0193]

[0194] Where std[∈(t)] represents the standard deviation of the reconstruction error calculated at all times.

[0195] It is worth noting that after a measurement value is detected as an outlier, it should be removed to recalculate the spline smoothing result until all data used for calculation are detected as normal values.

[0196] After removing all abnormal points, the obtained spline function can be used to enhance the data. k Time (t1≤τ k ≤t n ), the enhanced data is:

[0197]

[0198] Similarly processing other rows, the enhanced data matrix is:

[0199]

[0200] Taking into account the correlation between the restored data, the final enhanced data is:

[0201]

[0202] 3.2. Track modeling based on spline constraints:

[0203] Due to the limitation of physics, the target trajectory will not change suddenly. In order to build a smooth target kinematic model, this application further uses splines to constrain the trajectory. n ] set κ control points on it, recorded as:

[0204] t1=T1<T2<...<T κ =t n (40)

[0205] In [t1,t n ]Add left node T on the left -1 ,T0, in [t1,t n ]Add right node T on the right κ+1 ,T κ+2 , so that it satisfies:

[0206] T -1 <T0<T1<..<T κ <T κ+1 <T κ+2 (41)

[0207] After setting a total of κ control points, the target trajectory can be characterized by a combination of cubic standard B-spline functions, namely:

[0208]

[0209] Where, ΔT i =T i+1 -T i is the node distance, B(·) represents the cubic standard B-spline function, which is a non-negative function on the interval [-2,2], specifically:

[0210]

[0211] In the spline-constrained trajectory model (42), there are a total of 3×k unknown parameters, which are expressed as:

[0212] β=[b x ,b y ,b z ] (44)

[0213] For the measurement equation at time t, its Jacobian matrix is:

[0214]

[0215] Where, Specifically:

[0216]

[0217] Where,

[0218] B k =B(t k ) (47)

[0219] Considering the special form of formula (46), formula (45) can be written as:

[0220]

[0221] Where, Denotes the Kronecker product. Similarly, after considering all moments, the Jacobian matrix of the parameter β in the kth iteration process is:

[0222]

[0223] Where,

[0224]

[0225] Where the superscript (k) represents the kth iteration.

[0226] In summary, similar to formula (6), the iterative algorithm with parameter β is:

[0227]

[0228] Where,

[0229]

[0230] The termination condition of the iteration (51) is set by referring to formula (8). The estimated parameter β is obtained After that, the target track can be obtained according to the following formula:

[0231]

[0232] 3.3. Collaborative localization algorithm based on error-sensitive feature selection:

[0233] Although enhanced data can be used to achieve integrated space-ground positioning based on trajectory modeling, current algorithms do not consider the coordination between the two. Specifically, the different station configurations of "space-based" and "ground-based" systems contribute differently to positioning accuracy. Therefore, a collaborative positioning algorithm is needed to maximize the system's positioning performance.

[0234] In order to analyze the configuration influence of “space-based” and “ground-based”, the measurement model is written as:

[0235]

[0236] Where Y s and Y g Represents the measurement data from “space-based” and “ground-based” respectively, F s (p) and F g (p) are the corresponding measurement equations, Λ s and Λ g are the corresponding measurement noise covariances.

[0237] By transforming formula (28), the correlation between data can be eliminated, that is:

[0238]

[0239] Where,

[0240]

[0241] Combining formula (15), it is easy to obtain the Jacobian matrix of the "space-based" and "ground-based" positioning solution iteration process. Let's decompose its singular value as:

[0242]

[0243] Where U s ,U g ,V s ,V g are orthogonal matrices with appropriate dimensions, Σ s and Σ g Has the following form:

[0244]

[0245] Moreover, the singular values ​​are arranged in descending order, namely:

[0246]

[0247] It is easy to get formula (54) point p k The first-order Taylor expansion at is:

[0248]

[0249] At this time, there are

[0250]

[0251] This means that for "space-based", the measurement error has a great influence on the characteristic direction of the positioning result. Insensitive (because it has a smaller magnification), similarly, for the "foundation", its measurement error has a significant impact on the characteristic direction of the positioning result. Insensitive.

[0252] Based on this, this application proposes a collaborative positioning algorithm based on error-sensitive feature selection. That is, in the feature direction that is not sensitive to errors, the deviation of the positioning result will not significantly affect the residual error of the solution. Therefore, the error-sensitive direction is selected for updating, that is, Σ s and Σ g Replace them with the following and

[0253]

[0254] At this point, the iterative update becomes:

[0255]

[0256] Note that although this formula requires prior information about position, its characteristic direction is insensitive to changes in position. Therefore, after predicting the target's possible range, a collaborative algorithm designed in advance based on the error-sensitive characteristics of "space-based" and "ground-based" positioning can achieve higher positioning accuracy. Furthermore, this algorithm can be used in conjunction with spline-constrained trajectory modeling methods.

[0257] In summary, the collaborative localization algorithm based on error-sensitive feature selection can be summarized as follows: Figure 3 shown.

[0258] The following simulation experiments use the integrated space-ground time difference positioning system as a typical practical application scenario, and compare the performance of different algorithms to further verify the correctness of this method:

[0259] The integrated space-ground time difference positioning system consists of two parts: the space-based passive time difference positioning system and the ground-based passive time difference positioning system. The space-based passive time difference positioning system includes four satellites and a public satellite ground station, while the ground-based passive time difference positioning system includes four ground base stations 1, 2, 3, and 4.

[0260] The specific parameters of the satellite ground station and ground base station are shown in Table 1.

[0261] Table 1 Specific parameters of satellite ground stations and ground base stations

[0262]

[0263] Among them, the satellite ground station in Table 1 refers to the satellite differential signal receiver in the space-based time difference positioning system, which is used to eliminate atmospheric refraction errors and improve the time difference measurement accuracy.

[0264] According to the above model derivation process, the correctness of the method proposed in this application is verified by analyzing the simulation results of three parts, namely, the accuracy evaluation of two types of passive time difference positioning systems in the monitoring area, the measurement enhancement based on spline smoothing, and the comparison of different positioning algorithms.

[0265] 1) Accuracy evaluation results of the monitoring area

[0266] Here, GDOP is used as the accuracy evaluation indicator within the monitoring area. The satellite coordinates in the space-based time difference positioning system are based on the average position during the observation period. The specific ECEF coordinates are shown in Table 2.

[0267] Table 2 Average location parameters during the observation period

[0268]

[0269]

[0270] The GDOP evaluation results for the space-based time difference positioning system in latitude show that the system is more sensitive to measurement errors in latitude. The GDOP evaluation results for the space-based time difference positioning system in elevation show that the accuracy of the space-based time difference positioning system in elevation is uncontrollable.

[0271] The GDOP indicator for ground-based time-of-day positioning systems in latitude shows that they have high positioning accuracy in most areas. However, in certain areas, their accuracy may degrade significantly. The GDOP indicator for elevation shows that while their accuracy in elevation has significantly improved compared to space-based passive time-of-day positioning systems, it still falls short of meeting requirements.

[0272] In order to more clearly compare the positioning accuracy of the two types of positioning systems in different dimensions, the mean GDOP of the two types of positioning systems in different dimensions within the monitoring area was calculated. The results are shown in Table 3.

[0273] Table 3 Mean GDOP in the monitoring area under different configurations

[0274]

[0275] As can be seen from the above table, the space-based time difference positioning system has higher positioning accuracy in longitude, and the ground-based time difference positioning system has higher positioning accuracy in latitude and elevation.

[0276] 2) Element enhancement based on spline smoothing:

[0277] Before performing positioning calculation, the measurement data must be preprocessed first to supplement missing values, eliminate outlier data, and reduce random errors in the measurement data. Here, the spline smoothing method is used for data preprocessing. The enhanced results of the measurement data of the space-based time difference positioning system are as follows: Figure 4 As shown in the figure, the ground-based time difference positioning system measurement data also uses the same data preprocessing method to enhance the data, and the results are as follows: Figure 5 shown. Figure 4 and Figure 5 It shows that the data becomes smoother after processing, which can reduce the impact of random errors on the measurement results.

[0278] At the same time, the residual fluctuation ranges of the differences between the preprocessed data and the original data are approximately 2μs and 10μs respectively. The specific residual statistical results are shown in Table 4.

[0279] Table 4. Residual statistics of data enhancement

[0280]

[0281] From the statistical results in Table 4, we can see that the mean residual between the enhanced data and the original measurement data is close to 0, and the data fluctuation is not large. That is, the data after spline smoothing can effectively reduce the random errors in the measurement data, making the data more continuous, which is an indispensable step in the subsequent target positioning solution.

[0282] 3) Comparison of different positioning algorithms:

[0283] The algorithm comparison mainly considers three algorithms: a single positioning system target track calculation algorithm, a trajectory fusion positioning algorithm, and a collaborative positioning algorithm based on error-sensitive feature selection; and considers three situations: original data, enhanced data, and spline constraints.

[0284] In order to avoid the influence of the initial value of iteration on the results, the initial points of all iterations are selected as: [7, -110, 10 4 ], the control points of all spline constraints are selected as:.

[0285] The results of positioning by both "space-based" and "ground-based" positioning systems Figure 6 and Figure 7 .in, Figure 6 is the positioning result under the original data, Figure 7 It is the positioning result after data enhancement; the horizontal axis in the figure represents the observation time; the sub-graphs of each figure represent the results of latitude (top), longitude (middle) and elevation (bottom) from top to bottom.

[0286] comprehensive Figure 6 and Figure 7The results show that there are significant differences between the "space-based" and "ground-based" solutions in latitude and elevation, but the positioning results in longitude are similar, which is consistent with the accuracy analysis results of GDOP. Therefore, during the iterative solution process, the measurement data of the two systems must be integrated to improve the solution accuracy in all three dimensions.

[0287] The positioning results of the integrated space and sky are shown in Figure 8 and Figure 9 .in, Figure 8 It is the result of fusion positioning and collaborative positioning after data enhancement. Figure 9 It is the result of fusion positioning and collaborative positioning after using spline constraints; similarly, the horizontal axis in the figure represents the observation time; the sub-graphs of each figure represent the results of latitude (top), longitude (middle) and elevation (bottom) from top to bottom.

[0288] comprehensive Figure 8 and Figure 9 The positioning results show that the ballistic data fusion algorithm and the collaborative positioning algorithm based on error-sensitive feature selection achieve similar positioning results in latitude and longitude, which proves the correctness of the algorithm in this application. The difference in elevation between the two algorithms is due to the unstable elevation solution of the two systems, which is consistent with the expectations of the elevation GDOP analysis. Compared with the ballistic data fusion algorithm, the collaborative algorithm in this application has less fluctuation in the solution results and is more stable.

[0289] In order to further verify the accuracy of the collaborative algorithm, the positioning error under different methods was calculated by comparing with the true value of the target track to further measure the performance of each algorithm. Here, the following indicators are used:

[0290]

[0291] Where [B, L, H] is the true "latitude and longitude height" of the target; is the target's "latitude and longitude" estimated by different algorithms; [x, y, z] is the target's true ECEF coordinates; are the target ECEF coordinates estimated by different algorithms; ACC B ,ACC L ,ACC H ,ACC Total They represent latitude error, longitude error, elevation error and total error respectively.

[0292] The error results in different dimensions are shown in Figure 10 、 Figure 11 、 Figure 12 、 Figure 13 , the specific statistical results are shown in Table 5. In addition, Figure 14 The error bars of the total error of the solution results under different algorithms are given.

[0293] These charts show that when the space-based time-of-day positioning system operates alone, its positioning errors in latitude and elevation are relatively large; when the ground-based time-of-day positioning system operates alone, its positioning error in elevation is relatively large. In the integrated space-ground positioning process, both fusion positioning and collaborative positioning significantly improve positioning accuracy. This is due to the improved system configuration achieved through space-ground integration. Fusion positioning still suffers from large elevation positioning errors, while collaborative positioning significantly improves elevation accuracy. Of course, this corresponds to a slight increase in longitude positioning error, which is acceptable.

[0294] Overall, the positioning accuracy of the collaborative positioning algorithm based on error-sensitive feature selection proposed in this application is significantly better than other algorithms; based on data enhancement, the positioning error is 4588 meters, which is better than the 8316 meters of fusion positioning; under spline constraints, the positioning error is 2540 meters, which is better than the 5397 meters of fusion positioning.

[0295] Table 5 Positioning accuracy of latitude and longitude under different solution methods (mean ± standard deviation)

[0296]

[0297] The above description of the disclosed embodiments is intended to enable any person skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other embodiments without departing from the spirit and scope of the present disclosure. Therefore, the present disclosure is not limited to the embodiments presented herein but is intended to be consistent with the broadest scope of the principles and novel features disclosed herein.

[0298] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for collaborative positioning of space-ground integrated aircraft targets, characterized in that: include: Acquiring measurement data of an aircraft target, the measurement data including space-based measurement data based on a space-based time difference positioning system and ground-based measurement data based on a ground-based time difference positioning system; Performing enhancement processing on the measurement data by using a spline function to obtain enhanced measurement data, wherein the enhancement processing refers to removing outliers in the measurement data and filling missing values ​​in the measurement data; Constructing a co-location measurement model; performing a nonlinear iterative positioning solution on the target position of the aircraft based on the enhanced measurement data and the collaborative positioning measurement model, and eliminating error-sensitive features during the nonlinear iterative positioning solution process; The target trajectory of the aircraft target is determined based on the positioning solution results.

2. The method for coordinated positioning of a ground-ground integrated aircraft target according to claim 1, wherein: The co-location measurement model is in the form of: Among them, p represents the position of the aircraft target, Y s Y is the space-based measurement data, g is the ground-based measurement data, F s (p) is the measurement equation of the space-based time difference positioning system, specifically: F g (p) is the measurement equation of the ground-based time difference positioning system, specifically: Where, is the position of the i-th satellite, is the position of the satellite ground station corresponding to the i-th satellite, is the position of the i-th ground base station; Λ s is the measurement noise covariance matrix corresponding to the space-based measurement data, Λ g is the measurement noise covariance matrix corresponding to the ground-based measurement data.

3. The method for coordinated positioning of a ground-ground integrated aircraft target according to claim 2, wherein: Before performing nonlinear iterative positioning solution on the aircraft target position according to the enhanced measurement data and the collaborative positioning measurement model, the method further includes: The following method is used to eliminate the correlation between the enhanced post-test metadata: Where, 4. The method for coordinated positioning of a ground-ground integrated aircraft target according to claim 3, wherein: The following nonlinear iterative formula is used to perform nonlinear iterative positioning solution on the target position of the aircraft: Where p k+1 represents the target position of the aircraft at the k+1th iteration, p k represents the target position of the aircraft at the kth iteration; Eliminating error-sensitive features during the nonlinear iterative positioning solution process specifically includes: Construct the Jacobian matrix in the nonlinear iterative process, and perform singular value decomposition on the Jacobian matrix in the nonlinear iterative process to obtain a diagonal matrix Σ containing singular values s and the diagonal matrix Σ g , wherein the Jacobian matrix in the nonlinear iterative process includes F s (p) Jacobian matrix J with respect to position s , and F g (p) Jacobian matrix J with respect to position g , Singular values ​​satisfy Among them, U s ,U g ,V s ,V g All are obtained through singular value decomposition and are orthogonal matrices with corresponding dimensions; The diagonal matrix Σ s The smallest singular value in the diagonal matrix Σ g The minimum singular value in is used as the error-sensitive feature, and the error-sensitive feature is replaced by 0 to eliminate the influence, and the updated diagonal matrix is ​​obtained. And the updated diagonal matrix 5. The method for coordinated positioning of a ground-ground integrated aircraft target according to claim 4, wherein: During the nonlinear iterative positioning solution of the aircraft target position, the iteration stop condition is: ||p k+1 -p k ||<e Or k = k max , Where ε is the preset first convergence threshold, k max The first maximum number of iterations is preset.

6. The method for coordinated positioning of a ground-ground integrated aircraft target according to claim 4, wherein: Also includes: The following target trajectory constraints are added to the collaborative positioning measurement model: Where, T i For the time interval [t1,t n ] set up γ control nodes, and are the model parameters to be determined, the superscripts x, y, and z are the three-dimensional coordinates of the target position p of the aircraft in space, and ΔT i =T i+1 -T i is the node distance, B(·) is the cubic standard B-spline function, which is a non-negative function on the interval [-2,2], specifically:

7. The method for coordinated positioning of a ground-ground integrated aircraft target according to claim 6, wherein: The model parameters to be determined and Determine according to the following process: All the model parameters to be determined and Written in vector form as follows: β=[b x ,b y ,b z ]; According to the collaborative positioning measurement model at time t, the Jacobian matrix J of the collaborative positioning measurement model with respect to the parameter β is constructed. t,β , specifically: Where, represents the Kronecker product, B γ =B(T γ ) is determined according to the cubic standard B-spline function; Calculate all actual measurement times τ1,τ2,…,τ n , let t=τ1,τ2,…,τ n , then according to the Jacobian matrix J tβ Get the Jacobian matrix in the second nonlinear iterative process Specifically: According to the Jacobian matrix And the following nonlinear iterative formula is used to perform nonlinear iterative positioning solution on the vector β: Where, Afterwards, the model parameters to be determined are determined according to the solution results of the vector β. and 8. The method for coordinated positioning of a ground-ground integrated aircraft target according to claim 7, wherein: During the nonlinear iterative positioning solution process for vector β, the iteration stop condition is: k=k 2max ; Where ε2 is the preset second convergence threshold, k 2max The second maximum number of iterations.

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