Non-cooperative target observability method and device based on monocular image

Abstract

The invention provides a non-cooperative target observability method and device based on a monocular image, and the method comprises the following steps: firstly, deducing a relative motion equation under a spherical coordinate system, including an accurate nonlinear two-body differential equation and a linear time-invariant motion differential equation suitable for a near-circular orbit, and obtaining a linear time-invariant motion equation; the method is used for describing dynamic characteristics of relative track states. And secondly, by constructing an observability matrix, the observability of the system is deeply analyzed, key factors influencing the observability matrix are clarified, and the significant influence of the relative orbit configuration on the observation performance of the system is emphatically discussed. Based on an analysis result, a suggestion for optimizing relative orbit configuration design is provided, and a theoretical basis is provided for improving navigation precision. And finally, verifying the effectiveness of the observability analysis method by using numerical simulation.

Description

Technical Field

[0001] The present invention relates to the technical field of aerospace navigation, and particularly to a method and device for the observability of non-cooperative targets based on monocular images. Background Art

[0002] With the deepening of human exploration of space and the continuous increase in the launch frequency of artificial satellites, a large number of space debris and defunct satellites pose an increasingly severe threat to the safety of on-orbit spacecraft. These problems have given rise to key tasks such as debris removal and on-orbit servicing. However, since space debris and defunct satellites usually lack communication capabilities and are typical non-cooperative targets, their relative navigation and control face huge technical challenges.

[0003] In order to achieve high-precision relative state measurement and estimation of non-cooperative targets, autonomous relative navigation technology has received extensive attention. Currently, relative navigation methods based on various sensors such as lidar, microwave radar, and optical cameras have been deeply studied. Among them, optical cameras, with their characteristics of low power consumption, low cost, compactness, and portability, have become an ideal choice for future autonomous relative navigation tasks, especially navigation systems based on monocular sequence images have greater practical application potential. However, due to the lack of prior information for non-cooperative targets, the availability of observation data and system observability directly determine the performance of the navigation algorithm.

[0004] In the relative navigation task of spatial non-cooperative targets using monocular sequence images, a series of sequence image information obtained by an optical camera, combined with a navigation filtering algorithm, can estimate the relative position and velocity of the target. However, the accuracy of navigation filtering highly depends on the accuracy of the initial relative orbit state. For non-cooperative targets, the initial orbit parameters are usually unknown or have large errors, which poses a severe challenge to subsequent filtering estimation. Therefore, how to efficiently and accurately determine the initial relative orbit information has become the key to improving navigation accuracy and filtering convergence speed.

[0005] Observability analysis plays an important role in relative orbit determination research. Woffinden et al. proposed an observability criterion for angle measurement systems based on a linearized model, showing that relative distance is usually unobservable without orbit maneuvers. However, the linearized model is difficult to accurately describe the nonlinear characteristics of complex orbit dynamics. Geller et al. analyzed the observability of a vision-based nonlinear relative navigation system in cylindrical coordinates and demonstrated that local observability of the system can be achieved without orbit maneuvers in some cases, but this method is more applicable to in-plane tasks and has limited support for complex orbit configurations. Kaufman et al. used the Lie derivative method to analyze the observability of multi-order nonlinear systems, and the conclusion shows that the angle measurement system is locally observable in most cases, but this method has a high computational complexity and is difficult to apply to spacecraft navigation tasks with strict real-time requirements. In addition, some studies have proposed observability quantification indicators based on the singular value decomposition of the observation matrix and the Fisher information matrix. Although these methods perform well in evaluating system observability, the computational requirements of high-dimensional matrices pose challenges to the real-time computing capabilities of spacecraft.

[0006] In summary, the following problems exist in the prior art: for non-cooperative targets based on monocular images, how to set the relative orbit configuration to increase the observability of the system. Summary of the Invention

[0007] The purpose of the present invention is to solve the problem of how to set the relative orbit configuration to increase the observability of the system for non-cooperative targets based on monocular images.

[0008] To this end, on the one hand, an embodiment of the present invention provides a method for the observability of non-cooperative targets based on monocular images, and the method includes the following steps:

[0009] Combining the two-body orbit dynamics equation with the kinematic equation in the spherical coordinate system to establish a relative motion dynamics model applicable to non-cooperative targets;

[0010] Based on the relative motion dynamics model, construct an observability matrix;

[0011] Analyze the key factors affecting the observability matrix according to the observability matrix;

[0012] Optimize the key factors to provide a theoretical basis for improving relative navigation accuracy.

[0013] On the other hand, an embodiment of the present invention provides an apparatus for the observability of non-cooperative targets based on monocular images, including:

[0014] An initial unit for combining the two-body orbit dynamics equation with the kinematic equation in the spherical coordinate system to establish a relative motion dynamics model applicable to non-cooperative targets;

[0015] A construction unit, configured to construct an observability matrix based on a relative motion dynamics model;

[0016] An analysis unit, configured to analyze key factors affecting the observability matrix according to the observability matrix;

[0017] A configuration unit, configured to optimize the key factors to provide a theoretical basis for improving relative navigation accuracy.

[0018] The above technical solution has the following beneficial effects: The present invention conducts systematic observability analysis research on the non-cooperative target relative navigation problem based on monocular sequence images. By constructing an observation matrix and analyzing its rank and condition number, the key factors affecting the system observability are systematically explored, and the influence of the orbital configuration on the system observability is clarified. On this basis, a scheme for optimizing the orbital configuration design is proposed to improve the observability and numerical stability of the system. Through numerical simulation, the variation law of observability under different orbital conditions is verified. The results show that under three consecutive measurements, the measurement time interval and initial orbital conditions, such as eccentricity, inclination angle, and relative distance, have important effects on observability. A shorter time interval (such as Δt = 5s) can improve the observability of the system, while a longer time interval (such as Δt = 10s) will lead to a weakened observation ability. In terms of the initial orbital conditions, the system observability is significantly enhanced under low eccentricity, low inclination angle, and small relative distance (such as e s = 0, i s = 10°, r = 500m), while the improvement of the system observability is slower under high eccentricity, high inclination angle, and large relative distance (such as e s = 0.1, i s = 60°, r = 5000m). Therefore, reasonably optimizing the measurement time interval and initial orbital conditions can effectively improve the observation ability of the system. Description of the Drawings

[0019] Figure 1 is a flowchart of a non-cooperative target observability method based on monocular images provided by an embodiment of the present invention;

[0020] Figure 2 is a schematic structural diagram of a non-cooperative target observability device based on monocular images provided by an embodiment of the present invention;

[0021] Figure 3 is a schematic plan view of a space target in a spherical coordinate system provided by an embodiment of the present invention;

[0022] Figure 4 is a three-dimensional schematic diagram of a space target in a spherical coordinate system provided by an embodiment of the present invention;

[0023] Figure 5It is a sensitivity curve graph of the measurement value to the relative semi-major axis provided by an embodiment of the present invention.

[0024] Figure 6 It is a graph showing the change of the rank of the observability matrix of the first implementation manner provided by an embodiment of the present invention over time.

[0025] Figure 7 It is a graph showing the change of the condition number of the observability matrix of the first implementation manner provided by an embodiment of the present invention over time.

[0026] Figure 8 It is a graph showing the change of the rank of the observability matrix of the second implementation manner provided by an embodiment of the present invention over time.

[0027] Figure 9 It is a graph showing the change of the condition number of the observability matrix of the second implementation manner provided by an embodiment of the present invention over time.

[0028] Figure 10 It is a graph showing the change of the rank of the observability matrix of the third implementation manner provided by an embodiment of the present invention over time.

[0029] Figure 11 It is a graph showing the change of the condition number of the observability matrix of the third implementation manner provided by an embodiment of the present invention over time. Specific implementation manner

[0030] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0031] The technical solution of the present invention is to construct an observability matrix, and then further analyze the factors affecting the observability matrix. The factor with the greatest influence is the relative orbit configuration, and the relative orbit configuration needs to be further optimized, which gives suggestions on how to design the orbit better for the subsequent design of the relative orbit configuration.

[0032] In the embodiments of the present invention, as Figure 1 , a method for the observability of non-cooperative targets based on monocular images is provided, and the method includes the following steps:

[0033] S101: Combine the two-body orbit dynamics equation with the kinematic equation in the spherical coordinate system to establish a relative motion dynamics model applicable to non-cooperative targets;

[0034] During the relative orbit determination process, since the non - linear motion equation in the spherical coordinate system is not a function of the orbital angular displacement, its linearized equation remains valid at any large relative orbit spacing. Therefore, compared with the traditional rectangular coordinate system, using the spherical coordinate system to describe the initial relative orbit of spacecraft has more advantages. The dynamic model of the relative motion between spacecraft in the spherical coordinate system is established by using the multi - scale method. On this basis, the present invention deduces the relative motion dynamic model in detail by combining the two - body orbit dynamic equation and the kinematic equation in the spherical coordinate system. The two - body orbit dynamic equation of the tracking spacecraft and the non - cooperative target in the inertial coordinate system is:

[0035]

[0036] Where the subscript s represents the tracking spacecraft; the subscript m represents the non - cooperative target; r represents the position vector; a represents the acceleration vector; r represents the distance between the spacecraft and the central celestial body (the earth in this invention); μ is the gravitational constant.

[0037] In order to better describe the relative motion law of space targets, the present invention selects a fixed reference orbit plane, which coincides with the initial orbit plane of the tracking spacecraft, and deduces the relative motion equation in the spherical coordinate system. Here, the origin is chosen as the center of the earth, and the direction of i ρ -i θ is used as the orbit plane of the tracking spacecraft and the non - cooperative target, and the direction of i φ is used as the direction perpendicular to the i ρ -i θ plane to establish the spherical coordinate system of space targets, as shown in Figure 3 and Figure 4 shown.

[0038] In the spherical coordinate system, the tracking spacecraft and the non - cooperative target are respectively represented as ρ s (t), θ s (t), φ s (t) and ρ m (t), θ m (t), φ m (t). Therefore, the kinematic equations (inertial position, velocity vector and acceleration vector) of the tracking spacecraft in the spherical coordinate system are as follows:

[0039]

[0040] Where v represents the velocity vector; represents the unit vectors in three directions.

[0041] Combining Equation (1) and Equation (5), the dynamic equation of the tracking spacecraft in the spherical coordinate system can be expressed as:

[0042]

[0043] Similarly, the dynamic equation of a space target in the spherical coordinate system can be expressed as:

[0044]

[0045] The present invention defines the relative orbit state as:

[0046]

[0047] Then the second derivative of the relative orbit state is:

[0048]

[0049] where δ ρ , δ θ , δ φ is the relative orbit state; are respectively the first derivatives with respect to time corresponding to δ ρ , δ θ , δ φ .

[0050] Without considering other perturbing forces, the chaser spacecraft only moves in the reference plane, i.e., φ s ≡0. Substituting ρ m = ρ s + δ ρ , θ m = θ s + δ θ and φ m = φ s + δ φ into (9) gives:

[0051]

[0052] This is the exact non - linear two - body differential equation of the relative orbit state in the spherical coordinate system. Generally, it is assumed that the inertial state ρ s , θ s , φ s of the chaser spacecraft is known.

[0053] Furthermore, under the assumption that the distance between the chaser spacecraft and the target is short - range and the chaser spacecraft is in a nearly circular orbit Performing a Taylor series expansion on Equation (10), the dynamic equation of the relative orbit state in the spherical coordinate system is obtained as follows:

[0054]

[0055] where δ ρ represents the relative distance in the radial direction; δ θRepresents the relative azimuth angle; δ φ Represents the relative elevation angle; Represents the average angular velocity of the orbit of the tracking spacecraft; R s Represents the orbital radius of the tracking spacecraft.

[0056] Compared with the classical CW equations, the relative orbital state equations in the spherical coordinate system are not functions of δ θ and Therefore, its linearized equations are valid for any large δ θ and This is significantly different from the range of application of the CW equations, whose validity is usually limited to small relative displacement conditions.

[0057] S102: Construct an observability matrix based on the relative motion dynamics model;

[0058] S103: Analyze the key factors affecting the observability matrix according to the observability matrix;

[0059] S104: Optimize the key factors to provide a theoretical basis for improving relative navigation accuracy.

[0060] The relative motion dynamics model is specifically:

[0061]

[0062] where X is the relative orbital state vector in the spherical coordinate system; A represents the system matrix.

[0063] Analyze the observability matrix, specifically:

[0064]

[0065] where Φ is the state transition matrix and h represents the measurement matrix.

[0066] Analyze the observability matrix, specifically including analyzing the time interval and the relative orbital configuration.

[0067] The state transition matrix Φ is specifically:

[0068]

[0069] where t k represents the k-th moment, t0 represents the initial moment, and A represents the system matrix.

[0070] Let the relative orbital state vector in the spherical coordinate system be Then the dynamic equation (11) can be written in differential equation form as follows:

[0071]

[0072] Wherein:

[0073]

[0074]

[0075] If the initial relative orbit state is known as Then the solution of the differential equation (12) is:

[0076] X(t) = e At X0 = Φ(t k , t0)X0 (15)

[0077] Wherein,

[0078]

[0079] The measurement equation in the spherical coordinate system:

[0080] In the relative motion of a space target, the measurement based on the line of sight (LOS) is an important way to obtain the relative position and orbit state of a non-cooperative target. By continuously acquiring a sequence of images at fixed time intervals, the motion trajectory of the target changing with time can be captured, and thus its relative motion state can be deduced. In order to more accurately describe the relative position of the non-cooperative target with respect to the tracking spacecraft, the present invention deduces a LOS measurement equation applicable to the spherical coordinate system based on a monocular sequence of images.

[0081] Combined with Figure 3 and Figure 4 The given geometric relationships, a LOS measurement equation based on the sequence of images is introduced in the spherical coordinate system. Assuming that the optical camera measures the line-of-sight angles of the target with respect to the tracking spacecraft as α and β, then the position of the target with respect to the tracking spacecraft is:

[0082]

[0083] Furthermore, as Figure 1 and Figure 2 shown, the LOS measurement equation can be obtained as:

[0084]

[0085] The final measurement equation can be written as:

[0086]

[0087] Where α and β represent the true measured values; v represents the measurement noise, which is usually assumed to be Gaussian white noise with zero mean and variance R.

[0088] The LOS measurement equation (19) is an accurate non - linear measurement equation in the spherical coordinate system derived without any assumptions, ensuring high - precision and reliable measurements, and is applicable to the analysis of complex relative motions of space targets.

[0089] Observability:

[0090] Observability is an effective means to analyze the accuracy of initial relative orbit state estimation. Usually, when conducting observability analysis on a non - linear system, the Lie derivative method is a commonly used means. However, as shown in equation (19), the relative navigation model in the spherical coordinate system is a strongly non - linear model involving trigonometric functions. Proving observability analysis using high - order Lie derivatives involves a large number of complex trigonometric calculations, and it is difficult to obtain an analytical solution without a large amount of linearization, while linearization will omit the non - linear terms that provide angle - only observability. Therefore, in the present invention, by constructing an observability matrix H, combining the state - transition matrix and the measurement geometry vector matrix, the observability of the initial relative orbit state is evaluated using the sequence image information at the current moment, avoiding complex Lie derivative calculations and better maintaining the non - linear characteristics of the system.

[0091] Observability analysis:

[0092] For three consecutive measurement values at given \(t\) k , \(k = 0,1,2\), the form of the observability matrix H is:

[0093]

[0094] The specific form of the state - transition matrix \(\varPhi\) can be seen in equation (16).

[0095] The measurement geometry vector \(h\) T \((t\) k ) has the following form:

[0096]

[0097] Where:

[0098]

[0099] Where Each measurement geometry vector \(h\) T \((t\) k ) reflects the direction and sensitivity of the information about \(X\) provided by the measurement values \(\alpha(t\) k ) and \(\beta(t\) k ). The information in \(h\) T \((t\) k ) is transferred through the state - transition matrix \(\varPhi(t\) kThe information of the initial relative orbital state X0 can be effectively converted from (t0). Fundamentally speaking, this is a geometric problem. The core lies in analyzing whether the six row vectors in the matrix H can fully cover the six-dimensional space where X0 is located, so as to determine whether X0 is uniquely determined.

[0100] Furthermore, t is obtained. k , for k = 0, 1, 2, the measurement geometric vector h T (t k ) and the state transition matrix Φ(t k , t0) is:

[0101]

[0102] Therefore, the observability of the initial relative orbital state is further analyzed. The observability matrix H can be written as:

[0103]

[0104] where

[0105]

[0106]

[0107] According to the expressions of each element in the observability matrix H, it can be found that the composition of the observability matrix H is not only related to the time interval t k - t0, but also jointly affected by the relative state (such as δ ρ , δ θ , δ φ etc.) and system dynamic parameters (such as the orbital radius R s of the tracking spacecraft, the average angular velocity n, etc.). According to Equation (20), at the moment t0, the first row of the matrix h is obtained by multiplying the identity matrix with the matrix h T (t0), and the matrix h T (t0) provides the direct information of the system initial state, while the state transition matrix Φ(t0, t0) is the identity matrix. Therefore, the first row of the matrix H maintains linear independence. At the moments t1 and t2, the other rows of the matrix H are composed of h T (t1)Φ(t1, t0) and h T (t2)Φ(t2, t0), respectively containing the block matrices of the state transition matrices Φ(t1, t0) and Φ(t2, t0). The block matrices describe the evolution characteristics of the relative orbital state at different time points.

[0108] The elements of the state transition matrix are mainly composed of trigonometric functions and linear time variables (such as sin(n(t k - t0)) or cos(n(t k-t0))). These elements generate different values over time. Since these elements generate different values over time, it is normally possible to ensure the linear independence of each row of the state transition matrix. However, when the time interval t k -t0 is short, the change in the system state at different observation times is insufficient, resulting in an enhanced inter-row correlation of the state transition matrix. In addition, the periodicity of the trigonometric functions causes the values of sin(n(t k -t0)) and cos(n(t k -t0)) to be close at certain time points, further exacerbating the linear correlation between the matrix rows.

[0109] In addition to the influence of the above factors, the initial relative orbit state variables (such as δ ρ , δ θ , δ φ ) also play an important role in the observability of the matrix. When these variables approach symmetric values or have a small change range, the measurement sensitivity is significantly reduced, resulting in a lack of sufficient independence of the rows in the observability matrix. In addition, the initial state change is too small to significantly affect the values of the state transition matrix, further exacerbating the linear correlation between the matrix rows.

[0110] In summary, in the case of three consecutive measurements, although the observability matrix H can reflect a certain observation ability, due to the enhanced inter-row correlation of the state transition matrix and the combined effects of factors such as time interval, trigonometric function periodicity, and initial relative orbit state, the rows of the matrix H are not completely linearly independent, resulting in the observability matrix H being rank-deficient, and the system is not completely observable in this case.

[0111] Influence of relative orbit configuration on relative orbit determination accuracy:

[0112] The relative orbit determination accuracy is determined by the relative orbit configuration. Therefore, a reasonable selection of the relative orbit configuration is crucial for improving the performance of relative orbit determination estimation. This section will deeply analyze the influence of the relative orbit configuration on the relative orbit determination estimation accuracy and propose suggestions for optimizing the orbit configuration for relative orbit determination problems.

[0113] Assume that the chaser spacecraft and the target spacecraft are respectively operating on different low-Earth orbits. Due to the coupling of the relative orbit states, it is theoretically difficult to analyze the influence of the relative orbit configuration on the relative orbit determination accuracy. For this reason, using relative orbit elements to describe the relative motion is an effective method, which can not only clearly characterize the dynamic characteristics of the relative motion but also effectively decouple the complex influence of the orbit configuration on the state estimation. According to the relative motion state equation (11), the conversion relationship between the relative position (δ ρ , δ θ , δ φ ) and the relative orbit elements can be expressed as:

[0114]

[0115] λ = M + Ω + ω (51)

[0116] In the formula: R s represents the distance from the earth's center to the tracking spacecraft; ω s represents the argument of perigee of the tracking spacecraft; δ a represents the relative semi-major axis; δ e represents the relative eccentricity; δ λ represents the relative mean angle; δ i represents the relative inclination; M represents the mean anomaly; Ω represents the right ascension of the ascending node. Substituting formula (51) into the measurement equation (18), the relational expression between the measured values α, β and the relative orbital elements can be obtained as follows:

[0117]

[0118] In the formula: a s represents the semi-major axis of the tracking spacecraft; e s represents the eccentricity of the tracking spacecraft; other parameters are the same as above. It can be seen from formula (52) that the relative orbit determination estimation accuracy can be expressed by the relative orbital elements. Among them, the relative true anomaly changes with time, while other orbital elements remain unchanged when the orbital perturbation is ignored. In addition, it should be noted that in order to deeply discuss the relationship between the relative orbit determination estimation accuracy and the relative orbital elements, we analyzed the following two cases respectively: the relative motion outside the orbital plane of the tracking spacecraft and the relative motion within the orbital plane of the tracking spacecraft.

[0119] Relative motion outside the plane of the tracking spacecraft:

[0120] When the relative motion is outside the orbital plane of the tracking spacecraft, the tracking spacecraft and the target are on different inclined orbits. In this case, the relative orbital inclination δ i plays a key role in the relative motion. Here, it is assumed that (δ a , δ e , δ Ω ) = 0, and based on the assumption that the relative motion satisfies a nearly circular orbit (i.e., e s ≈0). Substituting these conditions into formula (52), it can be simplified as:

[0121]

[0122] According to formula (53), since the measured value α does not contain the relative orbital inclination δ i , only the partial derivative of the measured value β with respect to the relative orbital inclination δ i is discussed, and the form is as follows:

[0123]

[0124] Wherein:

[0125]

[0126] Substituting these results into Equation (54), the partial derivative of the measured value β with respect to δ i is:

[0127]

[0128] According to Equation (57), when the relative orbital inclination δ i increases, the value of the partial derivative decreases, indicating that the effect of the measurement on the error magnification factor is continuously weakening. Therefore, when using monocular sequence images in the spherical coordinate system for relative orbit determination, we can make the following suggestions:

[0129] REMARK 1. When using monocular sequence images in the spherical coordinate system for initial relative orbit determination, the sensitivity of the measurement to the orbital inclination δ i is negatively correlated with the relative orbital inclination δ i . Therefore, when designing or planning the orbital maneuver of the tracker, the relative orbital inclination δ i should be increased as much as possible to improve the measurement accuracy and the estimation accuracy of relative orbit determination. This conclusion is consistent with the numerical results in the literature. However, the present invention more deeply analyzes the internal relationship between the relative inclination δ i and the measured value and provides theoretical support.

[0130] Relative motion in the plane of the tracking spacecraft:

[0131] The influence of the relative orbital inclination δ i on the measured value has been discussed above. However, when the relative motion occurs in the orbital plane of the tracking spacecraft, the relative orbital inclination δ i will always be zero. In this case, the influence of other relative orbital elements on the measured value becomes more significant. Among them, the relative mean anomaly δ λ is coupled with the right ascension of the ascending node relative to the equator δ Ω , reflecting the phase of the target in the relative orbital configuration and having time-varying characteristics, but the influence of these two on the shape of the relative orbital configuration is the smallest. Therefore, the roles of δ λ and δ Ω in improving the estimation accuracy of relative orbit determination are relatively limited and will not be discussed here. Next, this section will focus on discussing the relationship between the relative semi-major axis δ a , the relative eccentricity δ e and the measured value.

[0132] Since the relative motion occurs within the orbital plane of the tracking spacecraft, the relative orbital inclination δ i is zero. Substituting this into Equation (52), we have:

[0133]

[0134] According to Equation (58), since the measured value β does not contain the relative semi-major axis δ a , we only discuss the partial derivative of the measured value α with respect to the relative semi-major axis δ a , which is in the following form:

[0135]

[0136] where:

[0137] N = sin(-2δ a sinω s +a s δ λ ) (60)

[0138]

[0139] Since it is difficult to analyze the variation law of Equation (59) analytically, simulation is used to analyze the sensitivity of the measured value to the relative semi-major axis δ a . The parameter values are set according to the actual background as: e s = 0.001, a s = 7e6m, δ λ = 0.001rad, δ e = 0.0005. The sensitivity variation curve of the measured value to the relative semi-major axis is shown as Figure 5 . The figure shows the sensitivity performance when the relative semi-major axis δ a varies in the range of 0 to 500m. The results show that as the relative semi-major axis δ a increases, the envelope shows a downward trend, which means that the effect of the measurement on the error magnification factor is continuously weakening.

[0140] According to Equation (58), the partial derivative of the measured value with respect to the relative eccentricity δ e is:

[0141]

[0142] where:

[0143]

[0144] After simplification, the partial derivative of the measured value with respect to the relative eccentricity δe The partial derivatives of

[0145]

[0146] According to Equation (69), when the relative eccentricity δ e increases, the first term decreases, and the second term also decreases. Therefore, decreases as the relative eccentricity δ e increases, which means that the effect of the measurement on the error magnification factor is weakening.

[0147] In summary, according to Equations (59) and (69), when the relative semi-major axis δ a and the relative eccentricity δ e increase, the partial derivatives of the measurement with respect to δ a and δ e decrease, indicating that the effect of the measurement on the error magnification factor is continuously weakening. Therefore, when performing relative orbit determination using monocular sequence images in the spherical coordinate system, we can make the following suggestions:

[0148] REMARK 2. When performing initial relative orbit determination using monocular sequence images in the spherical coordinate system, the sensitivity of the measurement with respect to the relative semi-major axis δ a and the relative eccentricity δ e is negatively correlated with the relative semi-major axis δ a and the relative eccentricity δ e . Therefore, when designing or planning the tracker orbit maneuver, the relative semi-major axis δ a and the relative eccentricity δ e should be increased as much as possible to improve the measurement accuracy and the estimation accuracy of relative orbit determination.

[0149] It should be noted that when performing relative orbit determination using monocular sequence images in the spherical coordinate system, it may be affected by various factors such as lighting conditions, communication environment, and celestial body occlusion. Although the observation strategy can be optimized based on the analysis results of Remark 1 and Remark 2, the orbit design still needs to comprehensively consider these effects and meet the end requirements of the orbit control mission.

[0150] Simulation:

[0151] In this section, through the observability simulation analysis, the variation laws of the rank and condition number of the observation matrix of the system under different time intervals and initial conditions are studied, and the observability of the system and the numerical stability of the observation matrix are evaluated, providing an important reference basis for subsequent optimization of the observation strategy and improvement of the algorithm performance.

[0152] Observability simulation analysis:

[0153] According to the aforementioned observability analysis conclusion, in the case of three consecutive measurements, since the rank of the observability matrix H does not reach the dimension of the system state variables, the system is not fully observable. To further analyze the influence of factors such as time interval and initial relative orbit state on the system observability, simulation experiments are carried out in this section to verify the conclusion of the theoretical analysis.

[0154] First, verify the influence of the time interval on the rank and condition number of the observability matrix H. Set the initial simulation parameters as follows: the semi-major axis of the orbit a s = 7e6m, the eccentricity e s = 0, the inclination i s = 10°, the right ascension of the ascending node Ω s = 0, the argument of perigee ω s = 0, the true anomaly v s = 0, the initial relative distance is r = 500m, the time interval is Δt = 5s, and the number of measurements is N = 3 times. The results of the rank and condition number of the observability matrix H changing with time are obtained, as shown in Figure 6 、 Figure 7 shown.

[0155] Furthermore, we change the time interval to Δt = 10s, and keep the other simulation parameters unchanged. The results of the rank and condition number of the observability matrix H changing with time are obtained, as shown in Figure 8 、 Figure 9 shown.

[0156] By comparing the results of Figure 6 、 Figure 7 、 Figure 8 、 Figure 9 , it is found that when the time interval is set to Δt = 5s and Δt = 10, the rank of the observability matrix H gradually increases with the increase of the number of measurements (th in the figure represents the number of measurements), and the observation ability of the system is significantly improved. At the same time, with the increase of the time interval, the condition number of the matrix decreases significantly, which indicates that the numerical stability of the matrix H has been improved. However, although the condition number of the matrix H is large and there is no zero singular value, the system only has weak observability, but it can still obtain the initial relative orbit state with high precision. In addition, there are certain differences in the influence of the time interval on the rank and condition number of the observability matrix H. For example, when the time interval is 5s, the rank of the matrix H can reach 5, while when the time interval is 10s, its rank is only 4. This shows that, under the same number of measurements, appropriately shortening the time interval can effectively improve the observation ability of the system.

[0157] Further, verify the influence of the initial relative orbit state on the rank and condition number of the observability matrix H. Set different initial simulation parameters as follows: the semi-major axis of the orbit a s = 7e6m, the eccentricity e s= 0.1, inclination angle i s = 60°, right ascension of the ascending node Ω s = 0, argument of perigee ω s = 0, true anomaly v s = 0, the initial relative distance is r = 5000 m, the time interval is Δt = 5 s, and the number of measurements is N = 3 times. The results of the rank and condition number of the observability matrix changing with time under different initial conditions are obtained, as shown in Figure 10 、 Figure 11 shown.

[0158] It can be found through comparison that when the time interval is the same, different initial conditions have a significant impact on the changing trends of the rank and condition number of the observability matrix H. In Figure 6 , the initial conditions of the system (such as e s = 0, i s = 10°, r = 500 m) make the rank of the observability matrix H increase faster, from 2 at the first measurement to 5 at the third measurement, and the condition number decreases significantly, with obvious improvement in numerical stability. While in Figure 10 , due to the differences in the initial conditions (such as e s = 0.1, i s = 60°, r = 5000 m), the increase in the rank of matrix H slows down, only increasing from 2 to 4, and the decrease in the condition number is also relatively small. It can be concluded that the choice of initial conditions directly affects the observation ability and numerical stability of the system, and reasonable initial conditions can more efficiently improve the rank of the observability matrix H and optimize the decreasing trend of the condition number.

[0159] In the embodiment of the present invention, as shown in Figure 2 , a non-cooperative target observability device based on a monocular image is provided, including:

[0160] An initial unit 21, configured to establish a relative motion dynamics model applicable to non-cooperative targets by combining the two-body orbital dynamics equation and the kinematic equation in the spherical coordinate system;

[0161] A construction unit 22, configured to construct an observability matrix based on the relative motion dynamics model;

[0162] An analysis unit 23, configured to analyze the key factors affecting the observability matrix according to the observability matrix;

[0163] A configuration unit 24, configured to optimize the key factors to provide a theoretical basis for improving the relative navigation accuracy.

[0164] The relative motion dynamics model is specifically:

[0165]

[0166] Wherein, X is the relative orbital state vector in the spherical coordinate system; A represents the system matrix.

[0167] The observability matrix is specifically:

[0168]

[0169] Wherein, Φ is the state transition matrix, and h represents the measurement matrix.

[0170] The configuration unit is specifically used to optimize the time interval and the relative orbital configuration.

[0171] The state transition matrix Φ is specifically:

[0172]

[0173] Wherein, t k represents the k-th moment, t0 represents the initial moment, and A represents the system matrix.

[0174] The working principle of the non-cooperative target observability device based on a monocular image is the same as that of the non-cooperative target observability method based on a monocular image, and will not be elaborated here.

[0175] The present invention proposes a non-cooperative target observability method based on a monocular image, which is a spatial non-cooperative target observability analysis method based on the spherical coordinate system. The relative motion equation is systematically derived and the observation matrix is constructed. The key factors affecting the system observability are deeply analyzed, the influences of the orbital configuration, time interval, etc. on the system observability are quantitatively evaluated, and suggestions for optimizing the orbital design are proposed. Finally, the effectiveness of the method proposed by the present invention is verified through numerical simulation.

[0176] The present invention conducts a systematic observability analysis research on the non-cooperative target relative navigation problem based on a monocular sequence image. By constructing the observation matrix and analyzing its rank and condition number, the key factors affecting the system observability are systematically explored, and the significant influence of the orbital configuration on the system observability is clarified. On this basis, suggestions for optimizing the orbital configuration design are proposed to improve the system observability and numerical stability. Through numerical simulation, the observability variation law under different orbital conditions is verified. The results show that under three consecutive measurements, the measurement time interval and the initial orbital conditions (such as eccentricity, inclination angle, and relative distance) have an important influence on the observability. A shorter time interval (such as Δt = 5s) can improve the system observability, while a longer time interval (such as Δt = 10s) will lead to a weakened observation ability. In terms of the initial orbital conditions, low eccentricity, low inclination angle, and smaller relative distance (such as e s = 0, i s= 10°, r = 500 m), the system observability is significantly enhanced, while at high eccentricity, high inclination, and large relative distance (such as e s = 0.1, i s = 60°, r = 5000 m), the improvement of the system observability is slower. Therefore, reasonably optimizing the measurement time interval and the initial orbit conditions can effectively improve the observation ability of the system.

[0177] It should be understood that the specific order or hierarchy of steps in the disclosed process is an example of an exemplary method. Based on design preferences, it should be understood that the specific order or hierarchy of steps in the process can be rearranged without departing from the scope of the present disclosure. The appended method claims present the elements of the various steps in an exemplary order and are not intended to be limited to the specific order or hierarchy recited.

[0178] In the above detailed description, various features are combined in a single embodiment to simplify the present disclosure. This method of disclosure should not be interpreted as reflecting an intention that the embodiments of the claimed subject matter require more features than are clearly recited in each claim. On the contrary, as reflected in the appended claims, the present invention lies in a state with fewer features than all the features of the disclosed single embodiment. Therefore, the appended claims are hereby expressly incorporated into the detailed description, where each claim stands alone as a separate preferred embodiment of the present invention.

[0179] In order to enable any person skilled in the art to implement or use the present invention, the above-described disclosed embodiments have been described. For those skilled in the art, various modification methods of these embodiments are obvious, and the general principles defined by the present invention can also 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 given in the present invention, but is consistent with the broadest scope of the principles and novel features disclosed in this application.

[0180] The above description includes examples of one or more embodiments. Of course, it is impossible to describe all possible combinations of components or methods for the purpose of describing the above embodiments, but those of ordinary skill in the art should recognize that the various embodiments can be further combined and arranged. Therefore, the embodiments described in the present invention are intended to cover all such changes, modifications, and variations that fall within the scope of the appended claims. In addition, with respect to the term "comprising" used in the specification or claims, the manner in which this term encompasses is similar to the term "including," as interpreted when "including" is used as a transitional word in the claims. In addition, any term "or" used in the specification of the claims is intended to mean "non-exclusive or."

[0181] Those skilled in the art can also understand that the various illustrative logical blocks, units, and steps listed in the embodiments of the present invention can be implemented by electronic hardware, computer software, or a combination of both. To clearly show the interchangeability of hardware and software, the above-mentioned various illustrative components, units, and steps have been generally described in terms of their functions. Whether such functions are implemented by hardware or software depends on the specific application and the design requirements of the entire system. Those skilled in the art can use various methods to implement the described functions for each specific application, but such implementation should not be construed as exceeding the scope of protection of the embodiments of the present invention.

[0182] In the embodiments of the present invention, the various illustrative logical blocks or units can be implemented or operate the described functions through a general-purpose processor, a digital signal processor, an application-specific integrated circuit (ASIC), a field-programmable gate array or other programmable logic devices, discrete gate or transistor logic, discrete hardware components, or any combination of the above designs. The general-purpose processor can be a microprocessor. Optionally, the general-purpose processor can also be any conventional processor, controller, microcontroller, or state machine. The processor can also be implemented by a combination of computing devices, such as a digital signal processor and a microprocessor, multiple microprocessors, one or more microprocessors combined with a digital signal processor core, or any other similar configuration.

[0183] The steps of the methods or algorithms described in the embodiments of the present invention can be directly embedded in hardware, software modules executed by the processor, or a combination of the two. The software modules can be stored in a RAM memory, a flash memory, a ROM memory, an EPROM memory, an EEPROM memory, a register, a hard disk, a removable disk, a CD-ROM, or any other form of storage medium in the art. Exemplarily, the storage medium can be connected to the processor so that the processor can read information from the storage medium and write information to the storage medium. Optionally, the storage medium can also be integrated into the processor. The processor and the storage medium can be disposed in an ASIC, and the ASIC can be disposed in a user terminal. Optionally, the processor and the storage medium can also be disposed in different components of the user terminal.

[0184] In one or more exemplary designs, the functions described in embodiments of the present invention may be implemented in hardware, software, firmware, or any combination of the three. If implemented in software, these functions may be stored on a computer-readable medium or transmitted as one or more instructions or code on a computer-readable medium. A computer-readable medium includes both computer storage media and communication media that facilitate transfer of a computer program from one place to another. The storage media may be any available media that can be accessed by a general-purpose or special-purpose computer. By way of example, and not limitation, such computer-readable media can include RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store program code in the form of instructions or data structures and that can be accessed by a general-purpose or special-purpose computer, or a general-purpose or special-purpose processor. Additionally, any connection is properly termed a computer-readable medium. For example, if the software is transmitted from a website, server, or other remote source using a coaxial cable, fiber optic cable, twisted pair, DSL, or wireless means such as infrared, radio, and microwave, it is included in the definition of computer-readable medium. Disk and disc include compact disc, laser disc, optical disc, DVD, floppy disk, and Blu-ray disc, where disks usually reproduce data magnetically, while discs usually reproduce data optically with lasers. Combinations of the above should also be included within the scope of computer-readable medium.

[0185] The specific embodiments described above have further elaborated on the purpose, technical solutions, and beneficial effects of the present invention. It should be understood that the above description is only for the specific embodiments of the present invention and is not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for the observability of non-cooperative targets based on monocular images, characterized in that, The method includes the following steps: Combining the two-body orbital dynamics equation with the kinematic equation in the spherical coordinate system to establish a relative motion dynamics model applicable to non-cooperative targets; Constructing an observability matrix based on the relative motion dynamics model; Analyzing the key factors affecting the observability matrix according to the observability matrix; Optimizing the key factors to provide a theoretical basis for improving relative navigation accuracy.

2. The method for observable non - cooperative target based on monocular image according to claim 1, characterized in that The relative motion dynamics model is specifically: Where X is the relative orbital state vector in the spherical coordinate system; A represents the system matrix.

3. The method for observable non-cooperative target based on monocular images according to claim 2, characterized in that, The observability matrix is specifically: Where Φ is the state transition matrix and h represents the measurement matrix.

4. The method for observable non-cooperative target based on monocular image according to claim 2, characterized in that Optimizing the key factors specifically includes optimizing the time interval and optimizing the relative orbital configuration.

5. The method for observable non - cooperative target based on monocular images according to claim 3, wherein The state transition matrix Φ is specifically: where, t k represents the k-th moment, t0 represents the initial moment, and A represents the system matrix.

6. Non-cooperative target observability device based on monocular images, characterized in that Including: An initial unit for combining the two-body orbital dynamics equation with the kinematic equation in the spherical coordinate system to establish a relative motion dynamics model applicable to non-cooperative targets; A construction unit for constructing an observability matrix based on the relative motion dynamics model; An analysis unit for analyzing the key factors affecting the observability matrix according to the observability matrix; A configuration unit for optimizing the key factors to provide a theoretical basis for improving relative navigation accuracy.

7. The non-cooperative target observability device based on monocular images according to claim 6, characterized in that, The relative motion dynamics model is specifically: Where X is the relative orbital state vector in the spherical coordinate system; A represents the system matrix.

8. The non-cooperative target observability device based on a monocular image according to claim 7, characterized in that The observability matrix is specifically: Where Φ is the state transition matrix and h represents the measurement matrix.

9. The non-cooperative target observability device based on monocular images according to claim 7, characterized in that The configuration unit is specifically used to optimize the time interval and optimize the relative orbital configuration.

10. The non-cooperative target observability device based on a monocular image according to claim 8, characterized in that, The state transition matrix Φ is specifically: where, t k represents the k-th moment, t0 represents the initial moment, and A represents the system matrix.

Images