A global robust optimization based monocular state estimation method for space objects

Abstract

The embodiment of the application provides a kind of space target monocular state estimation method based on global robust optimization, comprising: establishing the monocular state estimation system model of space target, the monocular state estimation system model includes system state equation and measurement equation;According to the monocular state estimation system model, the state estimation value of each time of the space target in total duration is obtained by iterative calculation.This application establishes the monocular state estimation system model of space target based on camera bias, based on global robust estimation framework, minimizes the sensitivity of estimator to all possible distributions, and deduces global robust extended Kalman filter for nonlinear system model, which enhances the robustness to model uncertainty and improves the state estimation accuracy of space target.

Description

Technical Field

[0001] This invention relates to the field of navigation technology, specifically to a method for estimating the state of a space target, and more specifically, to a monocular method for estimating the state of a space target based on global robust optimization. Background Technology

[0002] Autonomous relative navigation for space targets of unknown shape and size without cooperative identifiers is a prerequisite for space missions such as on-orbit maintenance of failed satellites, space debris removal, and deep space exploration landings. It is also crucial for space target identification and perception, and space situation assessment. Autonomous relative navigation capabilities are constrained by limited onboard computing and storage resources. Currently used multi-sensor measurement data fusion methods suffer from system complexity, numerous devices, and data heterogeneity, hindering the autonomous operation of navigation systems. Optical sensors, due to their advantages of high resolution, long imaging distance, and simple equipment, as well as the intuitive and timely data they acquire, are the primary information source for autonomous navigation. Monocular state estimation of space targets is the core of autonomous relative navigation; it involves obtaining the target's relative position and attitude, and other relevant motion state parameters, relative to the spacecraft, by measuring images over a period of time using only a single optical camera.

[0003] Currently, for the problem of monocular state estimation of space targets without prior information, the industry has conducted relevant research on the construction of system models for state estimation. The core difficulty in system model construction lies in the inability to obtain distance measurement information through a monocular camera. To effectively overcome this problem, the main research methods include those based on nonlinear dynamics, orbital maneuvers, and camera bias. Current system model construction methods often assume that the established model is precisely known and that the noise is completely known Gaussian white noise. However, in real-world problems, for non-cooperative targets with no prior information, the state often cannot be accurately modeled. Furthermore, due to the presence of high-energy physical radiation with unknown characteristics in space, navigation systems exhibit various forms of error. In addition to modelable random and systematic errors, there are also unmodelable uncertainty errors caused by unclear mechanisms. The existence of such uncertainty errors reduces or even diverges the filtering accuracy, rendering traditional Kalman filtering algorithms unsuitable. Currently, there is also much research on robust navigation filtering algorithms.

[0004] To overcome the uncertainties in complex space environments, existing technologies have proposed various robust filtering methods to improve the reliability of navigation systems, including minimax filtering, maximum correlation entropy Kalman filtering, strong tracking filtering, and adaptive two-stage unscented Kalman filtering. However, these methods suffer from high computational complexity, difficulty in parameter tuning, and difficulty in adapting to complex dynamic systems, and cannot be efficiently and stably applied to monocular state estimation scenarios for space targets. Summary of the Invention

[0005] This invention provides a monocular state estimation method for spatial targets based on global robust optimization.

[0006] To achieve the above objectives, embodiments of the present invention provide a monocular state estimation method for space targets based on global robust optimization, comprising: establishing a monocular state estimation system model for a space target, the monocular state estimation system model including system state equations and measurement equations; and obtaining the state estimate values ​​of the space target at each time point within the total duration through iterative calculation based on the monocular state estimation system model.

[0007] Furthermore, based on the monocular state estimation system model, the state estimates of the space target at each moment within the total duration are obtained through iterative calculation, specifically including:

[0008] Based on prior information (such as historical data, past experience, etc.), determine the initial system state estimate and the initial most sensitive density covariance matrix of the space target; set the initial value of the iteration number t to 1; predict the system state at time t. Based on the monocular state estimation system model and the most sensitive density covariance matrix of the previous time step Solve for the filter gain matrix K at time t. t Furthermore, based on the filter gain matrix K at time t... t The nominal error covariance matrix P at time t is predicted. t ; By measuring data y t and the filter gain matrix K at time t t The predicted value of the system state at time t The system state estimate at time t is obtained by updating the system state. For the nominal error covariance matrix P at time t t The most sensitive density covariance matrix at time t is obtained by updating the matrix. The update iteration count is t = t + 1; when t < the maximum iteration count T, the above iterative calculation process is repeated. The initial step of the iterative calculation process is to predict the system state prediction value at time t. By summing up the system state estimates at all times, we can obtain the state estimates of the space target at each time.

[0009] Furthermore, predict the system state at time t. Specifically, this includes: based on the system state estimate from the previous moment. Using a monocular state estimation system model, the predicted system state value at time t is obtained.

[0010] Furthermore, the monocular state estimation system model is as follows:

[0011]

[0012] Where, x t This represents the state at time t. and They respectively represent satisfying and Gaussian white noise, δ is the Kronecker delta function, f(δx) t ) represents the state equation of a nonlinear system with respect to the state error, h(x) t B represents the measurement equation of a nonlinear system with respect to its state. t Let D be the process noise matrix. t To measure the noise matrix, y t For measurement vectors, This represents the state estimation error at time t+1;

[0013] The state vector of the monocular state estimation system for space targets is Where r = [x, y, z] represents the position of the spatial target relative to the monocular camera coordinate system. Let q = [q1, q2, q3, q0] represent the relative velocity, q = [q1, q2, q3, q0] represent the absolute attitude quaternion of the spatial target relative to the inertial frame, and ω = [ω1, ω2, ω3] represent the absolute angular velocity. ρ represents the ratio of inertia. m =[x m ,y m ,z m ], m=1,2,3 represent the coordinates of three feature points on the surface of the space target.

[0014] Furthermore, based on the system state estimate from the previous moment... Using a monocular state estimation system model, the predicted system state value at time t is obtained. The following methods shall be used:

[0015]

[0016] in,

[0017] Furthermore, solve for the filter gain matrix K at time t. t The following formula is used for calculation:

[0018]

[0019] Among them, A t To linearize the nonlinear state equations of the system, C t The observation matrix is ​​obtained by linearizing the nonlinear measurement equations of the system;

[0020] The nominal error covariance matrix P at time tt The following formula is used for calculation:

[0021]

[0022] Furthermore, by measuring data y t and the filter gain matrix K at time t t The predicted value of the system state at time t The system state estimate at time t is obtained by updating the system state. The following methods shall be used:

[0023] Δx t =K t [y t -h(x t )],

[0024] in

[0025] Furthermore, for the nominal error covariance matrix P at time t... t The most sensitive density covariance matrix at time t is obtained by updating the matrix. The following methods shall be used:

[0026] Calculate the target loss threshold τ t The value, then, find the one that makes The optimal solution is valid. Then, according to the following formula, the optimal solution is obtained. Update the most sensitive density covariance matrix at time t

[0027]

[0028] Furthermore, before setting the initial value t=1 for the number of iterations t, the method also includes: determining the maximum number of iterations T based on the preset sampling interval and total duration.

[0029] The above technical solution has the following beneficial effects:

[0030] Compared to other robust filtering algorithms, the method proposed in this technical solution utilizes the concept of global robust estimation. By balancing the dependence on the nominal model, it enables the system to adaptively adjust to process noise and measurement noise, making the algorithm more robust. Furthermore, while ensuring high robustness and estimation accuracy, it avoids excessive computational complexity, making it more suitable for the limited computing and storage resources on the satellite. This facilitates the autonomous operation of the navigation system on the satellite and provides reliable technical support for autonomous relative navigation in space missions such as on-orbit maintenance of failed satellites, space debris removal, and deep space exploration landing. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] Figure 1 This is a flowchart of a monocular state estimation method for space targets based on global robust optimization according to the present invention;

[0033] Figure 2 This is a comparative schematic diagram of the estimation error of the relative position of the spatial target under the condition of dynamic uncertainty in the system during the simulation experiment of a specific embodiment of the present invention;

[0034] Figure 3 This is a comparative diagram showing the estimation error of the relative velocity of a space target under dynamic uncertainty in a simulation experiment;

[0035] Figure 4 This is a comparative diagram showing the estimation error of the absolute quaternion of the space target under dynamic uncertainty of the system in the simulation experiment;

[0036] Figure 5 This is a comparative diagram showing the estimation error of the absolute angular velocity of a space target under dynamic uncertainty in a simulation experiment.

[0037] Figure 6 This is a comparative diagram showing the estimation error of the inertia ratio of the space target under dynamic uncertainty of the system in a simulation experiment;

[0038] Figure 7 This is a schematic diagram comparing the estimation errors of the coordinates of the first feature point on the surface of the space target under dynamic uncertainty of the system in a simulation experiment;

[0039] Figure 8 This is a schematic diagram comparing the estimation errors of the coordinates of the second feature point on the surface of the space target under dynamic uncertainty of the system in the simulation experiment;

[0040] Figure 9 This is a schematic diagram comparing the estimation errors of the coordinates of the third feature point on the surface of the space target under dynamic uncertainty of the system in a simulation experiment;

[0041] Figure 10 It is a comparison of the traces of the error covariance matrices of GREKF and EKF under dynamic uncertainty of the system in simulation experiments;

[0042] Figure 11This is a comparative diagram showing the estimation error of the relative position of a space target under the condition of observing outliers in a simulation experiment;

[0043] Figure 12 This is a comparative diagram showing the estimation error of the relative velocity of a space target under the condition of observing outliers in the simulation experiment;

[0044] Figure 13 This is a comparative diagram showing the estimation error of the absolute quaternion of a space target under the condition of observing outliers in the simulation experiment;

[0045] Figure 14 This is a comparative diagram showing the estimation error of the absolute angular velocity of a space target under the condition of observing outliers in a simulation experiment;

[0046] Figure 15 This is a comparative diagram showing the estimation error of the inertia ratio of a space target under the condition of observing outliers in the simulation experiment;

[0047] Figure 16 This is a schematic diagram comparing the estimation errors of the coordinates of the first feature point on the surface of a space target under the condition of observing outliers in a simulation experiment;

[0048] Figure 17 This is a schematic diagram comparing the estimation errors of the coordinates of the second feature point on the surface of the space target under the condition of observing outliers in the simulation experiment;

[0049] Figure 18 This is a schematic diagram comparing the estimation errors of the coordinates of the third feature point on the surface of the space target under the condition of observing outliers in the simulation experiment;

[0050] Figure 19 This is a comparison of the traces of the error covariance matrices of GREKF and EKF in simulation experiments under the condition of observing outliers. Detailed Implementation

[0051] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0052] like Figure 1 As shown, this embodiment of the invention provides a spatial target monocular state estimation method based on global robust optimization, including:

[0053] S101. Establish a monocular state estimation system model for a space target, wherein the monocular state estimation system model includes system state equations and measurement equations;

[0054] S102. Based on the monocular state estimation system model, the state estimation values ​​of the space target at each moment within the total duration are obtained through iterative calculation.

[0055] The following detailed explanation of the aforementioned method and the derivation process of each formula is provided through a specific embodiment:

[0056] 1) Monocular State Estimation System Model for Space Targets

[0057] First, we will introduce the monocular pose estimation method for non-cooperative targets in space and give the state-space model of the system.

[0058] Monocular state estimation of non-cooperative targets in space refers to estimating the motion state and navigation parameters of non-cooperative targets in space by measuring them with a monocular camera without prior knowledge. Due to the complexity of the space environment, the state and measurement models we establish are often inaccurate, i.e., they contain model uncertainties and statistical noise uncertainties.

[0059] Let the state variables of the state estimation in this paper be expressed as follows: Let r = [x, y, z] and v be the position r = [x, y, z] and velocity v of the target system relative to the camera system, respectively. The target system's absolute attitude quaternion q = [q1, q2, q3, q0], absolute angular velocity ω = [ω1, ω2, ω3], and inertia ratio relative to the inertial frame are: And the coordinates ρ of three key points on the target surface relative to the target's own system. m =[x m ,y m ,z m ], m=1,2,3,ρ m Let represent the three-dimensional coordinates of the m-th feature point. Assume that the motion of the spacecraft and the target is a two-body motion, and the distance between the target and the spacecraft is much smaller than the orbital radius of the spacecraft.

[0060] First, a state-space model of the system is defined, in which the relative position and relative velocity of the spacecraft and the non-cooperative target can be represented by the classical CW equations in the relative motion orbital dynamics of the spacecraft, while the absolute quaternion of the non-cooperative target's own system relative to the inertial frame, angular velocity and inertia ratio can be represented by the spacecraft attitude kinematics.

[0061] Assume the spacecraft and target are in two-body motion, and the distance between them is much smaller than the spacecraft's orbital radius. The position and velocity of the target relative to the camera system, without considering perturbation forces, satisfy the relative motion state equations (CW equations):

[0062]

[0063] in, Let r be the average angular velocity of the spacecraft, μ be the Earth's gravitational constant, and r be the mean angular velocity of the spacecraft. c This represents the orbital radius of the spacecraft.

[0064] Define the rotation matrix from the inertial frame to the target frame as:

[0065]

[0066] Among them, the attitude quaternion is And there are

[0067] Define quaternion operators It can represent the rotation between the inertial frame of reference and the target frame of reference.

[0068]

[0069] According to attitude kinematics, the absolute attitude quaternion equations of motion of the target system in the inertial frame are expressed as:

[0070]

[0071] in, ω x ,ω y ,ω z These are the angular velocities of the target along the three axes of the inertial frame, respectively. After linearizing the above equation, we have:

[0072]

[0073] in,

[0074] For a non-cooperative target undergoing free tumbling motion, the dynamic equation of its angular velocity relative to the inertial frame is:

[0075]

[0076] The linearized representation is as follows:

[0077]

[0078] in, δq is an estimated value of the angular velocity. v The vector part of δq is δω, where δω is the angular velocity error. and They are represented as follows:

[0079]

[0080] Since the non-cooperative target is a rigid body, when the properties of the rigid body remain unchanged, the principal moment of inertia and the inertia ratio are both constant values. At this point, the inertia ratio of the non-cooperative target... Represented as:

[0081]

[0082] in The target is the principal inertia of this system.

[0083] In the target body coordinate system, the coordinates of the key points on the target surface are always constant. Therefore, the key points on the surface in the target body coordinate system are represented as ρ1, ρ2, ρ3.

[0084] Therefore, according to formulas (1.1), (1.5), and (1.7), the error state equation of the target is expressed as:

[0085] δx t+1 =A t δx t +B t w t ,

[0086]

[0087] in Let represent the state estimation error at time t+1, and:

[0088]

[0089] The measurement model of the system is given below. It is assumed that the translation vector of the origin of the spacecraft camera system in the spacecraft body system is d, and the measurement information obtained in this system is the unit direction vector of the position of the feature points on the target surface in the satellite camera system. t =h(x t )=[e r1 (x t e r2 (x t ) … e rm (x t )] Τ The unit vector of the m-th surface keypoint in the spacecraft camera system is:

[0090]

[0091] in

[0092]

[0093] In the formula, r m C Let r represent the position vector of the keypoint on the surface of the m-th non-cooperative target in the camera frame.C denoted as , where r is the position vector of the non-cooperative target's centroid relative to the camera, r is the position vector of the target's centroid within the spacecraft's own coordinate system, and d is the offset vector of the camera's centroid relative to the spacecraft's body coordinate system. Let q be the rotation quaternion of the target system relative to the spacecraft camera system, and q be the attitude quaternion of the target relative to the inertial frame. s Let be the attitude quaternion of the spacecraft camera relative to the inertial frame. This represents the rotation matrix of the spacecraft camera relative to the spacecraft's orbital system. and Let represent the rotation matrix of the spacecraft camera system relative to the spacecraft body system and the rotation matrix of the spacecraft body system relative to the spacecraft orbit system, respectively.

[0094] In summary, the model of a monocular state estimation system for space targets can be expressed as follows:

[0095]

[0096] B t and D t These are the process noise matrix and the measurement noise matrix, respectively.

[0097] 2) Global robust estimation problem

[0098] Consider a nominal nonlinear time-varying state-space model:

[0099]

[0100] in y represents the state variable of the system. t For the system's observations, and To meet and Gaussian white noise, δ is the Kronecker delta function, B t and D t Let these be the process noise and measurement noise matrices of appropriate dimensions, and assume that... and It is a positive definite matrix. The objective here is state estimation, i.e., the observations at time t. Estimate the system state x at time t+1. t+1 Let g(y) t ) represents a given y t In the case of x t+1 The estimated value, It is a measurable function, assuming g(y) t ) has finite second moments, and let G denote the set of g. For convenience, let g(y) be denoted as g(y). t ):=gt With the objective of minimizing the mean square error of the estimate, the above state estimation problem can be approximated as solving the following optimization problem:

[0101]

[0102] Among them, Y t-1 ={y s ,0≤s≤t-1} represents the historical measurement value at time t. x represents t+1 and y t The joint random vector, p t (z t |Y t-1 )and Representing known Y t-1 time z t The nominal conditional probability density and the actual conditional probability density. Let represent the mean squared error loss function at time t.

[0103] As is well known, when the nonlinear system model shown in Equation (1.12) is accurate and the noise distribution is completely known Gaussian white noise, the state can be estimated using the Extended Kalman Filter (EKF) algorithm. However, in reality, there are often uncertainties in the model parameters and the statistical characteristics of the noise, causing the state model to deviate from the nominal model. Therefore, this paper draws on the idea of ​​global robust estimation and proposes a global robust extended Kalman filter algorithm. The optimal state estimate g at time t is obtained by solving the optimization problem in Equation (1.13). t *

[0104] The idea behind the Global Robust Estimation (GRE) problem is to set an estimator whose worst-case performance loss (i.e., the mean squared error loss of all possible uncertainties relative to the nominal model) does not exceed a predetermined threshold τ. Since directly constraining the loss under all possible distributions is very difficult, this paper utilizes Lagrange duality theory, introducing a dual variable k under all possible distributions. Within, find the unique optimal parameter k. * This parameter is used to define the most sensitive distribution (i.e., the worst-case distribution) and then solve for the global robust estimator.

[0105] GRE questions can be represented as:

[0106]

[0107] in It is defined in The set of all possible probability density functions on , The loss function defined above, This represents the target loss threshold, or the acceptable optimal loss relative to the nominal case. It represents the probability distance between the possible actual probability density and the nominal probability density.

[0108] Let (k) t * ,g t * (k) represents the optimal solution to the GRE problem at time t, according to (k) t * ,g t * From the optimality of () and the first constraint of (1.14), we can see that:

[0109]

[0110] If and only if When the equality holds, at this time This is called the most sensitive density.

[0111] Before solving the GRE problem, we first present the properties of the optimal solution to the GRE problem as shown in Theorem 1 and Theorem 2. The proofs of the two theorems can be found in the literature.

[0112] Theorem 1: Consider the GRE problem (1.14), if the nominal probability density p follows the mean... Covariance Matrix The Gaussian distribution, where

[0113]

[0114] The solution to problem (1.14) has the following properties.

[0115] 1) The most sensitive density of the GRE problem (1.14) mean vector Covariance Matrix It can be represented as

[0116]

[0117] 2) The optimal robust estimate is:

[0118]

[0119] and

[0120] 3) The nominal error covariance matrix is ​​as follows:

[0121]

[0122] And the most sensitive error covariance is

[0123]

[0124] Where k * The solution is to the following question:

[0125]

[0126] Theorem 1 gives the optimal solution to the global robust estimation problem and the most sensitive density. Optimal estimate and the most sensitive covariance It was also proven that solving the GRE problem is equivalent to solving formula (1.20).

[0127] From formula (1.20), we define

[0128] γ(k,P):=k ln det((kP -1 -I n ) -1 +I n (1.21)

[0129] It can be seen that γ(·,P) lies in (λ) max Differentiable on (P),∞), and γ(k,·) is in The upper part can be slightly different.

[0130] The monotonicity of the function under the first constraint in formula (1.20) is given below by Theorem 2.

[0131] Theorem 2: Consider the function defined in (1.21). Assume... And k > λ max (P), then the following facts hold true:

[0132] 1) γ(·,P) in (λ max (P),∞) is monotonically decreasing.

[0133] 2)

[0134] 3)

[0135] 4) If Then γ(k,P)≥γ(k,Q)>0

[0136] According to Theorem 2, the optimization problem in formula (1.20) is transformed into a problem of finding the zeros of a monotonic function. Therefore, we can obtain the following corollary 1.

[0137] Inference 1: Assumption Then there exists a unique k. * >λ max(P) makes

[0138]

[0139] Where k * It is the unique solution to (1.20). This corollary proves the existence and uniqueness of the solution to the GRE problem.

[0140] At this point, to solve the GRE problem shown in equation (1.14), this paper uses the KL divergence as a measure. probability distance between p

[0141]

[0142] Assuming nominal probability density in

[0143]

[0144] Then for any The calculation formula is:

[0145]

[0146] Compared to and It is strictly convex, and If and only if When the equation holds true, at this time

[0147] At this point, combining formula (1.13), the global robust estimation problem shown in formula (1.14) can be expressed as:

[0148]

[0149] in, make

[0150]

[0151] At this point, the constraints in (1.24) can be represented as a dynamic minimum game problem:

[0152]

[0153] first, Solution The following lemma 1 is given, and the proof can be found in reference

[18] .

[0154] Lemma 1: Given g t ∈G and k t ,satisfy Maximize function for

[0155]

[0156] Where M(k) t ) is a guarantee Factors.

[0157] From Lemma 1, it can be seen that when p t When it is a Gaussian distribution, It is also a Gaussian distribution. (In obtaining...) back, optimal solution Given by the following formula

[0158]

[0159] The GRE problem at this point is to solve...

[0160]

[0161] When the optimal solution is found When the global robust estimator and the most sensitive density are solved by formulas (1.28) and (1.27) respectively, the most sensitive error covariance is obtained by formula (1.19).

[0162] 3) Global Robust Extended Kalman Filter (GREKF)

[0163] The previous section introduced the solution method for the global robust estimation problem. This section, based on the above global robust estimation problem and combined with the system model (1.12), derives the global robust extended Kalman filter.

[0164] For model (1.12), firstly, estimate the model around the current prior state. Linearization is performed, resulting in:

[0165]

[0166] in, Due to the nominal model x t+1 =f(x) t ), y t =h(x t Therefore, the linearized model can be expressed as follows:

[0167]

[0168] in, For the model shown in formula (1.31), assuming a given Y t-1 Prior conditional probability density function At this point, the nominal transition probability density follows the following distribution:

[0169]

[0170] The pseudo-nominal density then has the following form:

[0171]

[0172] Using the properties of Gaussian integrals,

[0173]

[0174] Regarding covariance:

[0175]

[0176] Therefore, p t (z t |Y t-1 It follows a Gaussian distribution, and we have:

[0177]

[0178] By Lemma 1, the actual conditional probability density It also follows a Gaussian distribution. According to Theorem 1 and formula (1.31), the optimal robust estimate can be expressed as:

[0179]

[0180] Where K t That is, the gain matrix, expressed as:

[0181]

[0182] Most sensitive density obey

[0183]

[0184] in

[0185]

[0186] Furthermore, given Y t At that time, x t+1 The nominal conditional covariance matrix is ​​expressed as:

[0187]

[0188] The most sensitive density covariance is:

[0189]

[0190] in It is the unique solution to formula (1.42).

[0191]

[0192] in and:

[0193]

[0194] In summary, the implementation process of GREKF is summarized as Algorithm 1 in Table 1, where the input parameters... Used to evaluate the credibility of the nominal model, and to adjust the difference between the nominal distribution and the most sensitive distribution. When κ=1, the algorithm simplifies to the standard Kalman filter, that is, the nominal model is completely credible.

[0195]

[0196] Table 1. Flowchart of the Global Robust Extended Kalman Filter Algorithm

[0197] The following analysis explains why GREKF is superior to the traditional EKF, mainly in the following two aspects:

[0198] 1. Because GREKF can overcome the inherent limitation of EKF in linearizing nonlinear systems using first-order Taylor expansions, the GRE approach does not assume that the linearized model is completely accurate, but rather calculates the covariance matrix... This increases the range of estimation uncertainty and makes the calculation of gain K more cautious, thereby reducing the accuracy loss caused by over-reliance on the state model.

[0199] 2. GREKF does not require precise knowledge of the process noise covariance matrix and the measurement noise covariance matrix. The covariance matrix of the most sensitive distribution in the system is calculated through algorithm iteration, realizing the system's adaptive adjustment to process noise and measurement noise, enabling the system to better adapt to the actual noise environment.

[0200] According to Algorithm 1, the process of the monocular state estimation algorithm for spatial targets based on GREKF is summarized as Algorithm 2 in Table 2.

[0201]

[0202]

[0203] Table 2. Flowchart of Algorithm 2

[0204] 4) Simulation

[0205] To verify the effectiveness of the proposed method, a simulation of an optical autonomous relative navigation scenario for a non-cooperative target in space was performed using MATLAB. The simulation parameters set in this paper are shown in the table below.

[0206]

[0207] Table 3. Simulation Parameter Settings

[0208] To verify the robustness of the proposed GREKF to state noise and measurement noise, this specific embodiment designs two simulation experiments. In simulation experiment A, the process noise is set as time-varying noise with unknown statistical characteristics, simulating the unmodelable uncertainty error caused by the unknown mechanism in the system. In simulation experiment B, impulse noise is added to the observation equation to simulate situations such as feature point mismatch, target temporary occlusion, or sensor failure caused by the lack of image texture during observation by a monocular camera.

[0209] A. Verification of filtering performance under dynamic uncertainties in the system

[0210] This section verifies the performance of the GREKF algorithm when time-varying noise with unknown statistical properties exists in the state equation. The process noise matrix B is set. t =randi(500Q), Q = 1 × 10 -5 I 24×24 Set the measurement noise DD Τ =1×10 -2 I 9×9 Furthermore, there is no correlation between process noise and measurement noise, i.e., BD. Τ =0 24×9 Set a constant ratio. As input parameters, this paper sets κ = 1.005. Based on the space target state space model (1.11) established above, simulations were performed using EKF and GREKF. The state estimation errors of the relative position, relative velocity, absolute quaternion, absolute angular velocity-inertia ratio, and coordinates of target feature points in its own system under the two methods are compared as follows: Figure 2 — Figure 9 As shown.

[0211] Depend on Figure 2 — Figure 9 As can be seen, due to the strong nonlinearity of the state model and observation model in this paper, EKF introduces huge errors when making linear approximations of the model, making it difficult for the filter to converge well. The proposed GREKF transforms the problem into a minimax problem. By finding an estimator, it can maintain good performance even under the most sensitive distribution. It takes into account the uncertainty of the model and reduces the confidence in the model by adjusting κ, thus suppressing the divergence of the filter.

[0212] The traces of the error covariance matrices of GREKF and EKF in this paper are compared below. like Figure 10 As shown.

[0213] Trace of the error covariance matrix It is the sum of the variances of the estimation errors of all state variables, reflecting the overall uncertainty and accuracy of the filtering algorithm. Figure 10 It can be seen that the GREKF proposed in this paper... Smaller size and faster convergence speed indicate that the proposed GRKF has better estimation accuracy and robustness.

[0214] B. Filter performance verification under outlier conditions

[0215] This section verifies the performance of the GREKF algorithm when outliers exist in the measurement equations. The measurement noise in the real system model is set to obey a set... The impulse noise is denoted as ε (0 < ε << 1), where ε is the probability of impulse noise occurrence, α (α >> 1) is the amplification factor of impulse noise used to control the amplitude of outliers, and R is the nominal observation noise covariance matrix. In this paper, ε = 0.01 and α = 100 can be set. The process noise matrix BB Τ =Q, Q = 1 × 10 - 5 I 24×24 To define the covariance matrix of the nominal process noise, set the measurement noise DD. Τ =R=1×10 -2 I 9×9 Furthermore, there is no correlation between process noise and measurement noise, i.e., BD. Τ =0 24×9 Set a constant ratio. As input parameters, this paper sets κ = 1.005. Similarly, based on the space target state space model (1.11) established above, simulations were performed using EKF and GREKF. The state estimation errors of the relative position, relative velocity, absolute quaternion, absolute angular velocity-to-inertia ratio, and coordinates of target feature points in their own system were compared between the two methods. Figure 11 — Figure 18 As shown.

[0216] Depend on Figure 11 — Figure 18 It can be seen that GREKF exhibits stronger robustness when facing observational noise outliers. Similarly, comparing the traces of the error covariance matrices of GREKF and EKF in this paper... like Figure 19 As shown,

[0217] Depend on Figure 19It can be seen that, in the presence of outliers in the observations, GREKF significantly improves the accuracy and robustness of state estimation through the idea of ​​global robust estimation, while the traditional EKF fails in state estimation due to its over-reliance on the nominal model. The above experiments fully verify the superiority of the GREKF proposed in this paper.

[0218] The disclosed embodiments have been described above to enable any person skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be applied to other embodiments without departing from the spirit and scope of this disclosure. Therefore, this disclosure is not limited to the embodiments given herein, but is consistent with the broadest scope of the principles and novel features disclosed herein.

[0219] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment 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 within the scope of protection of the present invention.

Claims

1. A monocular state estimation method for spatial targets based on global robust optimization, characterized in that, include: A monocular state estimation system model for a space target is established, the monocular state estimation system model including system state equations and measurement equations; Based on the monocular state estimation system model, the state estimates of the space target at each moment within the total duration are obtained through iterative calculation.

2. The monocular state estimation method for space targets based on global robust optimization as described in claim 1, characterized in that, The step of obtaining the state estimate of the space target at each moment within the total duration through iterative calculation based on the monocular state estimation system model specifically includes: The initial system state estimate and the initial most sensitive density covariance matrix of the space target are determined based on prior information. Set the initial value of the iteration number t to t = 1; Predict the system state at time t Based on the monocular state estimation system model and the most sensitive density covariance matrix of the previous time step... Solve for the filter gain matrix K at time t. t Therefore, based on the filter gain matrix K at time t... t The nominal error covariance matrix P at time t is predicted. t ; By measuring data y t and the filter gain matrix K at time t t The predicted value of the system state at time t The system state estimate at time t is obtained by updating the system state. For the nominal error covariance matrix P at time t t The most sensitive density covariance matrix at time t is obtained by updating the matrix. The number of update iterations is t = t + 1; When t < the maximum number of iterations T, the above iterative calculation process is repeated. The initial step of the iterative calculation process is to predict the system state prediction value at time t. Summarize the system state estimates at all times. The state estimates of the space target at each time point are obtained.

3. The monocular state estimation method for spatial targets based on global robust optimization as described in claim 2, characterized in that, The predicted system state value at time t Specifically, it includes: Based on the system state estimate from the previous moment Based on the monocular state estimation system model, the predicted system state value at time t is obtained.

4. The monocular state estimation method for space targets based on global robust optimization as described in claim 3, characterized in that, The monocular state estimation system model is as follows: Where, x t This represents the state at time t. and They respectively represent satisfying and Gaussian white noise, δ is the Kronecker delta function, f(δx) t ) represents the state equation of a nonlinear system with respect to the state error, h(x) t B represents the measurement equation of a nonlinear system with respect to the state. t Let D be the process noise matrix. t To measure the noise matrix, y t For measurement vectors, This represents the state estimation error at time t+1; The state vector of the monocular state estimation system for the space target is: Where r = [x, y, z] represents the position of the spatial target relative to the monocular camera coordinate system. Let q = [q1, q2, q3, q0] represent the relative velocity, q = [q1, q2, q3, q0] represent the absolute attitude quaternion of the spatial target relative to the inertial frame, ω = [ω1, ω2, ω3] represent the absolute angular velocity, and l = [l x ,l y ,l z ] represents the ratio of inertia, ρ m =[x m ,y m ,z m ], m = 1, 2, 3 represent the coordinates of three feature points on the surface of the space target.

5. The monocular state estimation method for space targets based on global robust optimization as described in claim 4, characterized in that, The system state estimate based on the previous moment Based on the monocular state estimation system model, the predicted system state value at time t is obtained. The following methods shall be used: in, 6. The monocular state estimation method for space targets based on global robust optimization as described in claim 4, characterized in that, The solution of the filter gain matrix K at time t t The following formula is used for calculation: Among them, A t To linearize the nonlinear state equations of the system, C t The observation matrix is ​​obtained by linearizing the nonlinear measurement equations of the system; The nominal error covariance matrix P at time t t The following formula is used for calculation:

7. The monocular state estimation method for spatial targets based on global robust optimization as described in claim 4, characterized in that, The measurement data y t and the filter gain matrix K at time t t The predicted value of the system state at time t The system state estimate at time t is obtained by updating the system state. The following methods shall be used: Δx t =K t [y t -h(x t )], in 8. The monocular state estimation method for space targets based on global robust optimization as described in claim 4, characterized in that, The nominal error covariance matrix P at time t t The most sensitive density covariance matrix at time t is obtained by updating the matrix. The following methods shall be used: Calculate the target loss threshold τ t The value, then, find the one that makes The optimal solution is valid. Then, according to the following formula, through the optimal solution... Update the most sensitive density covariance matrix at time t.

9. The monocular state estimation method for space targets based on global robust optimization as described in claim 4, characterized in that, Before setting the initial value of the iteration number t to 1, the method further includes: determining the maximum iteration number T based on the preset sampling interval and total duration.

Images