A Mars rover landing phase navigation method and system

Abstract

An embodiment of the present invention provides a Mars rover landing navigation method and system, comprising: establishing a measurement model based on visible landmarks at the current moment; obtaining a Fisher information matrix for each visible landmark based on the measurement model; calculating the trace corresponding to each visible landmark; constructing a preferred landmark distribution configuration when the number of visible landmarks is at least three, with the constraints of selecting multiple visible landmarks as preferred landmarks and maximizing the sum of their traces while minimizing the number of preferred landmarks; solving the preferred configuration using a greedy algorithm to determine the preferred landmarks; and navigating the Mars rover to landing using the preferred landmarks. This technical solution dynamically determines the optimal number of landmarks at each moment, achieving high-precision autonomous navigation and overcoming the onboard computing resource redundancy caused by an excessive number of landmarks and the low navigation accuracy caused by an insufficient number of landmarks.

Description

Technical Field

[0001] The present invention relates to the field of planetary probe technology, and in particular to a navigation method and system for the landing phase of a Mars probe. Background Art

[0002] Autonomous precision landing is crucial for Mars exploration missions. Its primary prerequisite is that the Mars rover's lander be able to autonomously acquire high-precision state information such as position, velocity, and attitude—in other words, autonomous navigation—to navigate to the designated landing site. Due to the long duration and long distances of Mars exploration missions, the accumulated errors of commonly used inertial navigation systems are a major source of error affecting inertial navigation accuracy. To achieve a precise landing, this error must be accurately estimated and compensated during powered descent. During its orbital exploration of Mars, a Mars rover can obtain precise position information for Martian surface landmarks, providing an effective source of measurement information for autonomous navigation during the landing phase. Therefore, integrated navigation based on landmark information has become a hot research topic for autonomous navigation during the landing phase. Generally speaking, the more landmark information available, the higher the accuracy of the autonomous navigation system's state estimation. However, in deep space exploration, onboard storage and computing resources are very limited, making it impossible to store and resolve a large number of landmarks.

[0003] In order to reduce the number of observed landmarks as much as possible while ensuring navigation accuracy on a detector with limited onboard storage and computing resources, it is necessary to select the landmarks that contribute most to navigation accuracy for observation.

[0004] In the process of implementing the present invention, the inventors discovered that the prior art has at least the following problems:

[0005] There are currently several methods for selecting landmarks, but due to factors such as the distribution of landmarks during the Mars rover's landing phase, none of these methods can achieve the highest navigation accuracy at all stages. Therefore, improving the landing accuracy of Mars rovers is a challenge that needs to be addressed. Summary of the Invention

[0006] An embodiment of the present invention provides a Mars rover landing phase navigation method, which takes into account the characteristics of landmark distribution and can effectively improve the landing accuracy of the Mars rover.

[0007] To achieve the above objectives, on the one hand, an embodiment of the present invention provides a method for navigating the landing phase of a Mars rover, comprising: establishing a measurement model for visible landmarks based on visible landmarks at the current moment; obtaining a Fisher information matrix for each visible landmark according to the measurement model; calculating the trace of the Fisher information matrix corresponding to each visible landmark; when the number of visible landmarks is not less than 3, constructing a preferred configuration of the landmark distribution, wherein the constraints of the preferred configuration of the landmark distribution are: selecting multiple visible landmarks as preferred landmarks, and maximizing the sum of the traces of the preferred landmarks while minimizing the number of preferred landmarks; solving the preferred configuration using a greedy algorithm to determine the preferred landmarks; and performing landing navigation for the Mars rover using the preferred landmarks.

[0008] On the other hand, an embodiment of the present invention provides a Mars rover landing segment navigation system, including: a Fisher information matrix construction module, used to establish a measurement model of visible landmarks based on visible landmarks at a current moment; obtain the Fisher information matrix of each visible landmark according to the measurement model; calculate the trace of the Fisher information matrix corresponding to each visible landmark; a preferred configuration construction module, used to construct a preferred configuration of the landmark distribution when the number of visible landmarks is not less than 3, and the constraint conditions of the preferred configuration of the landmark distribution are: selecting multiple visible landmarks as preferred landmarks, and maximizing the sum of the traces of the preferred landmarks while minimizing the number of preferred landmarks; a preferred landmark acquisition module, used to solve the preferred configuration using a greedy algorithm to determine the preferred landmark; and a first navigation module, used to perform landing navigation of the Mars rover through the preferred landmarks.

[0009] The above technical solution has the following beneficial effects:

[0010] The technical solution of this application utilizes the Fisher information matrix to construct the navigation system's observability matrix. Combined with the CR lower bound to describe the observability of landmarks during the Mars landing process, the scalar function of the observability matrix is ​​maximized to obtain the optimal landmark distribution configuration. Furthermore, a greedy algorithm is introduced to adaptively determine the number of preferred landmarks. Compared to other algorithms, the greedy algorithm offers significant computational complexity advantages, requiring only a few vector additions and subtractions. This effectively addresses the severe limitations of onboard storage and computing resources in deep space exploration missions. However, traditional greedy algorithms are prone to falling into local optima. To account for the decreasing number of visible landmarks during the probe's landing, the convergence threshold in the greedy algorithm is set to a time-varying floating value, ensuring that the solution is as close to the global optimum as possible. The optimal number of landmarks is dynamically determined at each moment, enabling high-precision autonomous navigation and overcoming the onboard computing resource redundancy caused by an excessive number of landmarks and the low navigation accuracy caused by an insufficient number of landmarks. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0012] Figure 1 This is a flow chart of a Mars probe landing stage navigation method according to the present invention;

[0013] Figure 2 This is a diagram of the composition of a navigation system for the landing stage of a Mars probe according to the present invention;

[0014] Figure 3 is a schematic diagram of the coordinate system used by the navigation system of the present invention;

[0015] Figure 4 This is a schematic diagram of the relationship between the Mars probe and the landmarks in the present invention;

[0016] Figure 5 A schematic diagram of a probe landing trajectory and randomly distributed landmark images in a specific embodiment of the present invention;

[0017] Figure 6 is a schematic diagram showing the change in the number of visible landmarks during the descent of the detector in a specific embodiment of the present invention;

[0018] Figure 7 Schematic diagram of the number of preferred landmarks at different times in a specific embodiment of the present invention;

[0019] Figure 8 3. This is a comparison chart of the RMSE of position errors of the preferred landmarks and randomly selected landmarks on each axis in a specific embodiment of the present invention;

[0020] Figure 9 3. This is a comparison chart of the RMSE of the attitude errors of the preferred landmarks and randomly selected landmarks on each axis in a specific embodiment of the present invention;

[0021] Figure 10 1 is a comparison chart of the RMSE of the velocity error on each axis between the preferred landmark and the randomly selected landmark in a specific embodiment of the present invention;

[0022] Figure 11 It is a planar distribution diagram of some preferred landmarks in a specific embodiment of the present invention. DETAILED DESCRIPTION

[0023] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0024] like Figure 1 As shown, an embodiment of the present invention provides a Mars probe landing stage navigation method, characterized by comprising:

[0025] S101. Based on the visible landmarks at the current moment, a measurement model of the visible landmarks is established (see Formula 16).

[0026] S102. Obtaining the Fisher information matrix (i.e., observability matrix, see Formula 23) of each visible landmark based on the measurement model.

[0027] S103, calculating the trace of the Fisher information matrix corresponding to each visible landmark (see Formula 40);

[0028] S104. When the number of visible landmarks is not less than 3, construct a preferred configuration of landmark distribution. The constraints of the preferred configuration of landmark distribution are: selecting multiple visible landmarks as preferred landmarks, and maximizing the sum of the traces of the preferred landmarks while minimizing the number of the preferred landmarks (see Formula 37).

[0029] S105, using a greedy algorithm to solve the preferred configuration (refer to the subsequent formula 38 and algorithm 1) to determine the preferred landmark;

[0030] S106. Perform landing navigation for the Mars probe using the preferred landmarks.

[0031] To improve landing navigation accuracy, this application uses Fisher information to construct the observability matrix of the navigation system. The scalar function of the observability matrix is ​​maximized to obtain the optimal configuration (preferred configuration) of the landmark distribution. Based on this optimal configuration, a greedy algorithm is used to adaptively determine the number of landmarks selected at each moment. Considering the gradual decrease in the number of observable landmarks during landing, the convergence threshold of the greedy algorithm is set to a dynamic value related to landing time to obtain the optimal number of landmarks.

[0032] Furthermore, the Mars probe landing segment navigation method further includes:

[0033] S107: When the number of the visible landmarks is greater than zero and less than 3, all the visible landmarks are used as the preferred landmarks;

[0034] S108: When the number of the visible landmarks is zero, perform landing navigation in an inertial navigation manner.

[0035] When the number of observable landmarks falls below three, there's no need to prioritize them; all observable landmarks can be used for pose calculations. In the late stages of landing, when the number of visible landmarks drops to zero, the landmark-assisted inertial navigation system transitions to a pure inertial navigation system. Because the accumulated inertial navigation errors can't be effectively corrected in the late stages of landing, navigation accuracy degrades somewhat, but remains within a tolerable range.

[0036] Furthermore, in step S105, the convergence threshold of the greedy algorithm is a variable value.

[0037] Furthermore, the convergence threshold is in negative proportion to the landing time, and is in positive proportion to the minimum value of all visible landmark traces; wherein the landing time refers to the time elapsed from the start of the landing process to the current moment.

[0038] At the beginning of the landing process, a large number of observable landmarks are visible, including a large number of high-quality landmarks that contribute significantly to navigation accuracy. At this point, high navigation accuracy can be achieved by selecting only a small number of landmarks from the available list. Therefore, a large convergence threshold should be selected at the beginning of landing to avoid overselecting landmarks, which would lead to computational resource overload and accuracy redundancy. As the rover descends in altitude, the number of visible landmarks decreases as it approaches the landing site, and their contribution to navigation accuracy decreases. If a large number of landmarks is still selected as the number of observable landmarks decreases, the number of selected landmarks may be too small, resulting in insufficient navigation accuracy. Therefore, when using a greedy algorithm, the convergence threshold should be a decreasing function of landing time, constructed using an inverse proportional function as shown in Equation 39.

[0039] Furthermore, the step S106 further includes:

[0040] S1061. Establish a dynamic model for the Mars rover landing process (see Formula 13).

[0041] S1062, linearizing the dynamic model using an extended Kalman filter (EKF) to obtain a linearized state equation;

[0042] S1063, performing landing navigation for the Mars probe in a combined navigation manner based on the linearized state equation and the preferred landmark, where the combined navigation refers to a navigation manner combining inertial navigation and landmark navigation;

[0043] The step S102 specifically includes:

[0044] S1021, converting the measurement model into a measurement equation;

[0045] S1022. Linearize the measurement equation using an extended Kalman filter to obtain a measurement matrix;

[0046] S1023. Obtain a Fisher information matrix for each visible landmark according to the measurement matrix.

[0047] like Figure 2 As shown, an embodiment of the present invention provides a Mars probe landing stage navigation system, characterized by comprising:

[0048] A Fisher information matrix construction module 21 is configured to establish a measurement model of visible landmarks based on the visible landmarks at the current moment; obtain a Fisher information matrix for each visible landmark according to the measurement model; and calculate a trace of the Fisher information matrix corresponding to each visible landmark;

[0049] a preferred configuration constructing module 22 for constructing a preferred configuration of the landmark distribution when the number of the visible landmarks is not less than 3, wherein the constraints of the preferred configuration of the landmark distribution are: selecting a plurality of the visible landmarks as preferred landmarks, and maximizing the sum of the traces of the preferred landmarks while minimizing the number of the preferred landmarks;

[0050] A preferred landmark acquisition module 23 is configured to solve the preferred configuration using a greedy algorithm to determine the preferred landmark;

[0051] The first navigation module 24 is used to perform landing navigation for the Mars probe using the preferred landmarks.

[0052] Furthermore, the Mars rover landing segment navigation system also includes:

[0053] a second preferred landmark obtaining module 25, configured to use all the visible landmarks as the preferred landmarks when the number of the visible landmarks is greater than zero and less than 3;

[0054] The second navigation module 26 is configured to perform landing navigation by inertial navigation when the number of the visible landmarks is zero.

[0055] Furthermore, in the preferred landmark acquisition module 23 , the convergence threshold adopted by the greedy algorithm is a variable value.

[0056] Furthermore, the convergence threshold is in negative proportion to the landing time, and is in positive proportion to the minimum value of all visible landmark traces; wherein the landing time refers to the time elapsed from the start of the landing process to the current moment.

[0057] Furthermore, the first navigation module 24 is specifically configured to establish a dynamic model of the Mars rover's landing process; linearize the dynamic model using an extended Kalman filter to obtain a linearized state equation; and perform landing navigation for the Mars rover using a combined navigation method based on the linearized state equation and the preferred landmarks, wherein the combined navigation method is a navigation method combining inertial navigation and landmark navigation.

[0058] The Fisher information matrix construction module 21 is further used to: convert the measurement model into a measurement equation; linearize the measurement equation through an extended Kalman filter to obtain a measurement matrix; and obtain the Fisher information matrix of each visible landmark based on the measurement matrix.

[0059] The method of the present invention is described below with a specific embodiment, and the implementation process of the specific embodiment is as follows:

[0060] 1. Mars landing navigation system model:

[0061] Landing a probe on Mars is an important step in realizing Mars exploration. It is necessary to determine the position, attitude, and velocity of the probe relative to the selected reference system. For ease of description, the following three coordinate systems are introduced: landing coordinate system, carrier coordinate system, and camera coordinate system. Figure 3 shown.

[0062] The landing coordinate system (L system) is centered on the predetermined landing point, with the z axis perpendicular to the landing plane and pointing upward, the y axis located on the landing plane pointing in the direction of the planet's rotation, and the x axis pointing in the direction of the planet's rotation. L Axis, y L axis and z L The axes together form a right-handed coordinate system.

[0063] Carrier coordinate system (B system) Carrier coordinate system is a coordinate system fixed on the detector body, and its coordinate origin is the center of mass of the detector, x B Axis, y B axis and z B The axes are usually defined about the principal axes of inertia of the detector.

[0064] The camera coordinate system (C system) takes the optical center of the camera as the origin of the coordinate system, x C y C The axis is parallel to the x and y axes of the image coordinate system, and the optical axis of the camera is z C Axis, the coordinate system satisfies the right-hand rule.

[0065] 1.1 Kinetic model

[0066] In order to solve the problem that traditional dynamic modeling is difficult to obtain an accurate planetary landing dynamic model, this paper directly uses the IMU (inertial navigation system) to establish a dynamic model and gives the probe landing dynamic equation based on the IMU output. Assuming that the probe is affected by gravity and thrust, the probe landing dynamic model can be described as

[0067]

[0068] in L v and L r is the position and velocity relative to the landing coordinate system (L system); is the quaternion from L to B, b a and b ω is the drift bias of the accelerometer and gyroscope; L a thrust is the control acceleration vector; L g is the gravitational force, which is calculated as a constant; n g is the unmodeled gravitational acceleration; n wa and n wω is the drift deviation noise; ω=[ω x ω y ω z ] is the angular velocity of the detector in frame B. Ω(ω) is defined as

[0069]

[0070] in is ω=[ω x ω y ω z ] is defined as the antisymmetric matrix of

[0071]

[0072] The output value of IMU a imu and ω imu It can be expressed as

[0073]

[0074] Among them C q is the attitude rotation matrix corresponding to the quaternion q, L ω G is the angular velocity of the planet in the L system, n a and n ω is the drift noise of acceleration and angular velocity, is zero-mean Gaussian white noise with covariance. Q is the covariance matrix

[0075]

[0076] 1.2 Landmark-based measurement model (or observation model)

[0077] Using the pinhole projection model, the camera is at t k Moment, for landmark p j The measurement is

[0078]

[0079] Where f is the focal length of the camera; is the noise-free measurement; is the measurement noise, and its covariance matrix is is the vector from the spaceborne camera to the landmark, and is calculated as follows:

[0080]

[0081] L p j is the coordinate of the landmark in the L system, which can be obtained by comparing the captured image with the landmark database in the landing map; represents the map error, and its covariance is Represents the coordinates of the detector in the L system.

[0082] Then the lander navigation state vector Has the following forms

[0083]

[0084] Calculate the landmark p according to the state vector of the navigation system j The expected measurement value of

[0085]

[0086] in

[0087]

[0088] Combining the state equation and measurement equation of landmark navigation (1) and (6), the following can be written:

[0089]

[0090] where z imu =(a imu ,ω imu )’s IMU inertial measurement, To observe the coordinates of the landmark points, several landmark points composition, N is the number of observed landmarks.

[0091]

[0092] Linearize the state equation:

[0093]

[0094] and G is the Jacobian matrix, defined as follows, where

[0095]

[0096] Linearize the measurement equation:

[0097]

[0098] Measurement Matrix The definition is as follows:

[0099]

[0100] in

[0101]

[0102] Then the covariance matrix of the navigation state error can be updated by numerical integration

[0103]

[0104] in Update the state and state variance of the navigation system using the Extended Kalman Filter (EKF)

[0105]

[0106] 2. Landmark selection method based on Fisher information matrix

[0107] 2.1 Fisher Information Matrix and CRLB

[0108] The Fisher (FIM) information matrix is ​​defined as the inverse of the CRLB (Cramer-RaoLowerBound), which is the lowest lower bound that the state estimate covariance can achieve under ideal conditions. The CRLB characterizes the uncertainty of the minimum target that can be obtained for a given set of measurements in the state system. The inverse of the CRLB is the FIM, which represents the amount of information contained in a given set of measurements in the state estimate. Mathematically, the CRLB is defined as

[0109]

[0110] Among them, x is the vector to be estimated, is the estimated value of x obtained from the measured data z, P is the covariance matrix of the estimation error, and C is the lowest lower bound of the state error covariance matrix, namely CRLB, whose inverse J is FIM.

[0111] Consider a nonlinear system with the following state equations and measurement equations:

[0112]

[0113] where x k represents the system state at time k, z k represents the measurement information at time k; v k is the systematic error, r k is the measurement error, assuming v k With r k is Gaussian white noise, r k ~N(0,R k ),v k ~N(0,Q k ), f(·) and h(·) represent the measurement functions of the state model and the measurement model, and their Jacobian matrices are in is the gradient operator of x

[0114] The recursive formula for the nonlinear system FIM is:

[0115]

[0116] FIM has the following two important properties:

[0117] 1) In the landmark selection, for the observable landmarks of the detector at a certain moment, the scalar function of FIM will increase monotonically with the increase of the number of landmarks, that is, N→∞, U(J N )→∞.

[0118] 2) Under the condition that landmarks can be observed, the FIMs of multiple landmarks can be calculated by superposition. For the system model in formula (22), assuming that the number of candidate landmarks is N, the FIMs of N landmarks can be obtained by recursion.

[0119]

[0120] 2.2. Landmark Optimization Scheme

[0121] In the landmark selection problem, if only the current position of the detector is considered, assuming that the current detector position is fixed, then for the landmarks that can be observed at that moment, the accumulated FIM information benefits of all observed landmarks are

[0122]

[0123] From the measurement matrix in (17) and (18), we can know

[0124]

[0125] Assume that the measurement noise of each landmark is uncorrelated and has the same variance, σ1=σ2=…=σ N

[0126] but

[0127]

[0128] FIM can evaluate the performance of landmark navigation. Its mathematical expression is in matrix form. Different scalars M need to be selected to optimize FIM. However, using scalars to replace matrices may lead to information loss. Therefore, the selection of scalar functions is crucial. Currently, the indicators for measuring the optimal configuration of landmarks mainly include D-excellent, A-excellent, E-excellent, etc.

[0129] The D-optimal correspondence is the determinant of FIM, namely:

[0130] Μ D (J) = det(J) (28)

[0131] Since the FIM is a symmetric positive definite matrix, its determinant is the product of all eigenvalues, which is proportional to the volume of the hyperellipsoid defined by the quadratic form accompanying the FIM matrix. Therefore, the physical meaning of maximizing det(J) is to minimize the volume of the hyperellipsoid.

[0132] The E-optimal correspondence is the minimum eigenvalue of FIM, that is:

[0133] Μ E (J) = min{eig(J)} (29)

[0134] From the above analysis, we can see that the physical meaning of maximizing min{eig(J)} is to minimize the maximum axial length of the hyperellipsoid.

[0135] The A-optimal correspondence is the trace of FIM, that is:

[0136] Μ A (J)=tr(J) (30)

[0137] The physical meaning of maximizing tr(J) is to minimize the variance of the average estimate.

[0138] The existing technology has verified that the A-optimal index has better performance than D-optimal and E-optimal for target selection problem by numerical simulation. In this paper, the trace of A-optimal FIM is used as a scalar function to optimize FIM.

[0139]

[0140] Since the matrix trace operation is commutative in matrix multiplication, we have

[0141]

[0142] Notice is an antisymmetric matrix with a main diagonal of 0. and At the current moment, it can be approximately regarded as a fixed value and is not affected by the choice of landmark. Then the trace of FIM can be written as

[0143]

[0144] Where C0 is a constant, so maximizing the trace of the FIM matrix is ​​equivalent to maximizing From (18), we can get

[0145]

[0146] Then maximizing the trace of the FIM matrix is ​​equivalent to

[0147]

[0148] is the vector from the spaceborne camera to the landmark. Figure 4 As shown in Figure 3, for the optimal observation configuration, the value of the corresponding FIM track is only related to the number of landmarks and the relative positions of the landmarks and the detector.

[0149] The landmarks observed by the probe's onboard camera at different times are different. The closer the probe is to the landing site, the fewer landmarks the onboard camera can observe. The landmarks that the probe can observe at time k must meet the following conditions:

[0150]

[0151] α is the field of view angle, d is the reference direction vector of the camera optical axis in the L system, and δβ is the maximum camera error caused by the reference direction vector.

[0152] 2.3 Determination of the number of preferred landmarks

[0153] Use U=tr(J N) is used to describe the effect of landmark selection on navigation accuracy. Different landmark configurations and numbers will result in different U. Generally, the more landmarks selected, the higher the navigation accuracy. However, too many landmarks will severely overload the onboard computing resources. In previous landmark selection problems, the number of preferred landmarks is generally a fixed value, and the number of preferred landmarks at each moment is the same. The contribution of landmarks to navigation accuracy varies at different moments. The above method cannot achieve the highest navigation accuracy at each stage. The landmark selection problem for the landing phase of the probe can be reduced to finding the maximum value of Equation (35) under the constraints of Equation (36), and the number of preferred landmarks is as small as possible, that is:

[0154]

[0155] Greedy algorithms are a common method for finding optimal solutions. They divide the solution process into several steps, each of which is greedy, selecting the optimal solution for the current state, hoping that the resulting stacked solution will also be the optimal solution. This paper combines FIM with a greedy algorithm to determine the configuration and number of optimal landmarks.

[0156] Let B represent the set of all available landmarks. The goal is to find a subset D containing the fewest landmarks so that at each imaging time t k , the following constraints always hold

[0157]

[0158] in The set of candidate landmark points is S(t k )=(BD)∩A(t k ), A(t k ) indicates that at t k The landmarks that are visible at all times. U(D) is the landmark navigation accuracy obtained from the landmark dataset D. The algorithm flow is shown in Table 1. Convergence threshold U min This is an optional parameter that can be set to a fixed or dynamic value depending on the number of visible landmarks.

[0159] If U min If the value is too small, too many landmarks will be selected, which will cause a serious load on the onboard computing resources. min If the value is too large, too few landmarks will be selected, resulting in insufficient navigation accuracy. At the beginning of landing, there are many landmarks that can be observed, and there are a large number of high-quality landmarks that contribute greatly to navigation accuracy. At this time, only a small number of landmarks can be selected from the observable landmarks to achieve higher navigation accuracy. Therefore, a larger U should be selected at the beginning of landing. minAvoid selecting too many landmarks, which will cause computing resource load and precision redundancy. As the probe descends in altitude, the closer it gets to the landing point, the fewer landmarks are visible, and the lower the contribution of landmarks to navigation accuracy. If a larger U is still selected when the number of observable landmarks decreases, min , the number of preferred landmarks may be too small, resulting in insufficient navigation accuracy. When the number of observable landmarks is less than 3, there is no need to optimize the landmarks, and all observable landmarks are used for pose calculation.

[0160] In summary, min It should be a decreasing function of landing time t, and the simplest inverse proportional function is used to construct U min , as follows. is the trace of the FIM information matrix of the observable landmark that contributes the least to navigation accuracy. a is an optional parameter as follows, which is used to control U min The range of change:

[0161]

[0162]

[0163] Table 1. Greedy algorithm flow for landmark selection based on Fisher information matrix

[0164] 3. Simulation

[0165] In order to evaluate the preferred landmark solution proposed in this specific embodiment, numerical simulation was performed using MATLAB.

[0166] 3.1 Simulation parameter settings

[0167] The Mars landing process was simulated, assuming that the landing phase lasted 100 seconds. The navigation camera recorded images up to 50 meters at a rate of 1 Hz. The field of view (FOV) of the camera was 50, the focal length was 2000 pixels, and the image noise was 1 pixel. Assuming that the inertial navigation unit (IMU) was LN-200, providing inertial measurement values ​​at 50 Hz, the actual state of the probe at the initial moment is shown in Table 2. Assuming that the initial state error of the position was 100 meters, the initial state error of the velocity was 1 m / s, the initial state error of the attitude of each axis was 1°, and the angular velocity of rotation was [0 0 0.2]° / s. Assuming that the distance from the landmark point to the local horizontal plane follows a normal distribution with a standard deviation of 2 meters, an irregular landing surface was generated. Assuming that the landmarks are randomly distributed on the irregular surface with an average density of 100 / km 2 , the standard deviation of the horizontal position error is 2 m. The process noise is Q. The local gravity noise is assumed to have a standard deviation of 1×10 -1 m / s 2 Gaussian white noise.

[0168] Q=diag([2.4×10 -14 I32.5×10 -14 I32.4×10 -7 I31.2×10 -7 I31×10 -8 I3])

[0169] Table 2 The actual state of the detector at the initial moment

[0170]

[0171]

[0172] 3.2 Simulation Experiment Results

[0173] like Figure 5 As shown in the figure, the probe's Mars landing orbit and the distribution of landmarks during simulation are given. Figure 6 The figure shows the number of visible landmarks at each imaging moment during the probe's descent. For a given landmark density, there are approximately 650 landmarks in the landing area. Therefore, if all available landmarks are used for navigation, approximately 650 landmarks must be stored onboard, which is extremely challenging given the limited storage and computing resources in planetary landing missions. In order to reduce the number of landmarks selected for landmark navigation, Algorithm 1 is used to solve the landmark number selection problem. In Algorithm 1, U min Set as a is an optional parameter. Table 3 shows U min The relationship between the number of all landmarks selected during the landing process and the running time of the simulation program, U min The larger the value, the more landmarks are selected, and the longer the average and maximum running time of the corresponding simulation program. min This will result in too many landmarks being selected. min After it reaches a certain value, further reduction will not significantly improve navigation accuracy. min , at this time U min This can be considered infinite, meaning that no landmark selection is performed and all observed landmarks are combined for pose calculation. When navigation accuracy reaches a high level, increasing the number of observed landmarks has a limited impact on navigation accuracy. In the late stages of landing, when the number of visible landmarks in D drops to zero, the landmark-assisted inertial navigation system transitions to a pure inertial navigation system. Because the accumulated inertial navigation errors cannot be effectively corrected in the late stages of landing, navigation accuracy diverges somewhat, but remains within a tolerable range.

[0174] Table 3. Different U min The number of selected landmarks and the running time

[0175]

[0176] In order to evaluate the accuracy of the landmark optimization scheme, the FIM is combined with the greedy algorithm to obtain the number and configuration of the optimal landmarks at each moment. According to the above simulation results, the convergence threshold U in the greedy algorithm is set to min Set to min(U(D)) / 150t, the number of preferred landmarks at each moment is as follows Figure 7 , randomly select the same number of landmarks as the original one at each moment and compare the navigation errors of the two on each axis.

[0177] Figure 8 、 Figure 9 、 Figure 10 The mean squared error (RMSE) of position, velocity, and attitude is shown. For the same number of landmarks, the error and RMSE for position and attitude along each axis are lower when selecting landmarks at the initial landing stage than when selecting landmarks randomly. Later in the landing stage, as the number of observable landmarks decreases, the error increases, but remains within a tolerable range. Notably, there is no significant difference in yaw angle error between the two. This is because the yaw angle is unobservable when measuring only with known landmarks, so regardless of the selected landmarks, the yaw angle does not change significantly.

[0178] Regarding velocity errors and RMSE in each axis, at the beginning of landing, the velocity error for the selected landmarks was lower than that for the randomly selected landmarks, but both remained at a relatively high level. Over time, the velocity error significantly decreased as the landmark measurements were repeatedly corrected for the inertial navigation system. The velocity error for the selected landmarks converged faster than the velocity error for the randomly selected landmarks. Later in landing, as the number of visible landmarks decreased, the errors for the two methods remained relatively low, with no significant difference. This is because the landmark measurements do not directly include velocity information, making the correction for the velocity error indirect. The estimate of the probe's velocity is primarily derived from the dynamic model, resulting in underdetermined measurement information and unstable state estimation. In the absence of landmark measurements, the errors for the two methods were not significantly different.

[0179] Figure 11 The planar distribution of some selected landmarks is shown. We selected the moment when many landmarks are visible during the initial landing phase, starting at the 5th second and sampling every 5 seconds for a total of 6 times. The landmark configuration shows that the landmarks are relatively scattered, mostly located at the edges of the image. For a single landmark, the trace of the FIM information matrix is:

[0180]

[0181] Projecting the point of the camera coordinate system to the pixel coordinate system, we can get

[0182]

[0183] Comparing (40) and (41), if the FIM is larger, then The bigger, The smaller it is, the more it reflects (41), that is, |x in the pixel coordinate system i |,|y i The larger the |, the more the landmarks are distributed at the edge of the image. The area of ​​the polygon enclosed by the landmarks at the edge of the image is proportional to the distance from the landmark to the probe's projection on the landing surface; the larger the distance, the larger the area of ​​the polygon. The area of ​​the polygon enclosed by the landmarks at the edge of the image can be used to approximate the accuracy of the landmark measurement model. Ideally, the optimal landmark distribution should be centered on the probe's projection point, with landmarks located at the very edge of the image captured by the onboard camera, forming a regular polygon. However, due to the influence of the onboard camera's field of view, focal length, and the distribution of landmarks on the Martian surface, as shown in the landmark distribution images at 20, 25, and 30 seconds, landmarks may not necessarily be located at the edge of the image; they may be concentrated on one side of the probe.

[0184] The above description of the disclosed embodiments is intended to enable any person skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other embodiments without departing from the spirit and scope of the present disclosure. Therefore, the present disclosure is not limited to the embodiments presented herein but is intended to be consistent with the broadest scope of the principles and novel features disclosed herein.

[0185] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A Mars rover landing phase navigation method, characterized in that: include: Based on the visible landmarks at the current moment, a measurement model of the visible landmarks is established; According to the measurement model, a Fisher information matrix of each visible landmark is obtained; Calculate the trace of the Fisher information matrix corresponding to each visible landmark; When the number of the visible landmarks is not less than 3, constructing a preferred configuration of the landmark distribution, wherein the constraints of the preferred configuration of the landmark distribution are: selecting a plurality of the visible landmarks as preferred landmarks, and maximizing the sum of the traces of the preferred landmarks while minimizing the number of the preferred landmarks; Solving the preferred configuration using a greedy algorithm to determine the preferred landmark; The Mars probe is navigated for landing using the preferred landmarks.

2. The Mars probe landing segment navigation method according to claim 1, wherein: Also includes: When the number of the visible landmarks is greater than zero and less than 3, all the visible landmarks are used as the preferred landmarks; When the number of the visible landmarks is zero, landing navigation is performed in an inertial navigation manner.

3. The Mars probe landing segment navigation method according to claim 2, wherein: In the process of solving the preferred configuration using the greedy algorithm, the convergence threshold of the greedy algorithm is a variable value.

4. The Mars probe landing segment navigation method according to claim 3, wherein: The convergence threshold is in negative proportion to the landing time, and is in positive proportion to the minimum value of all visible landmark traces; wherein the landing time refers to the time elapsed from the start of the landing process to the current moment.

5. The Mars probe landing segment navigation method according to claim 1, wherein: The method of performing landing navigation on the Mars probe by using the preferred landmarks further includes: Establish a dynamic model of the Mars rover landing process; Linearizing the dynamic model through an extended Kalman filter to obtain a linearized state equation; performing landing navigation for the Mars probe in a combined navigation manner according to the linearized state equation and the preferred landmark, wherein the combined navigation refers to a navigation manner combining inertial navigation and landmark navigation; Obtaining the Fisher information matrix of each visible landmark according to the measurement model specifically includes: converting the measurement model into a measurement equation; Linearizing the measurement equation by using an extended Kalman filter to obtain a measurement matrix; According to the measurement matrix, the Fisher information matrix of each visible landmark is obtained.

6. A Mars rover landing stage navigation system, characterized in that: include: A Fisher information matrix construction module is configured to establish a measurement model for visible landmarks based on the currently visible landmarks; obtain a Fisher information matrix for each visible landmark based on the measurement model; and calculate a trace of the Fisher information matrix corresponding to each visible landmark. a preferred configuration construction module, configured to construct a preferred configuration of the landmark distribution when the number of the visible landmarks is not less than 3, wherein the constraints of the preferred configuration of the landmark distribution are: selecting a plurality of the visible landmarks as preferred landmarks, and maximizing the sum of the traces of the preferred landmarks while minimizing the number of the preferred landmarks; A preferred landmark acquisition module, configured to solve the preferred configuration using a greedy algorithm to determine the preferred landmark; The first navigation module is used to perform landing navigation for the Mars probe through the preferred landmarks.

7. The Mars probe landing stage navigation system according to claim 6, wherein: Also includes: a second preferred landmark acquisition module, configured to use all the visible landmarks as the preferred landmarks when the number of the visible landmarks is greater than zero and less than 3; The second navigation module is configured to perform landing navigation in an inertial navigation manner when the number of the visible landmarks is zero.

8. The Mars probe landing stage navigation system according to claim 7, wherein: In the preferred landmark acquisition module, the convergence threshold of the greedy algorithm is a variable value.

9. The Mars probe landing stage navigation system according to claim 8, wherein: The convergence threshold is in negative proportion to the landing time, and is in positive proportion to the minimum value of all visible landmark traces; wherein the landing time refers to the time elapsed from the start of the landing process to the current moment.

10. The Mars probe landing stage navigation system according to claim 6, wherein: The first navigation module is specifically configured to establish a dynamic model of the Mars rover landing process; linearize the dynamic model using an extended Kalman filter to obtain a linearized state equation; and perform landing navigation for the Mars rover using a combined navigation method based on the linearized state equation and the preferred landmarks, wherein the combined navigation method is a navigation method combining inertial navigation and landmark navigation. The Fisher information matrix construction module is further used to: convert the measurement model into a measurement equation; linearize the measurement equation through an extended Kalman filter to obtain a measurement matrix; and obtain the Fisher information matrix of each visible landmark based on the linearized measurement matrix.

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