A reliable state estimation is essential for an autonomous vision-based navigation system such as a mobile robot to enable accurate localization and environment perception with respect to undefined environments[1].Reliable perception systems depend on the availability of sufficient informative sensor observations and environmental information to ensure a continued accurate performance[2]. State estimation methodologies assume the existence and preservation of observability (the ability of the system states to be reconstructed from system output)[3]. However, this preserved observability condition may be violated in environments with limited or scarce information, resulting in increased estimation uncertainty and even divergence, especially for monocular vision-based autonomous systems.

2.1.5 重复性考察 按照“2.1.4”项下分别制备Lut-SD和Lut-PC-SD供试品溶液，各6份。按照“2.1.1”项下色谱条件分别进样，结果显示Lut-SD峰面积的RSD为0.79%，Lut-PC-SD峰面积的RSD为0.62%。

In recent years, observability analysis techniques have received significant attention. Observability analysis provides a tool to evaluate the observability conditions with respect to the current system state and environment. Observability-constrained active control techniques leverage observability analysis to quantify the implications of sensor observations on a state estimate accuracy toward an informed trajectory selection[3], faster estimator convergence[4], and optimal sensor placement[5]. Observability-constrained vision navigation systems[6-8] detect the unobservable direction and reduce the estimation inconsistency by explicitly prohibiting spurious information gain. Trajectory is optimized to guarantee the sensing observability and controlling stability of the system[9]. Sampling trajectories are selected to maximize observability to localize the robot and construct the map of the environment[10-11]. Path planning has also been incorporated with visibility constraints towards the goal of less exploration time in unknown environments[12]. However, these studies focused on the observability analysis of the current system states, without considering the future observability and impact of future motions on the system observability. Local observability prediction can be of great value in many problematic situations where the reconstruction of the state is difficult and need to be sensed actively, such as robot localization in an unknown environment[9]. By characterizing the impact of future motion on system observability, this technique enables informed selection of future motions to avoid the potential observability degradation, and consequently to improve state estimation performance.

In this work, an online methodology is proposed, seeking to predict the local observability conditions and suggest observability-constrained motion directions toward enabling robust state estimation and safe operation for an autonomous system in unknown environments.The formulation leverages efficient numerical observability analysis and motion primitive technique to realize the local observability prediction, and accordingly suggest the future motion directions to avoid the potential estimation degradation due to observability deficiency. Following the prior work[13], the empirical observability Gramian (EOG)[14] is employed to enable a real-time local observability evaluation. A motion primitive[15] technique is utilized to enable local path sampling and observability-constrained motion suggesting. We assess the implication of potential motions on the system observability and resulting state estimation performance by evaluating the observability of potential trajectories and seek to preserve the estimation consistency by explicit motion direction selection.

The proposed approach is specialized to a monocular visual-inertial state estimation framework to assess the viability of the proposed approach to correctly predict the observability of future motions and effectively making motion suggestions to avoid the potential state estimation degeneracy of the perception system. Monocular visual-inertial state estimation methodology is a representative vision-based perception strategy that enables autonomous operation with resource-constrained systems such as a micro aerial vehicle and commodity devices.This choice of sensing modalities also represents a particularly challenging state estimation formulation due to the lack of the direct metric depth observation[16]. It is thereby essential for such a system to assure a full-state observability to achieve the state estimation accuracy.

1 Methodology

end.

1.1 EOG-based observability evaluation for mono V-I estimator

The optimization-based monocular visual-inertial state estimation problem is formulated with respect to a sliding window that contains n visual keyframes and a local map containing m landmarks observed by the key frames, which is solved via a recursive optimization strategy. The full state parameters to be estimated are formulated as a vector X∈10n+m+3,

·Other directions are moderately suggested, in which the observability condition is believed to be able to provide sufficient information to ensure reasonable state estimation performance.

血管腔内修复术治疗Standford B型主动脉夹层临床疗效 …………………… 陈 豪，等(9):1079

(1)

where and are the relative translation, relative rotation represented as a quaternion, and linear velocity of the kth keyframe with respect to the initial state, respectively. The jth landmark is represented by using depth λj with respect to the first keyframe in the window that observes the landmark. The gravity vector in the initial state is denoted as g0∈3. The process and measurement models are defined the same as those in prior work[13,19], and the recursive optimization aims to find a configuration of system parameters that minimize the sum of the Mahalanobis distance of all measurement errors[19]:

(2)

where zimu and zcam are inertial measurement unit (IMU) and camera measurements, rimu and rcam are the residuals of IMU and camera measurements, Pimu and Pcam are the corresponding residual covariance. An IMU pre-integration technique[20]is employed to represent the IMU measurement. The resulting integrated system is treated as sensor outputs in the optimization and EOG state-output simulation.

This measure directly represents the magnitude of the system outputs perturbation with respect to the perturbed system states, capturing the sensitivity of the system output with respect to the system states. Mathematically is equivalent with However, is significantly faster to compute.

在一本书的序言里，有学者这样写道：一些人把书法当作“艺术”而进行“艺术创作活动”，张扬着一种圣洁与高雅；一些人把书法当作“群众文化”而进行“群众文化活动”，显示着一派热闹与狂欢；一些人把书法当作“学术”而进行“学术研究活动”，追求一种深思与沉静。没错，书法由这几种状态组成，每种状态都起到了非常重要的作用。随着经济的发展，社会的进步，把书法作为一种休闲的生活方式也渐渐成为人们选择的对象。把书法放在休闲文化视野下进行探究，有什么样的意义和价值呢，作者带着这样的好奇心开始探索，并把思考过程献给读者，就正于方家。

In this work, a scalar measure is introduced to quantify observability based on the EOG computation. Several measures have been used in recent literatures to evaluate the observability of nonlinear systems. The eigenvalues λ of the EOG represent the observability of each system parameter[21]. The local condition number, κ=λmax/λmin, defines the relative scaling between the most and least observable parameters and indicates the degree to which the observability is dominated by a subset of parameters. Consequently, a large value of the condition number suggests disparate observability between parameters leading to degraded state estimation performance. As the condition number reflects a relative scale, in cases where all of the parameters have equally poor observability, the condition number is still small, and thus does not accurately reflect the degraded conditions.The mean of the eigenvalues can be used to capture the average observability of all parameters. In order to decrease the computational overhead associated with computation of the EOG eigenvalues, we propose an alternative observability measure. Noting that the EOG is a symmetric matrix that is dominated by diagonal entries and the fact that the trace of a square matrix equals the sum of its eigenvalues, the mean of diagonal coefficients of the EOG matrix diagW is used, and denoted by as

(3)

The system observability is analyzed given the monocular vision-based sliding window state estimation formulation by the efficient EOG computation[13]. The EOG provides insight into the sensitivity of the system outputs with respect to the perturbed system states and captures the ability of the estimator to reconstruct the system states given the sensor outputs by numerically simulating the system state-output behaviors. Crucially, computation of the EOG is independent of state estimation and is therefore a viable observability analysis technique, which makes it possible to perform the observability prediction even in a degraded estimation scenario.Benefiting from the additive property, the EOG can be efficiently computed by partitioning the system output into sub-vectors and exploiting the underlying formulation sparsity of the EOG. The full EOG W is readily computed by perturbing the system initial conditions x∈n directly in positive and negative directions and simulating the state-output 2n times.

学困生问题不仅影响到学生个体的发展，而且影响到我县、我校教育的总体质量。新课程要求老师在教学过程中关注每一个学生，转化学困生。因此，建立合理有效的学困生教育援助机制，是我国，也是我校当前教育发展中一件刻不容缓的事情。在这样的背景下，笔者2016年12月成立了《激情教育用于学困生教育援助》的研究课题小组，经过两年的调查研究分析，通过激情教育对于学困生的实施，调动了学困生学习的积极性，使他们渐渐提高了学习成绩。

1.2 Generation and observability evaluation of motion primitive

Motion primitives are incorporated with the EOG evaluation to enable a motion extrapolation and subsequent local observability prediction. The EOG is computed for motion primitive end points based on the current state to enable the observability prediction locally.

A motion primitive generation strategy[15] is employed to compute primitives based on a discretized set of initial and final conditions with different trajectory durations. While the approach extends readily to three dimensions, in this work,for simplicity of presentation, we compute motion primitives for a system in two dimensions. The computation is decoupled into translation and heading trajectory generation with higher-order end point constraint bounds that correspond to the expected rates of motion exhibited during the simulation and experimental studies. After the computation of the motion primitive library, a look-up-table is generated to enable efficient online queries to find the appropriate end point states for observability evaluation.

After the generation of motion primitives, each motion primitive end point is treated as a future key frame and added into the sliding window, and then the EOG can be computed with respect to the extended sliding window to get the observability measure as represented in sect. 1.1. To ensure the accuracy of observability evaluation, the expected camera observations for each end point are predicted individually based on the end point state and estimated environment by re-projecting all the landmarks in the local map using an appropriate camera measurement model. A minimum limit of feature depth is applied during the camera observation prediction, so that very close features can be eliminated to avoid observability value blips caused by the introduced large parallax, and actually these features are hard to be tracked due to the large tracking distance in consecutive frames.

2.2 丙泊酚ECe的量效关系 Probit结果(图1)显示：丙泊酚ECe50为5.14 μg/mL(95% CI 4.90～5.38)，ECe95为6.07 μg/mL(95% CI 5.72～6.96)。

1.3 Trajectory observability evaluation

To predict the local observability condition and suggest next-step motion direction, a trajectory tree with specified number of levels and branches is generated to realize extrapolation. As shown in Fig.1, a 3-level extrapolation frame with 3-branch motion primitives is generated, and totally 27 potential trajectories in the local region based on the current state are created. The observability conditions of potential trajectories composed of a series of motion primitive end points are evaluated by synthesizing the observability measure of involved end points. For simplicity of representation and without loss of sensitivity due to wide camera FOV, we compute each motion primitive with three spreading branches. The orientation of the system is instantaneously in the direction of the motion.

Fig.1 Example of a 3-level extrapolation frame with 3-branch motion primitives

Using the trajectory tree with multiple level extrapolation, the observability evaluation enables local observability prediction with a certain degree to avoid a sudden dead end from which the state estimator may not recover. The observability cost for each trajectory is computed using a weighted strategy, i.e. the closer steps use the larger weighting factor, based on the fact that the closest step has more accurate observability evaluation and is more crucial in near-term motion execution than later steps.Thus for a specified trajectory with N steps (end points), the observability measure K can be computed using all the observability measures ki of end points and preset weighting factors wi

(4)

where the weighting factors subject to w1>…>wi>…>wN, and i=1 corresponds the closest step. For example, the cost of trajectory S-S2-S23-S231 in Fig.1 can be computed using the involved three end points as

As the observability prediction for the first step is more accurate than later steps, a more conservative strategy can be applied by executing one-step motion according to the multi-level evaluation result, without loss of foresight. Under this scenario, it is preferable to evaluate the observability measure for a motion direction instead of a specified trajectory. The observability cost for each motion direction can be computed using all the observability measures of the involved motion primitives.

(5)

in which, N is the number of levels, M is the number of motion primitives in each level of one motion direction, k(i,j) is the observability measure of the jth motion primitive in ith level, and the motion primitives in the same level use identical weighting factor wi. Considering the example in Fig. 1, the future motion for current state S is spread out with three motion directions S1,S2,S3, and the observability cost of each direction can be evaluated using the involved 13 end points. For example, the observability cost of the second directionis computed as

(6)

Fig.2 Motion suggestions for a predefined simulation scenario and straight trajectory

Thus the observability constrained motion direction can be suggested according to the resulting observability measures, and then can be incorporated with other motion constraints to yield an informed motion planning for the next step. Note that in the actual application of this strategy, the system doesn’t have to wait for the completion of the one-step execution to start the next motion suggestion. Instead, a denser motion suggestion can be generated and followed after each state estimation of a new coming frame, so that the new sensor observations can be added into the system and the environment information can be updated to yield a more accurate local observability prediction and consequently better motion suggestion.

1.4 Observability-constrained motion direction suggestion

After computing the observability cost for all the motion directions, the following strategy in Algorithm 1 can be used to propose the motion suggestion. An example of motion suggestion along a predefined trajectory in a simulated environment is shown in Fig.2. The corresponding online observability prediction results in three directions (left, forward, or right) is shown in Fig.3. Different motion directions are suggested due to the different landmark distribution in three stages. A threshold is used to identify the “forbidden direction”. Motion planner prefers the motion direction with a higher observability measure.

Fig.3 Observability prediction and resulting motion direction suggestion

贵州开磷化肥有限责任公司总经理陈忠华则对这种现象表示无奈，他认为这种现象普遍，也给企业带来了各种各样的影响，但是企业对这种事情除了走法律程序外别无他法。而法律诉讼又会给企业增加无形的成本。

Assume there are m motion directions to be evaluated.

Initial condition:

③底座：作用是固定支撑板、水池座。通过部分配合和部分定位的形式，将几个部件紧紧地连接在一起，如图3所示。

Kmax=0;

imax=1;

forbidden_directions.clear();

Loop i: from 1 to m

if Ki<Thobs, then forbidden_directions.push_back(i);

end.

对湖南省常德市各县市区农户家中收获的早籼稻谷随机抽样140份，每个样品以四分法分出约50g稻谷，用砻谷脱壳，经过旋风磨磨成米粉至40目筛水平。经过原吸法全部检测后取其中16份含镉样本进行试验。

Results:

2.2.3.1 密度(X1)与施K2O(X4)的农艺效应分析。对产量回归方程令X2(施N)=0、X3(施P2O5)=0，则得：Y1、4=2 153.52+35.60X1+70.18X4-71.09X12-99.63X42+86.94X1X4。

if Ki>Kmax, then Kmax=Ki, imax=i;

Algorithm 1 Strategy of motion direction suggestion

This section briefly summarizes relevant concepts related to monocular visual-inertial state estimator and EOG-based observability analysis based on prior works[2,13,15,17-19], and introduces a method to predict the observability of future motions and propose motion direction suggestions.

end loop.

“所谓混合式学习就是要把传统学习方式的优势和网络化学习的优势结合起来，也就是说，既要发挥教师引导、启发、监控教学过程的主导作用，又要充分体现学生作为学习过程主体的主动性、积极性与创造性”（何克抗教授）。李克东教授进一步指出，混合式学习形式上是在线学习与面对面学习的混合。但其更深层次是包括了基于建构主义、行为主义、认知主义等不同教学理论的教学模式混合。教师主导活动和学生主体参与活动的混合，课堂教学与在线学习不同学习环境的混合，不同教学媒体和教学资源的混合，自主学习和协作学习不同学习方式的混合，课堂讲授和虚拟教室的混合。

·Forbidden_directions indicates the directions in which the system is believed to experience an observability-deficient condition and prone to estimation degradation or failure;

·imax indicates the most-suggested direction. Even in the worst case where Kmax<Thobs, this is the best we can do to keep the system moving forward towards the goal;

煤炭资源开采由浅部向深部发展是客观的必然规律，也是世界上众多产煤国家面临的共同问题。德国、波兰、俄罗斯、英国等的开采深度部分矿区超过1000m[1,2]，目前我国东部新汶、平顶山、淮南、徐州、开滦、邢台等矿区相继进入了超千米开采阶段，最大开采深度到1450m[3,4]。煤炭资源进入超千米开采后，地应力急剧增高、围岩节理裂隙发育，巷道围岩呈现出明显的软岩变形特征，导致巷道维护极其困难，成为制约超千米深井煤炭资源高效开采的关键。

A reasonable extrapolation range is essential to make sure the system can make prediction with sufficient foresight and take action in advance to avoid an irreversible degraded situation. An extrapolation with too short distance cannot provide sufficient predictive information, while a large extrapolation distance cannot ensure the prediction accuracy as the system cannot get sufficient environment information and consequently cannot predict the sensor observation accurately. For example, in a confined environment the camera observation may change significantly along the trajectory and the system can hardly predict the feature observation for a far end point. The extrapolation distance is controlled by the velocity of the final state and extrapolation time duration. In this work, we assume the constant linear velocity magnitude and choose different extrapolation duration according to the scenario type. In a confined scenario, smaller duration is used, as the effective sensor observation prediction distance is limited by the environment. In an open scenario, a larger extrapolation duration can be used. The extrapolation width is controlled by the branch number and the heading separation between the branches. As a camera with wide FOV is employed in this study, the configuration of three branches and 45-degree separation is reasonable without any loss of sensitivity and computing efficiency.

2 Evaluation and Analysis

The proposed motion direction suggesting approach is evaluated given the optimization-based monocular visual-inertial state estimation formulation through simulation and real-world experiments. The perception system including a monocular camera and IMU (simulated and real) is carried along trajectories in different environments. By the simulation analysis we seek to demonstrate the expected ability and efficacy of the proposed approach both on the local observability prediction and motion direction suggestion. Our current study seeks to verify the effectiveness of the proposed methodology in real-world scenarios.

2.1 Implementation detail

Fig.5 Predicted observability, actual observability, and estimation covariance of the two trajectories

The simulation and experimental analysis leverage the same algorithm implementations, including the optimization-based sliding-window state estimator and local observability prediction-based motion suggestion as presented in sect. 1.4. We employ a time-synchronized monocular camera and IMU in the experiment. The model accurately simulates the associate sensor characteristics and uncertainty. Ceres solver[22] is utilized to solve the optimization problem, and analytic Jacobians are employed to ensure run-time performance. The full sliding window size of the state estimator is set to 30, and the update rate of optimization and motion suggestion is 10 Hz.The motion primitives are generated with three directions and four levels for a reasonable extrapolation distance and width, and consequently 120 observability measure of end points are evaluated. The EOG-based observability evaluation is established with a fixed perturbation size of 0.001 and translational states perturbed. Note that we use different threshold in simulation and experiment to detect the observability deficiency due to different scenario model. From the actual experiment we find that for the similar environment model (for example outdoor open scenario) a well-chosen threshold can be used and doesn’t need further adjustment.

2.2 Simulation results

In the simulation two pre-defined trajectories are tested in the same scenario (Fig.4). Straight trajectory-1 experienced observability degradation due to feature deficiency, while trajectory-2 is always involved in a feature-rich area. The observability measures of three motion directions are evaluated to make the prediction, and the actual current observability measure is used as a reference (Fig.5).

Fig.4 Pre-defined simulation scenario and two trajectories

Firstly, the observability deficiency in trajectory-1 (left column) is correctly predicted (by 8.5 s) with a threshold of 0.3 applied on the predicted observability measure. The correctness of the prediction can be verified by the actual observability measure and the consequent state estimation performance degradation indicated by the increasing covariance. Secondly, during the duration [60 s, 100 s], left direction is strongly suggested, while the actual motion disobeyed the suggestion and entered into the observability-deficient area, which results in the consequent uncertainty with a degraded state estimation. On the contrary, trajectory-2 (right column) executed a motion following the suggested direction to avoid the feature-deficient area, yielding a reasonable observability measure along the trajectory and having a consistent estimated performance. The estimation performance can be checked by both the estimation covariance (Fig.5) and estimated path (Fig.6). The observability deficiency in trajectory-1 results in a big jump in estimated path and end point, while trajectory-2 yields a result with limited uncertainty.

Fig.6 Visualized estimation results, including estimated path and features

Note that in trajectory-1, the prediction of the observability degeneracy occurred 8 s earlier than the actual occurrence of the degeneracy, permitting a motion planner to take actions before entering into a pathological scenario. Although trajectory-2 is much longer than trajectory-1, the state estimation along trajectory-2 preserved a better performance with the well selected motion direction. Ideally, the best trajectory can be selected as the motion direction that keeps the highest observability value, but in actual application the motion planning should be constrained by both the observability and user goal. Note that trajectory-2 is generated based on the direction suggestion in trajectory-1 and actual feature distribution model in the simulated environment.

2.3 Experimental results

In the experiment, the system moves in a hallway with different observability conditions representing degraded scenarios such as white wall, narrow space, sharp turning, and dark lighting. As shown in Fig.7,four representative cases and three prediction points are studied.

Fig.7 Experiment scenario illustrated by estimated path and environment features

Fig.8 Predicted observability in three directions, actual observability, and estimation covariance

Fig.9 Camera images overlaid with online motion direction suggestion in four representative cases

The observability measure in three motion directions are predicted and motion directions are suggested accordingly (Fig.8). The actual observability measure is given as a reference to verify the efficacy of the prediction, while the estimation covariance is used to evaluate the actual estimation performance. Four representative cases and three prediction points are marked. In case-1, forward motion is mostly suggested according to the highest observability prediction, and the actual motion followed this direction, which preserved a good observability condition with little state estimation uncertainty. In case-2, the potential degeneracy in forward motion is successfully predicted.While the system kept moving forward, as expected, it experienced an actual observability degeneracy, which results in an increased estimation covariance. Before the sharp turn in case-3, moving right is strongly recommended due to the highly confined environment. The suggestion is followed by an actual motion. As a result, the actual observability increased significantly and the estimation uncertainty decreased to a low level. In case-4, before the system entering the dark area the degeneracy in future motion is successfully predicted and the violation of the suggestion results in a significantly increased state uncertainty.

The four representative scenarios include two true-positive predictions (1, 3) and two true-negative predictions (2, 4). In the true positive cases, the system proposed “should go” direction (green arrows overlaid on the camera images), and the actual motion followed the suggestion and consequently yielded a good state estimation performance. On the contrary, in the true negative cases the system moved along the predicted “forbidden” direction (red arrows on the camera images), eventually entering the degenerate conditions and inducing significant state estimation degradation. The true-positive and true-negative cases demonstrate the correctness of the observability prediction in motion directions with informative and deficient sensor observation, respectively. The corresponding images (Fig.9) captured by the camera are given to exhibit the visual environment conditions. Green arrows (G) indicate the most suggested directions, blue (B) for the moderately suggested directions and red (R) for the forbidden directions. Note that the arrows indicating the motion suggestions are generated and overlaid on the camera image online.

Similar to the simulation test, the degenerate conditions are successfully predicted prior to the actual occurrence of the degeneracy. Three representative prediction points (A′,B′,C′), and the corresponding actual occurrence points (A, B, C) are checked, tA′=12.35 s, tA=12.85 s, tB′=78.75 s, tB=79.45 s, tC′=86.95 s, tC=88.35 s. The prediction is 0.5 s, 0.7 s, 1.4 s earlier than the degeneracy occurrence, respectively.

3 Conclusion

An online observability-constrained motion suggesting methodology is proposed in this paper. The proposed approach seeks to make informed motion suggestion for a representative monocular visual-inertial state estimation system to preserve the robust estimation performance. An efficient EOG-based observability evaluation technique and motion primitives are incorporated to enable a local observability prediction and real-time motion suggestion, which makes it possible to evaluate an observability for 120 end points locally within 25 ms using one thread on a 2.9 GHz Intel Core-i7 laptop.The approach is evaluated by both simulation and experiments. The results demonstrate the correctness of the local observability prediction and efficacy of the motion suggestion.

若为山村、远方工厂供电的配电线路，其负荷均分布在线路末端，则电压调节效果则与串联电容器位置无关，串补装置的最佳安装位置为线路最末端紧靠首个负荷的电源侧，此时串联电容器承受的故障应力最小，调压效果最佳。若配电线路全线均分布有负荷，为使得沿线电压均在合格范围，或者尽可能接近电压合格范围，则可以选择负荷最大时电压差为全线压降1/2左右的线路位置。当线路较长，使用一个串补装置不能达到预期的调压结果时，可以选择多处安装串补装置，并结合经济性评估，确定最优的串补方案。

The observability-constrained motion suggestion is an active strategy to ensure the state estimation performance of a vision-based autonomous system towards safe operation in an undefined environment. To achieve the goal, we will incorporate the proposed approach with the controlling system to enable observability-constrained planning in challenging operation environments.

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目前，南海航海保障中心正在开展广州海岸电台整体改造工程，已基本完成新海岸电台中控系统的研发工作，计划于近期进入系统测试阶段，整体改造工程将于2020年竣工，届时广州海岸电台将具备接入多个收发信台的能力。此外，南海航海保障中心已启动三亚海岸电台更新改造工程，新的中控台将设置在海口，并直接引用新开发的中控系统，另外新增莺歌海和木栏头收信台，整体提升三亚台中高频信号接收性能，该工程已完成初步设计工作，计划于2020年竣工。