Optimal Estimation Algorithm Research Articles

Using Bayesian Statistics in Enterprise Demography

Knowledge of the number of different kinds of enterprises that will be created in a coming year is essential information. It can be used in macroeconomic analyses and as a constituent of the background for economic policy.From a demographics point of view, we consider the creation (birth) of some enterprise as a basic indicator. It can also be approached from the point of view of inference, as the creation of enterprise is influenced by a wide variety of inputs. Enterprise creation may therefore be thought of as a random process.The analytic tools Bayesian statistics provide make it possible involve more kinds of information into statistical analysis and gradually update the parameter estimations. We used the conjugate family Poisson / gamma to estimate the number of enterprises to be created in a coming year. The considerations were concerned with the mean square error, which was used as the main criterion of the point estimation quality. We solved two kinds of problems: to find a Bayesian point estimation that has a smaller mean square error than the classical one in a predetermined interval, and, along with it, to model prior information in a very simple way.In finding some connection among the variables contained in the conjugate family Poisson / gamma, we solved both presented problems and also developed a simple algorithm for optimal point estimation of the Poisson distribution parameter. This algorithm was used to estimate the number of enterprises created.

Optimal estimation of the states of modulated semi-synchronous integrated flow of events in condition of its incomplete observability

This paper is focused on the problem of optimal estimation of the states (or the problem of filtering the intensity process) of the modulated semi-synchronous integrated flow of events, which is one of the mathematical models for an incoming streams of events (claims) in computer communication networks and which is related to the class of Markovian arrival processes (MAPs). The flow is considered in presence of a constant dead time. The algorithm for optimal estimation of the flow states is proposed. The decision about the flow state is made according to criterion of a posteriori probability maximum. This criterion allows to find the most complete characteristic of the flow state, which could be received from observations of the flow. The criterion minimizes the total probability of making a wrong decision. Also simulation experiments and numerical results are presented. Mathematics Subject Classification: 60G55 1434 M.A. Bakholdina and A.M. Gortsev

Estimating regional fluxes of CO<sub>2</sub> and CH<sub>4</sub> using space-borne observations of XCH<sub>4</sub>: XCO<sub>2</sub>

Abstract. We use the GEOS-Chem global 3-D atmospheric chemistry transport model to interpret XCH4:XCO2 column ratios retrieved from the Japanese Greenhouse Gases Observing Satellite (GOSAT). The advantage of these data over CO2 and CH4 columns retrieved independently using a full physics optimal estimation algorithm is that they are less prone to scattering-related regional biases. We show that the model is able to reproduce observed global and regional spatial (mean bias =0.7%) and temporal variations (global r2=0.92) of this ratio with a model bias < 2.5%. We also show that these variations are driven by emissions of CO2 and CH4 that are typically 6 months out of phase, which may reduce the sensitivity of the ratio to changes in either gas. To simultaneously estimate fluxes of CO2 and CH4 we use a maximum likelihood estimation approach. We use two approaches to resolve independent flux estimates of these two gases using GOSAT observations of XCH4:XCO2: (1) the a priori error covariance between CO2 and CH4 describing common source from biomass burning; and (2) also fitting independent surface atmospheric measurements of CH4 and CO2 mole fraction that provide additional constraints, improving the effectiveness of the observed GOSAT ratio to constrain flux estimates. We demonstrate the impact of these two approaches using numerical experiments. A posteriori flux estimates inferred using only the GOSAT ratios and taking advantage of the error covariance due to biomass burning are not consistent with the true fluxes in our experiments, as the inversion system cannot judge which species' fluxes to adjust. This reflects the weak dependence of XCH4:XCO2 on biomass burning. We find that adding the surface data effectively provides an "anchor" to the inversion that dramatically improves the ability of the GOSAT ratios to infer both CH4 and CO2 fluxes. We show that the regional flux estimates inferred from GOSAT XCH4:XCO2 ratios together with the surface mole fraction data during 2010 are typically consistent with or better than the corresponding values inferred from fitting XCH4 or the full-physics XCO2 data products, as judged by a posteriori uncertainties. We show that the fluxes inferred from the ratio measurements perform best over regions where there is a large seasonal cycle such as Tropical South America, for which we report a small but significant annual source of CO2 compared to a small annual sink inferred from the XCO2 data. We argue that given that the ratio measurements are less compromised by systematic error than the full physics data products, the resulting a~posteriori estimates and uncertainties provide a more faithful description of the truth. Based on our analysis we also argue that by using the ratios we may be reaching the current limits on the precision of these observed space-based data.

Angle Measurement of Robotic Fish Based on Kalman Filter

In water polo competition of robotic fish, due to the influence of factors like ripple disturbance, target point drift and image acquisition delay, the angle between robotic fish and water polo that competition platform return has great error. To improve the shortage, this article put forward an optimal angle estimation algorithm based on Kalman filter. Let the angle go through Kalman filter to eliminate error interference in process and measurement. So that output angle approach truth value. Results of experiment prove that this method can effectively get the better angle between robotic fish and water polo.

Distributed Fusion Estimation for Multisensor Multirate Systems with Stochastic Observation Multiplicative Noises

This paper studies the fusion estimation problem of a class of multisensor multirate systems with observation multiplicative noises. The dynamic system is sampled uniformly. Sampling period of each sensor is uniform and the integer multiple of the state update period. Moreover, different sensors have the different sampling rates and observations of sensors are subject to the stochastic uncertainties of multiplicative noises. At first, local filters at the observation sampling points are obtained based on the observations of each sensor. Further, local estimators at the state update points are obtained by predictions of local filters at the observation sampling points. They have the reduced computational cost and a good real-time property. Then, the cross-covariance matrices between any two local estimators are derived at the state update points. At last, using the matrix weighted optimal fusion estimation algorithm in the linear minimum variance sense, the distributed optimal fusion estimator is obtained based on the local estimators and the cross-covariance matrices. An example shows the effectiveness of the proposed algorithms.

The efficient optimal and suboptimal motion estimation algorithms

The new fast full-search motion estimation algorithm for optimal motion estimation is proposed in this paper. This algorithm presents fast computing method that calculates the tighter boundaries faster by exploiting the computational redundancy. The proposed algorithm, first, determines the possible motion vectors (PMVs) that are not rejected by the first two tighter boundaries to facilitate the prediction of the best initial motion vector (IMV) for the follow-up search. Thereafter, an optimal motion vector (OMV) will be traced out in the PMV set. The IMV greatly helps in the early rejection of impossible candidate blocks while tracing the OMV. Experimental results show that the proposed algorithm outperforms the other previous optimal motion estimation algorithms in reducing the number of computations on several video sequences. The proposed algorithm achieves about 156–456 speed-up gain over full search on several video sequences. But, the state-of-the-art algorithms such as adaptive MSEA and Winner Update algorithm with Integral image algorithms can achieve only about 72–382 speed-up gain over full search on the same video sequences. Finally, the proposed new fast full-search motion estimation algorithm is modified to suboptimal motion estimation algorithm, resulting only in a trivial average peak signal-to-noise ratio drop of about 0.2 dB, but it achieves a very fast computational speed.

Optimal estimation for global ground‐level fine particulate matter concentrations

We develop an optimal estimation (OE) algorithm based on top‐of‐atmosphere reflectances observed by the MODIS satellite instrument to retrieve near‐surface fine particulate matter (PM2.5). The GEOS‐Chem chemical transport model is used to provide prior information for the Aerosol Optical Depth (AOD) retrieval and to relate total column AOD to PM2.5. We adjust the shape of the GEOS‐Chem relative vertical extinction profiles by comparison with lidar retrievals from the CALIOP satellite instrument. Surface reflectance relationships used in the OE algorithm are indexed by land type. Error quantities needed for this OE algorithm are inferred by comparison with AOD observations taken by a worldwide network of sun photometers (AERONET) and extended globally based upon aerosol speciation and cross correlation for simulated values, and upon land type for observational values. Significant agreement in PM2.5 is found over North America for 2005 (slope = 0.89; r = 0.82; 1‐σ error = 1 µg/m3 + 27%), with improved coverage and correlation relative to previous work for the same region and time period, although certain subregions, such as the San Joaquin Valley of California are better represented by previous estimates. Independently derived error estimates of the OE PM2.5 values at in situ locations over North America (of ±(2.5 µg/m3 + 31%) and Europe of ±(3.5 µg/m3 + 30%) are corroborated by comparison with in situ observations, although globally (error estimates of ±(3.0 µg/m3 + 35%), may be underestimated. Global population‐weighted PM2.5 at 50% relative humidity is estimated as 27.8 µg/m3 at 0.1° × 0.1° resolution.

LOW-COST NAVIGATION AND GUIDANCE SYSTEMS FOR UNMANNED AERIAL VEHICLES — PART 2: ATTITUDE DETERMINATION AND CONTROL

ABSTRACT This paper presents the second part of the research activity performed by Cranfield University to assess the potential of low-cost navigation sensors for Unmanned Aerial Vehicles (UAVs). This part focuses on carrier-phase Global Navigation Satellite Systems (GNSS) for attitude determination and control of small to medium size UAVs. Recursive optimal estimation algorithms were developed for combining multiple attitude measurements obtained from different observation points (i.e., antenna locations), and their efficiencies were tested in various dynamic conditions. The proposed algorithms converged rapidly and produced the required output even during high dynamics manoeuvres. Results of theoretical performance analysis and simulation activities are presented in this paper, with emphasis on the advantages of the GNSS interferometric approach in UAV applications (i.e., low cost, high data-rate, low volume/weight, low signal processing requirements, etc.). The simulation activities focussed on the AEROSONDE UAV platform and considered the possible augmentation provided by interferometric GNSS techniques to a low-cost and low-weight/volume integrated navigation system (presented in the first part of this series) which employed a Vision-Based Navigation (VBN) system, a Micro-Electro-Mechanical Sensor (MEMS) based Inertial Measurement Unit (IMU) and code-range GNSS (i.e., GPS and GALILEO) for position and velocity computations. The integrated VBN-IMU-GNSS (VIG) system was augmented using the inteferometric GNSS Attitude Determination (GAD) sensor data and a comparison of the performance achieved with the VIG and VIG/GAD integrated Navigation and Guidance Systems (NGS) is presented in this paper. Finally, the data provided by these NGS are used to optimise the design of a hybrid controller employing Fuzzy Logic and Proportional-Integral-Derivative (PID) techniques for the AEROSONDE UAV.

Optimal state estimation over communication channels with random delays

This paper is concerned with the optimal estimation of linear systems over unreliable communication channels with random delays. The measurements are delivered without time stamp, and the probabilities of time delays are assumed to be known. Since the estimation is time-driven, the actual time delays are converted into virtual time delays among the formulation. The receiver of estimation node stores the sum of arrived measurements between two adjacent processing time instants and also counts the number of arrived measurements. The original linear system is modeled as an extended system with uncertain observation to capture the feature of communication, then the optimal estimation algorithm of systems with uncertain observations is proposed. Additionally, a numerical simulation is presented to show the performance of this work.

An iterative algorithm based on model-reality differences for discrete-time nonlinear stochastic optimal control problems

An iterative algorithm, which is called the integrated optimal control and parameter estimation algorithm, is developed for solving a discrete time nonlinear stochastic control problem. It is based on the integration of the principle of model-reality differences and Kalman filtering theory, where the dynamic integrated system optimization and parameter estimation algorithm are used interactively. In this approach, the weighted least-square output residual is included in the cost function by appropriately monitoring the weighted matrix. An improved linear quadratic Gaussian optimal control model, rather than the original optimal control problem, is solved. Subsequently, the model optimum is updated using the adjusted parameters induced by the differences between the real plant and the model used. These updated solutions converge to the true optimum, despite model-reality differences. For illustration, the optimal control of a nonlinear continuous stirred tank reactor problem is considered and solved by using the method proposed.

Carrier-phase GNSS Attitude Determination and Control for Small Unmanned Aerial Vehicle Applications

As part of our recent research to assess the potential of low-cost navigation sensors for Unmanned Aerial Vehicle (UAV) applications, we investigated the potential of carrier-phase Global Navigation Satellite System (GNSS) for attitude determination and control of small size UAVs. Recursive optimal estimation algorithms were developed for combining multiple attitude measurements obtained from different observation points (i.e., antenna locations), and their efficiencies were tested in various dynamic conditions. The proposed algorithms converged rapidly and produced the required output even during high dynamics manoeuvres. Results of theoretical performance analysis and simulation activities are presented in this paper, with emphasis on the advantages of the GNSS interferometric approach in UAV applications (i.e., low cost, high data-rate, low volume/weight, low signal processing requirements, etc.). The simulation activities focussed on the AEROSONDE UAV platform and considered the possible augmentation provided by interferometric GNSS techniques to a low-cost and low-weight/volume integrated navigation system (presented in the first part of this series) which employed a Vision-Based Navigation (VBN) system, a Micro- Electro-Mechanical Sensor (MEMS) based Inertial Measurement Unit (IMU) and code-range GNSS (i.e., GPS and GALILEO) for position and velocity computations. The integrated VBN-IMU-GNSS (VIG) system was augmented using the inteferometric GNSS Attitude Determination (GAD)sensor data and a comparison of the performance achieved with the VIG and VIG/GAD integrated Navigation and Guidance Systems (NGS) is presented in this paper. Finally, the data provided by these NGS are used to optimise the design of a hybrid controller employing Fuzzy Logic and Proportional-Integral-Derivative (PID) techniques for the AEROSONDE UAV.

Retrieving vertical profile of aerosol extinction by multi-axis differential optical absorption spectroscopy

Using the oxygen dimer (O4 information measured by multi-axis differential optical absorption spectroscopy (MAX-DOAS)), an inversion method of vertical profile of aerosol extinction based on nonlinear optimal estimation algorithm is developed. At first we study how to calculate some parameters (weighting function, the covariance matrices of measurement and a priori) of the algorithm and design nonlinear iteration strategy suited to Chinese region where aerosol usually shows rapid variation and high load. Then this inversion method is verified by computer simulation combined with discussion about error source in three typical cases of low, high and elevated aerosol. After that a continuous observation is reported in the city of Hefei. The aerosol optical depth (AOD) derived from MAX-DOAS is compared with that of CE318 sun photometer and the correlation coefficient is 0.94. The total relative error of AOD is about 20%. In addition the aerosol extinction in the lowest altitude (0-0.3 km) is compared with that of visibility meter and the correlation coefficient is about 0.65. The total relative error of surface-near aerosol extinction is about 25%. Both of simulation verification and comparison experiment indicate that the inversion method can well rebuild the vertical profile of aerosol extinction in the troposphere.

Measuring tropospheric vertical distribution and vertical column density of NO2 by multi-axis differential optical absorption spectroscopy

The inversion method of the vertical profile and vertical column density (VCD) of tropospheric NO2 using multi-axis differential optical absorption spectroscopy (MAX-DOAS) is investigated in this paper. An inversion method of two-step procedure is operated. In this method firstly the aerosol vertical profile is retrieved. Then the vertical distribution of trace gases is retrieved based on the corresponding aerosol status. Nonlinear optimal estimation algorithm is extended to acquire NO2 profile to reduce the dependence of the inversion on priori information. It is more advantageous to automatically obtain trace gases profile. At first we investigate how to calculate some parameters (weighting function, the covariance matrices of measurement, and a priori information) of the algorithm and design nonlinear iteration strategy suited to the region where NO2 vertical distribution usually shows rapid variation. Then this inversion algorithm is verified by computer simulation in the cases of box profile and elevated profile of NO2. It is indicated that the distribution of NO2 below 2 km could be well rebuilt and the retrieval accuracy of surface-near NO2 volume mixing ratio is 0.6%. The study of how accurately this algorithm can rebuild the same true profile in three aerosol status of low aerosol, high aerosol and elevated aerosol indicates that similar retrieval results could be acquired. In addition, the effect of wrong aerosol status on the retrieving of NO2 profile and the error sources of this algorithm are analyzed. After that a continuous observation is reported in the city of Hefei. NO2 VCDs derived from MAX-DOAS are compared with those from satellite observations, and the correlation coefficient is 0.85. The surface-near NO2 concentrations measured by MAX-DOAS are compared with those from LP-DOAS, and the correlation coefficient is 0.76. In addition, the simplified MAX-DOAS inversion method of obtaining the trace gas profile usually uses invariable typical aerosol status as input. The comparison with the tropospheric NO2 VCD from simplified method indicates that the using of invariable typical aerosol status would cause large deviation of NO2 VCD, and its maximum relative deviation is about 112%. So exactly acquiring aerosol status, aerosol optical density especially, is necessary to exactly retrieve tropospheric NO2 vertical column density.

A new scheme for sulphur dioxide retrieval from IASI measurements: application to the Eyjafjallajökull eruption of April and May 2010

Abstract. A new optimal estimation algorithm for the retrieval of sulphur dioxide (SO2) has been developed for the Infrared Atmospheric Sounding Interferometer (IASI) using the channels between 1000–1200 and 1300–1410 cm−1. These regions include the two SO2 absorption bands centred at about 8.7 and 7.3 μm (the ν1 and ν3 bands respectively). The retrieval assumes a Gaussian SO2 profile and returns the SO2 column amount in Dobson units and the altitude of the plume in millibars (mb). Forward modelled spectra (against which the measurements are compared) are based on the Radiative Transfer for TOVS (RTTOV) code. In our implementation RTTOV uses atmospheric profiles from European Centre for Medium-Range Weather Forecasts (ECMWF) meteorological data. The retrieval includes a comprehensive error budget for every pixel derived from an error covariance matrix that is based on the SO2-free climatology of the differences between the IASI and forward modelled spectra. The IASI forward model includes the ability to simulate a cloud or ash layer in the atmosphere. This feature is used to illustrate that: (1) the SO2 retrieval is not affected by underlying cloud but is affected if the SO2 is within or below a cloud layer; (2) it is possible to discern if ash (or other atmospheric constituents not considered in the error covariance matrix) affects the retrieval using quality control based on the fit of the measured spectrum by the forward modelled spectrum. In this work, the algorithm is applied to follow the behaviour of SO2 plumes from the Eyjafjallajökull eruption during April and May 2010. From 14 April to 4 May (during Phase I and II of the eruption) the total amount of SO2 present in the atmosphere, estimated by IASI measurements, is generally below 0.02 Tg. During the last part of the eruption (Phase III) the values are an order of magnitude higher, with a maximum of 0.18 Tg measured on the afternoon of 7 May.

Sparse Optimal Motor Estimation (SOME) for Extracting Commands for Prosthetic Limbs

It is possible to replace amputated limbs with mechatronic prostheses, but their operation requires the user's intentions to be detected and converted into control signals to the actuators. Fortunately, the motoneurons (MNs) that controlled the amputated muscles remain intact and capable of generating electrical signals, but these signals are difficult to record. Even the latest microelectrode array technologies and targeted motor reinnervation can provide only sparse sampling of the hundreds of motor units that comprise the motor pool for each muscle. Simple rectification and integration of such records is likely to produce noisy and delayed estimates of the actual intentions of the user. We have developed a novel algorithm for optimal estimation of motor pool excitation based on the recruitment and firing rates of a small number (2-10) of discriminated motor units. We first derived the motor estimation algorithm from normal patterns of modulated MN activity based on a previously published model of individual MN recruitment and asynchronous frequency modulation. The algorithm was then validated on a target motor reinnervation subject using intramuscular fine-wire recordings to obtain single motor units.

Retrieval of the optical depth and vertical distribution of particulate scatterers in the atmosphere using O<sub>2</sub> A- and B-band SCIAMACHY observations over Kanpur: a case study

Abstract. Due to the well-defined vertical profile of O2 in the atmosphere, the strong A-band (757–774 nm) has long been used to estimate vertical distributions of aerosol/cloud from space. We extend this approach to include part of the O2 B-band (684–688 nm) as well. SCIAMACHY onboard ENVISAT is the first instrument to provide spectral data at moderate resolution (0.2–1.5 nm) in the UV/VIS/NIR including both the O2 A- and B-bands. Using SCIAMACHY specifications, we make combined use of these bands in an optimal estimation algorithm. Theoretical studies show that our algorithm is applicable both over bright and dark surfaces for the retrieval of a lognormal approximation of the vertical profile of particulate matter, in addition to its optical thickness. Synthetic studies and information content analyses prove that such a combined use provides additional information on the vertical distribution of atmospheric scatterers, attributable to differences in the absorption strengths of the two bands and their underlying surface albedos. Due to the high computational cost of the retrieval, we restrict application to real data to a case study over Kanpur through the year 2003. Comparison with AERONET data shows a commonly observed seasonal pattern of haziness, manifesting a correlation coefficient of r = 0.92 for non-monsoon monthly mean AOTs. The retrieved particulate optical thickness is found to be anti-correlated with the relative contrast of the Lambertian equivalent reflectivity (LER) at 682 nm and 755 nm by a coefficient of 0.788, confirming the hypothesis made in Sanghavi et al. (2010). Our case study demonstrates a stable physics-based retrieval of particulate matter using only SCIAMACHY data. The feasibility of our approach is enhanced by the information provided by measurements around the O2 B-band in addition to the A-band. Nonetheless, operational application to SCIAMACHY data remains challenged by radiometric uncertainties, yielding simultaneous retrieval of particle microphysical parameters impracticable and leading to over-reliance on climatological data. Addressing these issues in future instruments similar to SCIAMACHY, coupled with computational resources and speed-up of the current line-by-line radiative transfer calculations, can allow our approach to be extended to the global scale, particularly as it is not limited to dark surfaces.

On the role of visible radiation in ozone profile retrieval from nadir UV/VIS satellite measurements: An experiment with neural network algorithms inverting SCIAMACHY data

Theoretical evidence has been given on the role of visible (VIS) radiation in enhancing the accuracy of ozone retrievals from satellite data, especially in the troposphere. However, at present, VIS is not being systematically used together with ultraviolet (UV) measurements, even when possible with one single instrument, e.g., the SCanning Imaging Absorption spectroMeter for Atmospheric CartograpHY (SCIAMACHY). Reasons mainly reside in the defective performance of optimal estimation and regularization algorithms caused by inaccurate modeling of VIS interaction with aerosols or clouds, as well as in inconsistent intercalibration between UV and VIS measurements. Here we intend to discuss the role of VIS radiation when it feeds a retrieval algorithm based on Neural Networks (NNs) that does not need a forward radiative transfer model and is robust with respect to calibration errors. The NN we designed was trained with a set of ozonesondes (OSs) data and tested over an independent set of OS measurements. We compared the ozone concentration profiles retrieved from UV-only with those retrieved from UV plus VIS nadir data taken by SCIAMACHY. We found that VIS radiation was able to yield more than 10% increase of accuracy and to substantially reduce biases of retrieved profiles at tropospheric levels.

Improving Operational Performance of Active Magnetic Bearings Using Kalman Filter and State Feedback Control

In this paper, the application of optimal state estimation and optimal state feedback algorithms for real-time active magnetic bearing control is treated. A linear quadratic Gaussian controller, consisting of an extended Kalman filter and an optimal state feedback regulator, is implemented. It is shown that this controller yields improved rotor positioning accuracy, better system dynamics, higher bearing stiffness, and reduced control energy effort compared to the conventionally used proportional-integral-differential control approaches. In addition, a method for compensating unbalance-caused forces and vibrations of the magnetically levitated rotor is presented which is based on the estimation of unknown disturbance forces. All results achieved in this paper are verified by means of measurements.

Chaotic Sequence Optimization Algorithm for Estimation of Aquifer Parameters from Data of Pumping Test

Abstract With chaotic sequence optimization algorithm,the function optimization problem for analyzing data pumping test conducted in aquifer to estimate such aquifer parameters as transmissivity and storage coefficient was to be solved. With such different key parameters of the algorithm as the number of coarse search loops, the length of chaotic sequence and the initial guess value ranges of transmissivity of aquifer, simulation experiment was conducted to explore the effect of these key parameters on the convergence of the algorithm. The results show: 1) that chaotic sequence optimization algorithm may be successfully applied to solve the function optimization problem to analyses pumping test data for determining aquifer parameters of aquifer, 2) that the longer sequence length of chaotic sequence and the larger number of coarse search loops may not effectively improve the convergence of algorithm, 3) and that the range of initial guess value of transmissivity of aquifer may brings some influence on the convergence of algorithm, but does not affect the final result of computation. Compared with current methods, the chaotic sequence optimization method is of such advantages as that the principle of algorithm is easy to understand, the procedure of the algorithm is easier to be programmed and conducted,and the precision of aquifer parameters calculated may not be affected by artificial subjective factors. Finally, it is necessary to point out that this method is of wider scope of application.

Control and Robust Vision Relative Navigation for Autonomous Aerial Refueling

A relative navigation and control scheme based on multiple camera systems was presented for autonomous operations in close proximity for autonomous air refueling (AAR) mission. The relative navigation system employed non-iterative fast global optimal pose estimation algorithm, and the result was filtered and fused with velocity’s measurements to increase accuracy and robustness by using Kalman filtering algorithm. To attenuate effect of tanker’s vortex and atmospheric turbulence, an H-infinity tracking control law was designed for docking phase of air refueling. Simulation results showed that accuracy of both vision navigation system and trajectory tracking could meet requirements of aerial refueling.