Nonlinear Optimal Estimation Research Articles

Adaptive nonlinear information fusion preview control for autonomous surface vessels subject to measurement noises and unknown input saturations

AbstractThis study presents an adaptive nonlinear information fusion preview control (NIFPC) method for trajectory tracking of autonomous surface vessels (ASVs) subject to system uncertainty, measurement noise, and unknown input saturations. The NIFPC is developed based on the nonlinear information fusion estimation methodology, in which the system's future reference trajectory information, noise information, performance index requirements, and system dynamic model are all transformed into information equations related to control input, and then the current control action is obtained by fusing these previewed future information via the nonlinear information fusion optimal estimation. In order to avoid the unknown input saturation constraints, a fuzzy asymmetric saturated approximator (FASA) is designed and integrated into the controller, where the fuzzy logic system (FLS) is used to adaptively adjust the key boundary parameters of the approximator. As a result, the negative effects caused by system uncertainty and measurement noise can be effectively suppressed, while the completely unknown input saturation constraints in the system actuator are guaranteed not to be violated. The convergence of the tracking errors of the closed‐loop system is guaranteed via Lyapunov stability theory. Numerical simulation results have been provided to demonstrate the satisfactory performance of the proposed control scheme.

Joint State and Parameter Estimation for Hypersonic Glide Vehicles Based on Moving Horizon Estimation via Carleman Linearization

Aimed at joint state and parameter estimation problems in hypersonic glide vehicle defense, a novel moving horizon estimation algorithm via Carleman linearization is developed in this paper. First, the maneuver characteristic parameters that reflect the target maneuver law are extended into the state vector, and a dynamic tracking model applicable to various hypersonic glide vehicles is constructed. To improve the estimation accuracy, constraints such as path and parameter change amplitude constraints in flight are taken into account, and the estimation problem is transformed into a nonlinear constrained optimal estimation problem. Then, to solve the problem of high time cost for solving a nonlinear constrained optimal estimation problem, in the framework of moving horizon estimation, nonlinear constrained optimization problems are transformed into bilinear constrained optimization problems by linearizing the nonlinear system via Carleman linearization. For ensuring the consistency of the linearized system with the original nonlinear system, the linearized model is continuously updated as the window slides forward. Moreover, a CKF-based arrival cost update algorithm is also provided to improve the estimation accuracy. Simulation results demonstrate that the proposed joint state and parameter estimation algorithm greatly improves the estimation accuracy while reducing the time cost significantly.

Nitrous Oxide Profile Retrievals from Atmospheric Infrared Sounder and Validation

This paper presents an algorithm for the retrieval of nitrous oxide profiles from the Atmospheric InfraRed Sounder (AIRS) on the Earth Observing System (EOS)/Aqua using a nonlinear optimal estimation method. First, an improved Optimal Sensitivity Profile (OSP) algorithm for channel selection is proposed based on the weighting functions and the transmissions of the target gas and interfering gases, with 13 channels selected for inversion in this algorithm. Next, the data of the High-Performance Instrumented Airborne Platform for Environmental Research (HIAPER) Pole-to-Pole Observations (HIPPO) aircraft and the Earth System Research Laboratory (ESRL) are used to verify the retrieval results, including the atmospheric nitrous oxide profile and the column concentration. The results show that using AIRS satellite data, the atmospheric nitrous oxide profile between 300–900 hPa can be well retrieved with an accuracy of ~0.1%, which agrees with the corresponding Jacobian peak interval of selected channels. Analysis of the AIRS retrievals demonstrates that the AIRS measurements provide useful information to capture the spatial and temporal variations in nitrous oxide between 300–900 hPa.

New Constraints on Titan’s Stratospheric n-Butane Abundance

Abstract Curiously, n-butane has yet to be detected at Titan, though it is predicted to be present in a wide range of abundances that span over 2.5 orders of magnitude. We have searched infrared spectroscopic observations of Titan for signals from n-butane (n-C4H10) in Titan’s stratosphere. Three sets of Cassini Composite Infrared Spectrometer Focal Plane 4 (1050–1500 cm−1) observations were selected for modeling, having been collected from different flybys and pointing latitudes. We modeled the observations with the Nonlinear Optimal Estimator for MultivariatE Spectral AnalySIS radiative transfer tool. Temperature profiles were retrieved for each of the data sets by modeling the ν 4 emission from methane near 1305 cm−1. Then, incorporating the temperature profiles, we retrieved abundances of all of Titan’s known trace gases that are active in this spectral region, reliably reproducing the observations. We then systematically tested a set of models with varying abundances of n-butane, investigating how the addition of this gas affected the fits. We did this for several different photochemically predicted abundance profiles from the literature, as well as for a constant-with-altitude profile. Ultimately, though we did not produce any firm detection of n-butane, we derived new upper limits on its abundance specific to the use of each profile and to multiple different ranges of stratospheric altitudes. These results will tightly constrain the C4 chemistry of future photochemical modeling of Titan’s atmosphere and also motivate the continued search for n-butane and its isomer, isobutane.

Multi-structure non-linear semi-parametric optimal weighting parameters estimation algorithm based on adaptive sparse representation deconstruction model and integrative COD comprehensive model

For the combined orbit determination (COD) satellite-network system which is made of GEO-IGSO-MEO satellite-constellation and LEO satellites, the satellites-trajectory are not precise enough, because the meticulous satellite dynamics model, credible observation data model and optimal parameters estimation method are not taking into consideration. The high-level adaptive sparse-deconstruction dynamics model, non-linear semi-parametric combined orbit determination comprehensive model is put forward. By using the above models, adaptive weighting iterative wavelets decomposition algorithm of sparse-representation deconstruction model and multi-structure non-linear semi-parametric optimization weighted estimation algorithm of integrative combined orbit determination comprehensive models are designed. Simulated calculation results show that results showed that the high-precision sparse representation method and the optimization model estimation method can improve COD precision, and when comprehensive model systematic & random error parameters and adaptive sparse-representation deconstruction model parameters are estimated by integrative nonlinear semi-parametric comprehensive model synchronously, COD ultimate trajectory calculation estimation precision can get significant improvement.

Measurement of atmospheric water vapor vertical column concentration and vertical distribution in Qingdao using multi-axis differential optical absorption spectroscopy

The method of retrieving the vertical column density (VCD) and the atmospheric vertical profile of water vapor in visible blue band (434.0–451.5 nm) were studied by using the multi-axis differential optical absorption spectroscopy (MAX-DOAS). First, the method of retrieving the VCD of water vapor was studied. Owing the the fact that the water vapor absorption cross section is of high resolution and it cannot be effectively measured by MAX-DOAS, a convolved cross section with the instrument slit function was used. In addition, the correction factor for water vapor saturation absorption was also used to obtain the true VCD. Second, the water vapor profile retrieved by applying the nonlinear optimal estimation of the trace gas retrieval method (PriAM) was studied, including the effects of aerosol state and the priori profile on the water vapor retrieval. Influence on the water vapor retrieval from the aerosol prior profile linear changes was unapparent. High aerosol state has a significant influence on the water vapor profile retrieval and it was still within the total error tolerance. This indicates that the PriAM is applicable in the water vapor profile retrieval. Using this method, a continuous observation experiment was carried out at the MAX-DOAS Aoshan regional station in Qingdao. The retrieved water vapor VCD results were compared with the daily average data of the European Centre for Medium-Range Weather Forecasts (ECMWF), and the <i>R</i><sup>2</sup> is 0.93. The comparison of the near-surface water vapor concentration of MAX-DOAS retrieval with the ECMWF and sounding data of the University of Wyoming shows that <i>R</i><sup>2</sup> is larger than 0.70 and 0.66, respectively. The two comparison results demonstrate that PriAM can retrieve the atmospheric water vapor VCD and profile accurately. The vertical distribution characteristics of water vapor in Qingdao was analyzed, and the profile results show that the concentration of water vapor in Qingdao was distributed mainly under 1.5 km in height.

Total Column Ozone Retrieval From the Infrared Measurements of a Geostationary Imager

A new algorithm has been developed to retrieve total column ozone (TOZ) from the infrared measurements of a geostationary satellite imager such as the Advanced Himawari Imager (AHI) aboard Himawari-8 and the advanced meteorological imager flying with the second generation geostationary satellite of South Korea. Based on a nonlinear optimal estimation method, this operational algorithm iteratively retrieves TOZ from AHI thermal measurements under clear-sky conditions as well as over low clouds at 10-min intervals with 6-km spatial resolutions. The first guess for ozone is prepared by combining a monthly climatology with the daily updated TOZ from polar orbiting satellites, while the first guess for the temperature and humidity profiles are from a numerical weather prediction model. AHI contains only one ozone absorption channel ( $9.6~\mu \text{m}$ ), providing information contents (degrees of freedom for signal) of about 0.98 for the ozone retrieval. However, the study shows that the retrieved TOZ successfully captures the temporal and latitudinal variations of ozone flow particularly at mid- and high-latitudes. A validation using the Ozone Monitoring Instrument, Infrared Atmospheric Sounding Interferometer (IASI), and ozonesondes shows that the AHI TOZ are in a good agreement with the three references with mean difference of 2.5%, −0.5%, and 2.6%, respectively. This impressive performance is attributed to the improvements in both first-guess information and the accuracy of the retrieved temperature and humidity profiles. In particular, the good agreement shown in the comparison with the night-time IASI TOZ suggests potential benefits of using the retrieved TOZ for a continuous monitoring of global ozone evolution with high spatial resolution.

Measurement of CH3D on Titan at Submillimeter Wavelengths

Abstract We present the first radio/submillimeter detection of monodeuterated methane (CH3D) in Titan’s atmosphere, using archival data from of the Atacama Large Millimeter/submillimeter Array (ALMA). The J K = 21−11 and J K = 20−10 transitions at 465.235 and 465.250 GHz (∼0.644 mm) were measured at significance levels of 4.6σ and 5.7σ, respectively. These two lines were modeled using the Non-linear optimal Estimator for MultivariatE spectral analySIS (NEMESIS) radiative transfer code to determine the disk-averaged CH3D volume mixing ratio = 6.157 × 10−6 in Titan’s stratosphere (at altitudes >130 km). By comparison with the CH4 vertical abundance profile measured by Cassini–Huygens mass spectrometry, the resulting value for D/H in CH4 is (1.033 ± 0.081) × 10−4. This is consistent with previous ground-based and in situ measurements from the Cassini–Huygens mission, though slightly lower than the average of the previous values. Additional CH3D observations at higher spatial resolution will be required to determine a value truly comparable with the Cassini–Huygens CH4 measurements, by measuring CH3D with ALMA close to Titan’s equator. In the post-Cassini era, spatially resolved observations of CH3D with ALMA will enable the latitudinal distribution of methane to be determined, making this an important molecule for further studies.

A Model Following Based Real-Time Prediction and Monitoring of TFE-731 Turbofan Engine Compressors

An engine is the heart of an aircraft. It produces thrust, drives the generator, pumps the hydraulic system and provides compressed air for all the systems on the aircraft. Its health plays an essential role in flight safety. In the past, the standard operation procedure to evaluate the health status of engines usually depended on some specific parameters, like inter-stage turbine temperature, low-pressure spool rotating speed or high-pressure spool rotating speed. Once part of the parameters pass over certain safety boundaries that were previously set by the manufacturers or the operators, the engine would be regarded as an unhealthy engine. Nevertheless, in practical applications, such threshold-style mechanism cannot reflect engine fault immediately and therefore could lead to potential flight risk. To solve this issue, a precise forecast model of the engine has to be established. Consequently, this research is dedicated to develop algorithms for engine modeling as well as the identification of optimal parameters. For the TFE-731 engine, there are three section models considered, including low pressure compressor (LPC) model, high pressure compressor (HPC) model and overall turbofan dynamics model. Those models are derived with the consideration of physical isentropic compression equation as well as a data-driven regression technique. Experiments show that a precise modeling fitting can be achieved by using regression analysis and nonlinear optimal parameter estimation. Finally, to compare the prediction stability and accuracy, associated training models using neural network (NN) are also presented. Comparison studies verify that the proposed method is able to achieve stable as well as accurate TFE-731 real-time response prediction and monitoring.

Mapping of Jupiter’s tropospheric NH3 abundance using ground-based IRTF/TEXES observations at 5 µm

We report on results of an observing campaign to support the Juno mission. At the beginning of 2016, using TEXES (Texas Echelon cross-dispersed Echelle Spectrograph), mounted on the NASA Infrared Telescope Facility (IRTF), we obtained data cubes of Jupiter in the 1930–1943 cm−1 spectral ranges (around 5 µm), which probe the atmosphere in the 1–4 bar region, with a spectral resolution of ≈ 0.15 cm−1 and an angular resolution of ≈ 1.4”. This dataset is analysed by a code that combines a line-by-line radiative transfer model with a non-linear optimal estimation inversion method. The inversion retrieves the vertical abundance profiles of NH3 — which is the main contributor at these wavelengths — with a maximum sensitivity at ≈ 1–3 bar, as well as the cloud transmittance. This retrieval is performed on more than one thousand pixels of our data cubes, producing maps of the disk, where all the major belts are visible. We present our retrieved NH3 abundance maps which can be compared with the distribution observed by Juno’s MWR (Bolton et al., 2017; Li et al., 2017) in the 2 bar region and discuss their significance for the understanding of Jupiter’s atmospheric dynamics. We are able to show important latitudinal variations — such as in the North Equatorial Belt (NEB), where the NH3 abundance is observed to drop down to 60 ppmv at 2 bar — as well as longitudinal variability. In the zones, we find the NH3 abundance to increase with depth, from 100 ± 15 ppmv at 1 bar to 500 ± 30 ppmv at 3 bar. We also display the cloud transmittance–NH3 abundance relationship, and find different behaviour for the NEB, the other belts and the zones. Using a simple cloud model (Lacis and Hansen, 1974; Ackerman and Marley, 2001), we are able to fit this relationship, at least in the NEB, including either NH3-ice or NH4SH particles with sizes between 10 and 100 µm.

Atmospheric Profile Retrieval Algorithm for Next Generation Geostationary Satellite of Korea and Its Application to the Advanced Himawari Imager

In preparation for the 2nd geostationary multi-purpose satellite of Korea with a 16-channel Advanced Meteorological Imager; an algorithm has been developed to retrieve clear-sky vertical profiles of temperature (T) and humidity (Q) based on a nonlinear optimal estimation method. The performance and characteristics of the algorithm have been evaluated using the measured data of the Advanced Himawari Imager (AHI) on board the Himawari-8 of Japan, launched in 2014. Constraints for the optimal estimation solution are provided by the forecasted T and Q profiles from a global numerical weather prediction model and their error covariance. Although the information contents for temperature is quite low due to the limited number of channels used in the retrieval; the study reveals that useful moisture information (2~3 degrees of freedom for signal) is provided from the three water vapor channels; contributing to the increase in the moisture retrieval accuracy upon the model forecast. The improvements are consistent throughout the tropospheric atmosphere with almost zero mean bias and 9% (relative humidity) of root mean square error between 100 and 1000 hPa when compared with the quality-controlled radiosonde data from 2016 August.

Ozone Profile Retrievals From the Cross-Track Infrared Sounder

This paper presents an algorithm for the retrieval of ozone profiles from the Cross-track Infrared Sounder (CrIS) aboard the Suomi National Polar-orbiting Partnership satellite using a nonlinear optimal estimation method. The issue of channel selection is discussed. Based on a sensitivity analysis, we selected a spectral range of 990–1070 cm−1 for the ozone profile retrievals. Compared with ERA-Interim ozone profiles and eigenvector regression method profiles, the ozone climatology profile is better able to construct the a priori state. The retrieved CrIS profiles are in good agreement with smoothed high-vertical-resolution ozonesonde profiles. An analysis of the information content of the CrIS retrievals demonstrates that the CrIS measurements can provide useful information for capturing the spatial and temporal variations in ozone and are insensitive to ozone below 400 hPa. An error analysis revealed that smoothing error represents the main error source for the retrieved CrIS ozone profiles.

Method of adjoint particle filters in nonlinear Bayesian estimation problems with a high prior uncertainty

A modification of the widely known scheme for solving nonlinear Bayesian optimal estimation problems in which the state vector contains a parameter not varying during the estimation process is proposed. Such problems are often solved by a technique in which the varying part of the state vector is modeled using sequential Monte Carlo methods (particle filters) and the parameter is modeled as a conditional distribution associated with a specific trajectory (implementation of the moving component). Different modifications of this scheme differ mainly in the ways of modeling the parameter. In some recent works devoted to the problem of simultaneous localization and mapping, the vector parameter which consists of coordinates of unknown reference points (landmarks) is modeled using the generalized Kalman filter, Gaussian sum filters, and more specific methods. We consider a modification in which the parameter, as well as the moving part of the state vector, is modeled using particle filters. The main recurrence relationships between weights of particle filters are derived. The proposed computational algorithm is illustrated by an application to the problem of bearing-only simultaneous localization and mapping.

Real-time MHE-based nonlinear MPC of a Pendubot system

This paper addresses the real-time optimal control of a Pendubot using nonlinear model predictive control (NMPC) combined with nonlinear moving horizon estimation (MHE). This fast, under-actuated nonlinear mechatronic system apparently poses a challenging benchmark problem that may benefit from a nonlinear optimization scheme. To overcome the related computational difficulties we make use of the ACADO Code Generation tool allowing to export a highly efficient Gauss-Newton real-time iteration algorithm tailored to the nonlinear optimal control and estimation problem while respecting the imposed constraints.We show experimental results illustrating the overall closed-loop control performance, as well as the advantages of the nonlinear MHE-based NMPC scheme.

Unified nonlinear optimal flight control and state estimation of highly maneuverable aircraft

In this paper, a nonlinear flight control and a nonlinear state observer are designed in one unified framework for a high performance aircraft. The flight control is formulated as a nonlinear optimal control problem and the θ-D technique is utilized to design a closed-form optimal control law by solving the associated Hamilton–Jacobi–Bellman equation approximately via a perturbation process. Motivated by the notion that control and estimation are dual concepts, a new θ-D observer is developed to estimate the state used in the feedback by constructing the dual of the θ-D controller. Theoretical analysis of the proposed observer is given. Since both the optimal flight control and the state observer are unified in the same θ-D algorithm that leads to closed-form solutions to the optimal control and observer gains, this scheme greatly facilitates onboard implementation due to its computation efficiency. The unified design method is applied to a highly maneuverable aircraft operating at high angles of attack. Simulation results show that the θ-D control-θ-D observer suite exhibits excellent performance.

Kalman Filters versus Neural Networks in Battery State-of-Charge Estimation: A Comparative Study

Battery management systems (BMS) must estimate the state-of-charge (SOC) of the battery accurately to prolong its lifetime and ensure a reliable operation. Since batteries have a wide range of applications, the SOC estimation requirements and methods vary from an application to another. This paper compares two SOC estimation methods, namely extended Kalman filters (EKF) and artificial neural networks (ANN). EKF is a nonlinear optimal estimator that is used to estimate the inner state of a nonlinear dynamic system using a state-space model. On the other hand, ANN is a mathematical model that consists of interconnected artificial neurons inspired by biological neural networks and is used to predict the output of a dynamic system based on some historical data of that system. A pulse-discharge test was performed on a commercial lithium-ion (Li-ion) battery cell in order to collect data to evaluate those methods. Results are presented and compared.

Experimental Validation of Combined Nonlinear Optimal Control and Estimation of an Overhead Crane

This paper validates the combination of nonlinear model predictive control and moving horizon estimation to optimally control an overhead crane. Real-time implementation of this combined optimal control and estimation approach with execution times far below the sampling time was realized through the use of automatic code generation. Besides experiments that reflect good point-to-point performance, the approach showed to be good in disturbance rejection as well as in servo-tracking.

ATMOSPHERIC RETRIEVAL ANALYSIS OF THE DIRECTLY IMAGED EXOPLANET HR 8799b

Directly-imaged exoplanets are unexplored laboratories for the application of the spectral and temperature retrieval method, where the chemistry and composition of their atmospheres are inferred from inverse modeling of the available data. As a pilot study, we focus on the extrasolar gas giant HR 8799b for which more than 50 data points are available. We upgrade our non-linear optimal estimation retrieval method to include a phenomenological model of clouds that requires the cloud optical depth and monodisperse particle size to be specified. Previous studies have focused on forward models with assumed values of the exoplanetary properties; there is no consensus on the best-fit values of the radius, mass, surface gravity and effective temperature of HR 8799b. We show that cloudfree models produce reasonable fits to the data if the atmosphere is of super-solar metallicity and non-solar elemental abundances. Intermediately cloudy models with moderate values of the cloud optical depth and micron-sized particles provide an equally reasonable fit to the data and require a lower mean molecular weight. We report our best-fit values for the radius, mass, surface gravity and effective temperature of HR 8799b. The mean molecular weight is about 3.8, while the carbon-to-oxygen ratio is about unity due to the prevalence of carbon monoxide. Our study emphasizes the need for robust claims about the nature of an exoplanetary atmosphere to be based on analyses involving both photometry and spectroscopy and inferred from beyond a few photometric data points, such as are typically reported for hot Jupiters.

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.