Kalman filtering for positioning and heading control of ships and offshore rigs

In this article, we have described the main components of a ship motion-control system and two particular motion-control problems that require wave filtering, namely, dynamic positioning and heading autopilot. Then, we discussed the models commonly used for vessel response and showed how these models are used for Kalman filter design. We also briefly discussed parameter and noise covariance estimation, which are used for filter tuning. To illustrate the performance, a case study based on numerical simulations for a ship autopilot was considered. The material discussed in this article conforms to modern commercially available ship motion-control systems. Most of the vessels operating in the offshore industry worldwide use Kalman filters for velocity estimation and wave filtering. Thus, the article provides an up-to-date tutorial and overview of Kalman-filter-based wave filtering.

Extended Kalman filters using explicit and derivative-free local linearizations

We propose three variants of the extended Kalman filter (EKF) especially suited for parameter estimations in mechanical oscillators under Gaussian white noises. These filters are based on three versions of explicit and derivative-free local linearizations (DLL) of the non-linear drift terms in the governing stochastic differential equations (SDE-s). Besides a basic linearization of the non-linear drift functions via one-term replacements, linearizations using replacements through explicit Euler and Newmark expansions are also attempted in order to ensure higher closeness of true solutions with the linearized ones. Thus, unlike the conventional EKF, the proposed filters do not need computing derivatives (tangent matrices) at any stage. The measurements are synthetically generated by corrupting with noise the numerical solutions of the SDE-s through implicit versions of these linearizations. In order to demonstrate the effectiveness and accuracy of the proposed methods vis-à-vis the conventional EKF, numerical illustrations are provided for a few single degree-of-freedom (DOF) oscillators and a three-DOF shear frame with constant parameters.

Two-Stage Extended Kalman Filters with Derivative-Free Local Linearizations

This paper proposes a derivative-free two-stage extended Kalman filter (2-EKF) especially suited for state and parameter identification of mechanical oscillators under Gaussian white noise. Two sources of modeling uncertainties are considered: (1) errors in linearization, and (2) an inadequate system model. The state vector is presently composed of the original dynamical/parameter states plus the so-called bias states accounting for the unmodeled dynamics. An extended Kalman estimation concept is applied within a framework predicated on explicit and derivative-free local linearizations (DLL) of nonlinear drift terms in the governing stochastic differential equations (SDEs). The original and bias states are estimated by two separate filters; the bias filter improves the estimates of the original states. Measurements are artificially generated by corrupting the numerical solutions of the SDEs with noise through an implicit form of a higher-order linearization. Numerical illustrations are provided for a few single- and multidegree-of-freedom nonlinear oscillators, demonstrating the remarkable promise that 2-EKF holds over its more conventional EKF-based counterparts. DOI: 10.1061/(ASCE)EM.1943-7889.0000255. (C) 2011 American Society of Civil Engineers.

Kalman Filtering in R

Support in R for state space estimation via Kalman filtering was limited to one package, until fairly recently. In the last five years, the situation has changed with no less than four additional packages offering general implementations of the Kalman filter, including in some cases smoothing, simulation smoothing and other functionality. This paper reviews some of the offerings in R to help the prospective user to make an informed choice.

Model based learning of sigma points in unscented Kalman filtering

The unscented Kalman filter (UKF) is a widely used method in control and time series applications. The UKF suffers from arbitrary parameters necessary for a step known as sigma point placement, causing it to perform poorly in nonlinear problems. We show how to treat sigma point placement in a UKF as a learning problem in a model based view. We demonstrate that learning to place the sigma points correctly from data can make sigma point collapse much less likely. Learning can result in a significant increase in predictive performance over default settings of the parameters in the UKF and other filters designed to avoid the problems of the UKF, such as the GP-ADF. At the same time, we maintain a lower computational complexity than the other methods. We call our method UKF-L. ©2010 IEEE.

Model based learning of sigma points in unscented Kalman filtering

The unscented Kalman filter (UKF) is a widely used method in control and time series applications. The UKF suffers from arbitrary parameters necessary for sigma point placement, potentially causing it to perform poorly in nonlinear problems. We show how to treat sigma point placement in a UKF as a learning problem in a model based view. We demonstrate that learning to place the sigma points correctly from data can make sigma point collapse much less likely. Learning can result in a significant increase in predictive performance over default settings of the parameters in the UKF and other filters designed to avoid the problems of the UKF, such as the GP-ADF. At the same time, we maintain a lower computational complexity than the other methods. We call our method UKF-L. © 2011 Elsevier B.V.

COMPARATIVE-STUDY OF KALMAN FILTERING, SYNCHRONOUS EXCITATION AND NUMERICAL DERIVATIVE TECHNIQUES IN FLUOROMETRY

The performance of Kalman filtering, synchronous excitation and numerical derivative techniques for the resolution of overlapping emission spectra in spectrofluorimetry was studied. The extent of spectrum overlap was quantitatively described by the separation degree D(s), defined as the ratio of the peak separation to the full width at half-maximum of the emission spectrum of the interferent. For the system of Rhodamine B and Rhodamine 6G with a large D(s) of about 0.4, both Kalman filtering and synchronous techniques are able to resolve the overlapping spectra well and to give satisfactory results while the derivative spectra are still overlapped with each other. Moreover, the sensitivities are greatly decreased in derivative techniques. For more closely spaced spectra emitted by the complexes of Al and Zn with 7-iodo-8-hydroxyquinoline-5-sulphonic acid (Ferron)-hexadecyltrimethylammonium bromide, the synchronous excitation technique cannot completely separate the overlapping peaks, although it increases the separation degree from 0.25 in the conventional spectra to 0.37 in the synchronous spectra. On the other hand, Kalman filtering is capable of resolving this system. When the Al/Zn intensity ratio at the central wavelength of Al was > 1, however, the accuracy and precision of the estimates for Zn concentration produced by the Kalman filter became worse. In this event, the combination of synchronous excitation and Kalman filtering can much improve the analytical results.

RESOLUTION OF CLOSELY SPACED LINES WITH KALMAN FILTERING IN INDUCTIVELY COUPLED PLASMA ATOMIC EMISSION-SPECTROMETRY

Effects of some factors on the performance of our Kalman filter in discrimination of closely spaced overlapping signals were investigated. The resolution power of the filter for overlapping lines can be strengthened by reduction of the step size in scans. The minimum peak separation of two lines which the Kalman filter can effectively handle generally equals two to three times the step size in scans. Significant difference between the profiles of the analysis and interfering lines and multiple lines from matrix in the spectral window of the analysis line are very helpful for the Kalman filter to discern closely spaced analysis and interfering signals correctly, which allow the filter well to resolve the line pair with very small peak distance or even the entirely coincident lines.

KALMAN FILTERING FOR RESOLUTION OF OVERLAPPING LINES IN INDUCTIVELY COUPLED PLASMA ATOMIC EMISSION-SPECTROMETRY

A Kalman filter was developed for resolving overlapping lines in inductively coupled plasma atomic emission spectrometry (ICP-AES) and evaluated experimentally with the determination of La in the presence of Ho, and Cu in the presence of Pr. The whiteness of the innovation sequence for an optimal filter was explored to be the criterion for the correction of the wavelength positioning errors which may occur in spectral scans. Under the conditions of the medium-resolution spectrometer and 1.5 pm step size in scans, the filter effectively resolved the Cu/Pr line pair having a small peak separation of 4.8 pm. For the La/Ho line pair with a peak distance of 9.8 pm, an unbiased estimate for La concentration was still obtained even when the signal-to-background ratio was down to 0.048. Favourable detection limits for real samples were achieved. Unstructured backgrounds were modeled theoretically and all spectral scans therefore did not require the correction for solvent.

Invariant Information Local Sub-map Filter (IILSF) for Efficient Simultaneous Localisation and Mapping of Large Environments

This paper presents an Invariant Information Local Sub-map Filter (IILSF) as a technique for consistent Simultaneous Localisation and Mapping (SLAM) in a large environment. It harnesses the benefits of sub-map technique to improve the consistency and efficiency of Extended Kalman Filter (EKF) based SLAM. The IILSF makes use of invariant information obtained from estimated locations of features in independent sub-maps, instead of incorporating every observation directly into the global map. Then the global map is updated at regular intervals. Applying this technique to the EKF based SLAM algorithm: (a) reduces the computational complexity of maintaining the global map estimates and (b) simplifies transformation complexities and data association ambiguities usually experienced in fusing sub-maps together. Simulation results show that the method was able to accurately fuse local map observations to generate an efficient and consistent global map, in addition to significantly reducing computational cost and data association ambiguities.

Kalman tracking linear predictor for vowel intelligibility enhancement on european portuguese HMM based speech synthesis

The recent developments on Hidden Markov Models (HMM) based speech synthesis showed that this is a promising technology fully capable of competing with other established techniques. However some issues still lack a solution. Several authors report an over-smoothing phenomenon on both time and frequencies which decreases naturalness and sometimes intelligibility. In this work we present a new vowel intelligibility enhancement algorithm that uses a discrete Kalman filter (DKF) for tracking frame based parameters. The inter-frame correlations are modelled by an autoregressive structure which provides an underlying time frame dependency and can improve time-frequency resolution. The system’s performance has been evaluated using objective and subjective tests and the proposed methodology has led to improved results.

Augmented state Kalman filtering for AUV navigation

Addresses the problem of estimating the motion of an autonomous underwater vehicle (AUV), while it constructs a visual map ("mosaic" image) of the ocean floor. The vehicle is equipped with a down-looking camera which is used to compute its motion with respect to the seafloor. As the mosaic increases in size, a systematic bias is introduced in the alignment of the images which form the mosaic. Therefore, this accumulative error produces a drift in the estimation of the position of the vehicle. When the arbitrary trajectory of the AUV crosses over itself, it is possible to reduce this propagation of image alignment errors within the mosaic. A Kalman filter with augmented state is proposed to optimally estimate both the visual map and the vehicle position

Data assimilation: From photon counts to Earth System forecasts

Data assimilation – the set of techniques whereby information from observing systems and models is combined optimally – is rapidly becoming prominent in endeavours to exploit Earth Observation for Earth sciences, including climate prediction. This paper explains the broad principles of data assimilation, outlining different approaches (optimal interpolation, three-dimensional and four-dimensional variational methods, the Kalman Filter), together with the approximations that are often necessary to make them practicable. After pointing out a variety of benefits of data assimilation, the paper then outlines some practical applications of the exploitation of Earth Observation by data assimilation in the areas of operational oceanography, chemical weather forecasting and carbon cycle modelling. Finally, some challenges for the future are noted.

The ASSET intercomparison of ozone analyses: method and first results

This paper aims to summarise the current performance of ozone data assimilation (DA) systems, to show where they can be improved, and to quantify their errors. It examines 11 sets of ozone analyses from 7 different DA systems. Two are numerical weather prediction (NWP) systems based on general circulation models (GCMs); the other five use chemistry transport models (CTMs). The systems examined contain either linearised or detailed ozone chemistry, or no chemistry at all. In most analyses, MIPAS (Michelson Interferometer for Passive Atmospheric Sounding) ozone data are assimilated; two assimilate SCIAMACHY (Scanning Imaging Absorption Spectrometer for Atmospheric Chartography) observations instead. Analyses are compared to independent ozone observations covering the troposphere, stratosphere and lower mesosphere during the period July to November 2003. Biases and standard deviations are largest, and show the largest divergence between systems, in the troposphere, in the upper-troposphere/lower-stratosphere, in the upper-stratosphere and mesosphere, and the Antarctic ozone hole region. However, in any particular area, apart from the troposphere, at least one system can be found that agrees well with independent data. In general, none of the differences can be linked to the assimilation technique (Kalman filter, three or four dimensional variational methods, direct inversion) or the system (CTM or NWP system). Where results diverge, a main explanation is the way ozone is modelled. It is important to correctly model transport at the tropical tropopause, to avoid positive biases and excessive structure in the ozone field. In the southern hemisphere ozone hole, only the analyses which correctly model heterogeneous ozone depletion are able to reproduce the near-complete ozone destruction over the pole. In the upper-stratosphere and mesosphere (above 5 hPa), some ozone photochemistry schemes caused large but easily remedied biases. The diurnal cycle of ozone in the mesosphere is not captured, except by the one system that includes a detailed treatment of mesospheric chemistry. These results indicate that when good observations are available for assimilation, the first priority for improving ozone DA systems is to improve the models. The analyses benefit strongly from the good quality of the MIPAS ozone observations. Using the analyses as a transfer standard, it is seen that MIPAS is similar to 5% higher than HALOE (Halogen Occultation Experiment) in the mid and upper stratosphere and mesosphere (above 30 hPa), and of order 10% higher than ozonesonde and HALOE in the lower stratosphere (100 hPa to 30 hPa). Analyses based on SCIAMACHY total column are almost as good as the MIPAS analyses; analyses based on SCIAMACHY limb profiles are worse in some areas, due to problems in the SCIAMACHY retrievals.

Nonlinear data assimilation in geosciences: an extremely efficient particle filter

Almost all research fields in geosciences use numerical models and observations and combine these using data-assimilation techniques. With ever-increasing resolution and complexity, the numerical models tend to be highly nonlinear and also observations become more complicated and their relation to the models more nonlinear. Standard data-assimilation techniques like (ensemble) Kalman filters and variational methods like 4D-Var rely on linearizations and are likely to fail in one way or another. Nonlinear data-assimilation techniques are available, but are only efficient for small-dimensional problems, hampered by the so-called ‘curse of dimensionality’. Here we present a fully nonlinear particle filter that can be applied to higher dimensional problems by exploiting the freedom of the proposal density inherent in particle filtering. The method is illustrated for the three-dimensional Lorenz model using three particles and the much more complex 40-dimensional Lorenz model using 20 particles. By also applying the method to the 1000-dimensional Lorenz model, again using only 20 particles, we demonstrate the strong scale-invariance of the method, leading to the optimistic conjecture that the method is applicable to realistic geophysical problems. Copyright c 2010 Royal Meteorological Society