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

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.

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.

A STUDY ON THE INDICATION OF UNEXPECTED COMPONENTS BY KALMAN FILTERING IN FLUOROSPECTROPHOTOMETRY

The potential of Kalman filtering for indication of unexpected components in a mixture was experimentally evaluated by taking the spectrofluorimetric analysis of the tricomponent system;oi phenylalanine, tryhtophen and tyrosine as an example. According to

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.

EVALUATION OF THE RELIABILITY OF KALMAN FILTERING RESULTS IN INDUCTIVELY COUPLED PLASMA ATOMIC EMISSION-SPECTROMETRY

This paper deals with the evaluation of the reliability of the analytical results obtained by Kalman filtering. Two criteria for evaluation were compared: one is based on the autocorrelation analysis of the innovation sequence, the so-called NAC criterion; the other is the innovations number, which actually is the autocorrelation coefficient of the innovation sequence at the initial wavelength. Both criteria allow compensation for the wavelength positioning errors in spectral scans, but there exists a difference in the way they work. The NAC criterion can provide information about the reliability of an individual result, which is very useful for the indication of unmodelled emissions, while the innovations number should be incorporated with the normalization of the innovations or seek the help of the sequence itself for the same purpose. The major limitation of the NAC criterion is that it does not allow the theoretical modelling of continuous backgrounds, which, however, is convenient in practical analysis and can be taken with the innovations number criterion.

EVALUATION OF THE EFFECT OF WAVELENGTH POSITIONING ERRORS ON KALMAN FILTERING RESULTS IN INDUCTIVELY COUPLED PLASMA ATOMIC EMISSION-SPECTROMETRY

This work evaluates the effect of wavelength positioning errors in spectral scans on analytical results when the Kalman filtering technique is used for the correction of line interferences in inductively coupled plasma atomic emission spectrometry (ICP-AES). The results show that a positioning accuracy of 0.1 pm is required in order to obtain accurate and precise estimates for analyte concentrations. The positioning error in sample scans is more crucial than that in model scans. The relative bias in measured analyte concentration originating from a positioning error in a sample scan increases linearly with an increase in the magnitude of the error and the peak distance of the overlapping lines, but is inversely proportional to the signal-to-background ratio. By the use of an optimization procedure for the positions of scans with the innovations number as the criterion, the wavelength positioning error can be reduced and, correspondingly, the accuracy and precision of analytical results improved.

Accurate image capturing control of bottle caps based on iterative learning control and Kalman filtering

This paper investigates camera control for capturing bottle cap target images in the fault-detection system of an industrial production line. The main purpose is to identify the targeted bottle caps accurately in real time from the images. This is achieved by combining iterative learning control and Kalman filtering to reduce the effect of various disturbances introduced into the detection system. A mathematical model, together with a physical simulation platform is established based on the actual production requirements, and the convergence properties of the model are analyzed. It is shown that the proposed method enables accurate real-time control of the camera, and further, the gain range of the learning rule is also obtained. The numerical simulation and experimental results confirm that the proposed method can not only reduce the effect of repeatable disturbances but also non-repeatable ones.