Robust Kalman filter for rank deficient observation models

Koch, Karl‐Rudolf; Yang, Yuanxi

doi:10.1007/s001900050183

Cited by 91 publications

(47 citation statements)

References 10 publications

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“…In the paper by Koch and Yang (1998) downweighting is applied on the parameters. However, in this study, to be consistent with the previously developed SVD methodology (Rohm and Bosy, 2011;Rohm, 2012Rohm, , 2013) the downweighting of the parameters is not used.…”

Section: Kalman Filter Applicationmentioning

confidence: 99%

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Limited constraint, robust Kalman filtering for GNSS troposphere tomography

2014

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Abstract. The mesoscale variability of water vapour (WV) in the troposphere is a highly complex phenomenon and modelling and monitoring the WV distribution is a very important but challenging task. Any observation technique that can reliably provide WV distribution is essential for both monitoring and predicting weather. The global navigation satellite system (GNSS) tomography technique is a powerful tool that builds upon the critical ground-based GNSS infrastructure (e.g. Continuous Operating Reference Station -CORS -networks) that can be used to sense the amount of WV. Previous research shows that the 3-D WV field from GNSS tomography has an uncertainty of 1 hPa. However, all the models used in GNSS tomography heavily rely on a priori information and constraints from non-GNSS measurements. In this study, 3-D GNSS tomography models are investigated based on a limited constrained approach -i.e. horizontal and vertical correlations between voxels were not introduced, instead various a priori information were added into the system. A case study is designed and the results show that proposed solutions are feasible by using a robust Kalman filtering technique and effective removal of linearly dependent observations and parameters. Discrepancies between reference wet refractivity data derived from the Australian Numerical Weather Prediction (NWP) model (ACCESS) and the GNSS tomography model using both simulated and real data are 4.2 ppm (mm km −1 ) and 6.2 ppm (mm km −1 ), respectively, which are essentially in the same order of accuracy.

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Section: Kalman Filter Applicationmentioning

confidence: 99%

“…Consequently, the Kalman filter sequence as shown in Koch and Yang (1998) for filtering observations will be transformed to the following sequence:…”

Section: Kalman Filter Applicationmentioning

confidence: 99%

Limited constraint, robust Kalman filtering for GNSS troposphere tomography

2014

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“…As a matter of fact, since the Kalman filter is not completely resilient to outliers (due to its iterative strategy based on the Maximum A Posteriori), even in its robust version ( [19]), we apply RANSAC directly on the measurements to avoid outliers. Indeed, the multi-modality of the conditional density is only due to the output statistics: assuming that the posterior density of the hidden variables (the state of the system related to the registration) is unimodal, the EKF with RANSAC attempts to estimate the principal mode of the dynamic evolution.…”

Section: Morp-a064mentioning

confidence: 99%

A Fast RANSAC-Based Registration Algorithm for Accurate Localization in Unknown Environments using LIDAR Measurements

Fontanelli

Ricciato

Soatto

2007

2007 IEEE International Conference on Automation Science and Engineering

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Abstract-The problem of accurate localization using only measurements from a LIDAR sensor is analyzed in this paper. The sensor is rigidly fixed on a generic moving platform, which moves on a plane. Practical on-line applications of localization algorithms impose constraints on the execution time, problem that is addressed in this paper and compared with other existing solutions.Due to the nature of the sensor adopted, the localization algorithm is based on a fast and accurate registration algorithm, which is able to deal with noisy measurements, outliers and dynamic environments. The proposed solution relies on the RANSAC algorithm in combination with a Huber kernel in order to cope with typical nuisances in LIDAR measurements. The robust registration is successively used in combination with an Extended Kalman Filter to track the trajectory of the LIDAR over time, hence to solve the localization problem.Simulations and experimental results are reported to show the feasibility of the proposed approach.

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“…We choose 0%, 5%, ..., 85% outliers and for each of the filters we run 100 experiments and store the estimated motion. Then, we compute the mean and the standard deviation for each outlier level and for both the robust EKF (an extension of [13] to nonlinear systems) and KALMANSAC and plot the results in Figure 3. As one can see, the robust EKF consistently fails to produce any sensible estimate of motion as soon as some outliers are introduced in the measurements (Figure 3 left).…”

Section: Structure From Motionmentioning

confidence: 99%

KALMANSAC: robust filtering by consensus

Vedaldi¹,

Jin

Favaro

et al. 2005

Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1

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We propose an algorithm to perform causal inference of the state of a dynamical model when the measurements are corrupted by outliers. While the optimal (maximumlikelihood) solution has doubly exponential complexity due to the combinatorial explosion of possible choices of inliers, we exploit the structure of the problem to design a samplingbased algorithm that has constant complexity. We derive our algorithm from the equations of the optimal filter, which makes our approximation explicit. Our work is motivated by real-time tracking and the estimation of structure from motion (SFM). We test our algorithm for on-line outlier rejection both for tracking and for SFM. We show that our approach can tolerate a large proportion of outliers, whereas previous causal robust statistical inference methods failed with less than half as many. Our work can be thought of as the extension of random sample consensus algorithms to dynamic data, or as the implementation of pseudo-Bayesian filtering algorithms in a sampling framework.

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Robust Kalman filter for rank deficient observation models

Cited by 91 publications

References 10 publications

Limited constraint, robust Kalman filtering for GNSS troposphere tomography

Limited constraint, robust Kalman filtering for GNSS troposphere tomography

A Fast RANSAC-Based Registration Algorithm for Accurate Localization in Unknown Environments using LIDAR Measurements

KALMANSAC: robust filtering by consensus

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