Combined adaptive robust Kalman filter algorithm

Outlying observations are undesirable but possible elements of geodetic measurements. In such a context, the primary and trivial solution is to repeat “suspected” observations. The question arises: what if the measurements cannot be performed again, or if one cannot flag outliers easily and efficiently? In such a case, one should process data by applying methods that consider the possible occurrence of outlying observations. Historically, except for some previous attempts, the statistical approach to robust estimation originates in the 60s of the 20th century and refers to the pioneer papers of Huber, Tukey, Hampel, Hodges, and Lehmann. Also, the statistical procedures known as data snooping (data dredging) were developed at a similar time. It took not a long time before robust procedures were implemented for processing geodetic observations or adjustment of observation systems. The first works of Baarda and Pope encouraged other scientists or surveyors to elaborate robust procedures adapted for geodetic or surveying problems, which resulted in their rapid development in the last two decades of the 20th century. The question for the 21st century is whether robustness is still an important issue relating to modern measurement technologies and numerical data processing. One should realize that modern geodetic techniques do not decrease the probability of outlier occurrence. Considering measurement systems that yield big data, it is almost certain that outliers occur somewhere. The paper reviews different approaches to robust processing of geodetic observations, from the data snooping methods, random sampling, M-estimation, R-estimation, and Msplit estimation to robust estimation of the variance coefficient. Such a variety reflects different natures, origins, or properties of outliers and the apparent fact that there is no best and most efficient and universal robust approach. The methods presented are indeed the basis for future solutions based on, e.g., machine learning.

Section: M-estimationmentioning

confidence: 99%

Robust procedures in processing measurements in geodesy and surveying: a review

Duchnowski,

Wyszkowska

2024

“…To process GNSS measurements, a KF [23] is applied in a GNSS navigation filter. The state space model is…”

Section: Gnss Navigation Filtermentioning

confidence: 99%

“…To process all the information from the GNSS and INS, a KF [23] is applied as an integrated navigation filter. The filter comprises the state model and the measurement model.…”

Section: Integrated Navigation Filtermentioning

confidence: 99%

A distributed GNSS/INS integrated navigation system in a weak signal environment

Liu¹,

Gu²,

Mou³

et al. 2021

Traditional global navigation satellite systems (GNSS) based on vector tracking (VT) have various structures. However, some GNSS measurements have no connection with the dynamic of the user when the loop loses lock in the shade, e.g. urban canyon, tree shade, etc. To improve the navigation accuracy in a weak environment, a distributed GNSS/inertial navigation system (INS) integrated navigation system based on VT is proposed. The change in the pseudo-range rate and pseudo-range from the loop is employed in the GNSS receiver. The reliable navigation results can be output from a distributed navigation filter according to effective GNSS measurements and modified INS information. The field test shows that the proposed distributed GNSS/INS navigation system can achieve reliable navigation in weak signal environments.

“…Gu et al [11] present a trimmed moving total least-squares (MTLS) method, in which the total least-squares method with a truncation procedure is adopted to determine the local coefficients in the influence domain, which can deal with outliers and random errors of all variables without setting the threshold or adding small weights subjectively. Furthermore, Lin et al [12] propose a combined adaptive robust Kalman filter algorithm IGGIII to improve the accuracy and robust estimation.…”

Section: Introductionmentioning

confidence: 99%

A quality factor of forecasting error for sounding data in MBES

Yuan

Zhou

et al. 2022

The multi-beam sounding system achieves ultra-wide coverage and high-resolution measurement. Its significantly increased data density has great advantages in accurately depicting the topography of the seabed. However, it requires processing large amount of data. A preprocessing method that performs in real time, automatically identifies the outliers in multi-beam bathymetry data, and provides corresponding bathymetry estimates, is able to provide a lot of effective information for the post-processing for improving the data processing efficiency and ensuring data quality. In this work, we propose quality factor of forecasting error (QE) for detecting the outliers and forecasting the depth in multi-beam bathymetry data. On the basis of the existing quality factor model for seabed detection method, and under the assumption of smooth seafloor terrain, we use the quality factor (QF) to select a suitable seabed detection method and eliminate the sounding points which correspond to poor echo characteristics. The uncertainty inferred by the quality factor is used as the initial parameter of Kalman filter estimation and the depth value prediction model is formulated. The sounding sequence is sorted by the median value by using the sliding window method. After second fitting and Kalman filtering, the depth of each point is predicted. The quality factor model based on forecasting errors is adopted to simplify and unify the outlier detection standards. The selection rules of window length and detection threshold are deeply studied on the basis of simulations performed in this work. For appropriate parameters, the proposed algorithm shows a good detection capability for impulse anomalies, cluster anomalies, and seabed topography undulations. In addition, the proposed method gives smooth depth prediction values. The simulation results and analysis show that the proposed algorithm further detects the outliers in depth sequence on the basis of QF and forecasts the sounding point in real time. The QE threshold based on the relative depth is easy to select and is suitable for different sounding system. It provides effective outlier detection information for post-processing.