A method for mixed additive and multiplicative random error models with inequality constraints in geodesy

In a strapdown inertial navigation system (INS), the general displacement of a rigid body is traditionally separately modeled and analyzed, i.e., direction cosine matrix or quaternion for rotation analysis and vector for translation analysis. As a subsequent work of a companion paper (Wu et al., 2005), this paper adopts dual quaternion algebra, a most concise and unified mathematical tool for representing the general displacement of a rigid body, to analyze error characteristics of the strapdown INS. Two new error models in terms of quaternion algebra are developed: the additive dual quaternion error (ADQE) model and multiplicative dual quaternion error (MDQE) model. Both are expected to facilitate the future inertial navigation-based integrated navigation filter.

Light detection and ranging (LiDAR) has the advantage of simultaneous localization and mapping with high precision, making it one of the important sensors for intelligent robotics navigation, positioning, and perception. It is common knowledge that the random measurement error of global navigation satellite system (GNSS) observations is usually considered to be closely related to the elevation angle factor. However, in the LiDAR point cloud feature matching positioning model, the analysis of factors affecting the random measurement error of observations is unsophisticated, which limits the ability of LiDAR sensors to estimate pose parameters. Therefore, this work draws on the random measurement error analysis method of GNSS observations to study the impact of factors such as distance, angle, and feature accuracy on the random measurement error of LiDAR. The experimental results show that feature accuracy is the main factor affecting the measurement error in the LiDAR point cloud feature matching positioning model, compared with distance and angle factors, even under different sensor specifications, point cloud densities, prior maps, and urban road scenes. Furthermore, a simple random measurement error model based on the feature accuracy factor is used to verify the effect of parameter estimation, and the results show that the random error model can effectively reduce the error of pose parameter estimation, with an improvement effect of about 50%.

Flow rate measurement by kinematic wave detection in vertically upward, bubbly two-phase flows

Measurement data in the field of modern geodesy contains not only additive errors but also multiplicative errors related to signal strength. The existing models for dealing with mixed additive and multiplicative errors are mainly based on the linear form of unknown parameters and observations, and there are few studies on the nonlinear form of the two. In the parameter estimation method of the nonlinear mixed additive and multiplicative errors model, the initial value of the Gauss–Newton parameter estimation method is selected by previous experience. The initial value determined by this method deviates far from the true value due to a lack of experience, which will lead to inaccurate parameter estimation results. In order to solve this problem, based on the least squares principle and the introduction of the damping factor, this paper deduces the damping least squares parameter solution formula for the parameter estimation of the nonlinear mixed additive and multiplicative errors model. The superiority of the damping least squares algorithm is reflected in the adjustment of the damping factor, taking into account the advantages of the Gauss–Newton method and the steepest descent method, and some weighted selection is obtained in the two algorithms. The calculation and comparative analysis of the simulated cases show that the damped least squares method is more suitable for handling geodetic data with this nonlinear mixed additive and multiplicative errors model when the initial value deviates far from the true value.

Additive and multiplicative heteroscedastic error models are considered, and the relative efficiency of a number of Bayesian and sampling theory estimators, including some pre-test estimators,is investigated. The relative performance of the various estimators seems to depend more on sample size and the severity of the heteroscedasticity than it does on the underlying nature of the heteroscedasticity. In general the Bayesian estimators outperform the sampling theory estimators, and we make some useful recommendations concerning estimator choice.

Research on singular value decomposition algorithm for mixed additive and multiplicative error model

The ideas described in this paper are motivated by a basic problem in Multidimensional Scaling which is solved not quite satisfactory up to now. Suppose that there are given pairwise dissimilarities δij, 1 ≤ i, j ≤ n, as nonnegative real numbers between n objects. These originate from the special type of application and may be, for example in cartography, measurements of pairwise distances disturbed by additive random errors or, in psychology, individual assessments of the deviation in behaviour of n persons measured on a certain real scale. There are many other applications in a variety of fields, a structured overview may be obtained from de Leeuw & Heiser (1980, 1982).

In prediction, the percentage error is often felt to be more meaningful than the absolute error. We therefore extend the method of least squares to deal with percentage errors, for both simple and multiple regression. Exact expressions are derived for the coefficients, and we show how such models can be estimated using standard software. When the relative error is normally distributed, least squares percentage regression is shown to provide maximum likelihood estimates. The multiplicative error model is linked to least squares percentage regression in the same way that the standard additive error model is linked to ordinary least squares regression.

The Nash-Sutcliffe efficiency (NSE) is a widely used score in hydrology but is not common in the other environmental sciences. One of the reasons for its unpopularity is that its scientific meaning is somehow unclear in the literature. This study attempts to establish a solid foundation for NSE from the viewpoint of signal progressing. Thus, a forecast is viewed as a received signal containing a wanted signal (observations) contaminated by an unwanted signal (noise). This view underlines an important role of the error model between forecasts and observations. By assuming an additive error model, it is easy to point out that NSE is equivalent to an important quantity in signal processing: the signal-to-noise ratio. Moreover, NSE and the Kling-Gupta efficiency (KGE) are shown to be equivalent, at least when there are no biases, in the sense that they measure the relative magnitude of the power of noise to the power of variation of observations. The scientific meaning of NSE explains why it is reasonable to choose NSE=0 as the boundary between skilful and unskilful forecasts in practice, and this has no relation with the benchmark forecast that is equal to the mean of observations. Corresponding to NSE=0, the critical values of KGE is given approximately by 0.5. In the general cases, when the additive error model is replaced by a mixed adaptive-multiplicative error model, the traditional NSE is shown not to be a well-defined notion. Therefore, an extension of NSE is derived, which only requires to divide the traditional noise-to-signal ratio by the multiplicative factor. This has a practical implication: if the multiplicative factor is not considered, the traditional NSE and KGE underestimate (overestimate) the generalized ones when the multiplicative factor is greater (smaller) than one. In particular, the benchmark forecast turns out to be the worst forecast under the view of the generalized NSE.

A new approach in satellite retrievals, multi-parameter empirical retrievals, is introduced. It is shown that single-parameter retrievals, compared with multi-parameter retrievals, contain significant additional "artificial" systematic and random errors. These errors may be avoided using multi-parameter retrieval algorithms. Neural networks (NNs) are well suited for developing such multi-parameter retrieval algorithms. The NN approach for developing empirical multi-parameter algorithms is discussed. A new NN empirical algorithm (OMBNN3) which simultaneously retrieves four geophysical parameters: surface wind speed, columnar water vapor, columnar liquid water, and sea surface temperature from five special sensor microwave imager brightness temperatures (T19V, T19H, T22V, T37V, and T37H) is presented and compared with several single-parameter algorithms to illustrate advantages of the multi-parameter approach.

Least-squares health parameter identification techniques such as the Kalman filter have been massively used to solve the problem of turbine engine diagnosis. Indeed, such methods give a good estimate provided that the discrepancies between the model prediction and the measurements are zero-mean, white random variables. In turbine engine diagnosis, however, this assumption does not always hold due to the presence of biases in the model. This is especially true for transient operation. As a result, the estimated parameters tend to diverge from their actual values which strongly deteriorates the diagnosis. The purpose of this contribution is to present a Kalman filter diagnosis tool where the model biases are treated as an additional random measurement error. The new methodology is tested on simulated transient data representative of a current turbofan layout. While relatively simple to implement, the newly developed diagnosis tool exhibits a much better accuracy than the original Kalman filter in the presence of model biases.

Existing validation of mean wind speed estimates via reflectometry from global navigation systems of satellites (GNSS-R)—has been largely limited in spatial coverage to equatorial buoys or tropical cyclone events near continental United States. Two alternative validation techniques are presented for the Cyclone GNSS (CYGNSS) mission using surface-based observations along coasts and coral reefs instead of buoys, and triple collocation analysis (TCA) instead of a 1:1 gridded comparison for tropical cyclone (TC) events. For the surface-based analysis, Fully Developed Seas (FDS) v3.2 and NOAA v1.2 were compared to anemometer data provided by the Australian Bureau of Meteorology across the Australia and Pacific regions. Overall, the products performed similarly to previous studies with NOAA having higher correlations and lower errors than FDS, though FDS performed better than NOAA over the Australian dataset for high wind speed events. TCA was used to validate NOAA v1.2 and Merged v3.2 datasets with other satellite remotely sensed products from the Soil Moisture Active Passive (SMAP) mission and Synthetic Aperture Radar (SAR). Both additive and multiplicative error models for TCA were applied. The performance overall was similar between the two products, with NOAA producing higher errors. NOAA performed better than Merged for mean winds above 17 m/s as the large temporal averaging reduced sensitivity to high winds. For SMAP winds above 17 m/s, NOAA’s average bias (−2.1 m/s) was significantly smaller than the average bias in Merged (−4.4 m/s). Future ideas for rapid intensification detection and constellation design are discussed.

The goal of this study was to investigate the pharmacokinetic (PK) behaviour of dexmedetomidine in dogs administered as a pure enantiomer versus as part of a racemic mixture. Eight unmedicated intact purpose‐bread beagles were included. Two intravenous treatments of either medetomidine or dexmedetomidine were administered at 10‐ to 14‐day intervals. Atipamezole or saline solution was administered intramuscularly 45 min later. Venous blood samples were collected into EDTA collection tubes, and the quantification of dexmedetomidine and levomedetomidine was performed by chiral LC–MS/MS. All dogs appeared sedated after each treatment without complication. Plasma concentrations of levomedetomidine were measured only in the racemic group and were 51.4% (51.4%–56.1%) lower than dexmedetomidine. Non‐compartmental analysis (NCA) was performed for both drugs, while dexmedetomidine data were further described using a population pharmacokinetic approach. A standard two‐compartment mammillary model with linear elimination with combined additive and multiplicative error model for residual unexplained variability was established for dexmedetomidine. An exponential model was finally retained to describe inter‐individual variability on parameters of clearance (Cl1) and central and peripheral volumes of distribution (V1, V2). No effect of occurrence, levomedetomidine or atipamezole could be observed on dexmedetomidine PK parameters. Dexmedetomidine did not undergo significantly different PK when administered alone or as part of the racemic mixture in otherwise unmedicated dogs.

In large cohort studies, it often happens that some covariates are expensive to measure and hence only measured on a validation set. On the other hand, relatively cheap but error-prone measurements of the covariates are available for all subjects. Regression calibration (RC) estimation method (Prentice, 1982, Biometrika 69, 331-342) is a popular method for analyzing such data and has been applied to the Cox model by Wang et al. (1997, Biometrics 53, 131-145) under normal measurement error and rare disease assumptions. In this article, we consider the RC estimation method for the semiparametric accelerated failure time model with covariates subject to measurement error. Asymptotic properties of the proposed method are investigated under a two-phase sampling scheme for validation data that are selected via stratified random sampling, resulting in neither independent nor identically distributed observations. We show that the estimates converge to some well-defined parameters. In particular, unbiased estimation is feasible under additive normal measurement error models for normal covariates and under Berkson error models. The proposed method performs well in finite-sample simulation studies. We also apply the proposed method to a depression mortality study.

This paper focuses on the design of an observer-based backstepping controller (BC) for a nonlinear hydraulic differential cylinder system. The system is affected by some uncertainties including modeling errors, external disturbances, and measurement noise. An observer-based control approach is proposed to assure suitable tracking performance and to increase robustness against unknown inputs. The task to estimate system states as well as unknown inputs is performed by a linear proportional-integral-observer (PIO). Input–output linearization is used to linearize the nonlinear system model to be used for the PIO structure. On the other hand, BC is utilized based on nonlinear system model to construct the Lyapunov function and to design the control input simultaneously. Stability or negativeness of the derivative of every-step Lyapunov function is fulfilled. Structural improvement regarding the combination of BC and PIO is the main aim of this contribution. This is supported by a novel stability proof and new conditions for the whole control loop with integrated PIO. Furthermore, parameter selection of BC is elaborately considered by defining a performance/energy criterion. A complete robustness evaluation considering different levels of additional measurement noise, modeling errors, and external disturbances is presented for the first time in this contribution. Experimental results validate the advantages of proposed observer-based approach compared to PIO-based sliding mode control (PIO-SMC) and industrial standard P-controller.