Interval Smoother Research Articles

상태변수 오차기반 스무더를 이용한 자율이동체 자세오차 보상

In this study, the navigation information of a guided missile was calculated using a smoothing algorithm and used for improving the attitude estimation accuracy of the guided missile. The state variables of the backward filter, designed in the fixed interval smoother, were set to attitude errors in the same way as the forward filter of the fixed interval smoother, which was implemented as a linearized Kalman filter algorithm. To verify the performance of the proposed algorithm, simple guided missile simulations were performed, which confirmed that the attitude error of the guided missile was reduced when the fixed interval smoother was applied.

MODELLING NONLINEAR RELATION BY USING RUNNING INTERVAL SMOOTHER, CONSTRAINED B-SPLINE SMOOTHING AND DIFFERENT QUANTILE ESTIMATORS

This paper compares the small-sample properties of two non-parametric regression methods, running interval smoother and constrained b-spline smoothing. The running interval smoother method deals with estimation of a conditional quantile (or a measure of location) using different estimators and here our focus is on Harrell-Davis and newly proposed NO quantile estimators. The constrained b-spline smoothing method uses the quantile regression estimator while obtaining conditional quantile estimates. Constrained b-spline smoothing and running interval smoother methods are compared with a simulation study by using theoretical distributions. Furthermore, the methods are examined graphically to understand how they can model the relationship between variables. Constrained b-spline smoothing and running interval smoother with NO estimator outperformed running interval smoother with Harrell-Davis estimator in terms of mean squared error.

A Novel Method to Estimate the Full Knee Joint Kinematics Using Low Cost IMU Sensors for Easy to Implement Low Cost Diagnostics.

Traditional motion capture systems are the current standard in the assessment of knee joint kinematics. These systems are, however, very costly, complex to handle, and, in some conditions, fail to estimate the varus/valgus and internal/external rotation accurately due to the camera setup. This paper presents a novel and comprehensive method to infer the full relative motion of the knee joint, including the flexion/extension, varus/valgus, and internal/external rotation, using only low cost inertial measurement units (IMU) connected to the upper and lower leg. Furthermore, sensors can be placed arbitrarily and only require a short calibration, making it an easy-to-use and portable clinical analysis tool. The presented method yields both adequate results and displays the uncertainty band on those results to the user. The proposed method is based on an fixed interval smoother relying on a simple dynamic model of the legs and judicially chosen constraints to estimate the rigid body motion of the leg segments in a world reference frame. In this pilot study, benchmarking of the method on a calibrated robotic manipulator, serving as leg analogue, and comparison with camera-based techniques confirm the method’s accurateness as an easy-to-implement, low-cost clinical tool.

Dynamic displacement estimation using data fusion

The paper describes a Kalman filtering technique for dynamic displacement estimation using accelerometer and laser sensor measurements. Data fusion of measurements from multiple sensors can give the more accurate results because of different advantages of sensors. Since the acceleration and displacement have different sampling rates, the multi-rate Kalman filter is applied. The filter is expanded with the fixed interval smoother to improve reconstruction accuracy of displacements. A modelled signal consisting of two sinus functions and Gaussian distributed noise is used to validate developed state-space model.

Comparisons of Two Quantile Regression Smoothers

The paper compares the small-sample properties of two non-parametric quantile regression estimators. The first is based on constrained B-spline smoothing (COBS) and the other is based on a variation and slight extension of a running interval smoother, which apparently has not been studied via simulations. The motivation for this paper stems from the Well Elderly 2 study, a portion of which was aimed at understanding the association between the cortisol awakening response and two measures of stress. COBS indicated what appeared be an unusual form of curvature. The modified running interval smoother gave a strikingly different estimate, which raised the issue of how it compares to COBS in terms of mean squared error and bias as well as its ability to avoid a spurious indication of curvature. R functions for applying the methods were used in conjunction with default settings for the various optional arguments. The results indicate that the modified running interval smoother has practical value. Manipulation of the optional arguments might impact the relative merits of the two methods, but the extent to which this is the case remains unknown.

A spatiotemporal dynamic distributed solution to the MEG inverse problem

MEG/EEG are non-invasive imaging techniques that record brain activity with high temporal resolution. However, estimation of brain source currents from surface recordings requires solving an ill-conditioned inverse problem. Converging lines of evidence in neuroscience, from neuronal network models to resting-state imaging and neurophysiology, suggest that cortical activation is a distributed spatiotemporal dynamic process, supported by both local and long-distance neuroanatomic connections. Because spatiotemporal dynamics of this kind are central to brain physiology, inverse solutions could be improved by incorporating models of these dynamics. In this article, we present a model for cortical activity based on nearest-neighbor autoregression that incorporates local spatiotemporal interactions between distributed sources in a manner consistent with neurophysiology and neuroanatomy. We develop a dynamic maximum a posteriori expectation-maximization (dMAP-EM) source localization algorithm for estimation of cortical sources and model parameters based on the Kalman Filter, the Fixed Interval Smoother, and the EM algorithms. We apply the dMAP-EM algorithm to simulated experiments as well as to human experimental data. Furthermore, we derive expressions to relate our dynamic estimation formulas to those of standard static models, and show how dynamic methods optimally assimilate past and future data. Our results establish the feasibility of spatiotemporal dynamic estimation in large-scale distributed source spaces with several thousand source locations and hundreds of sensors, with resulting inverse solutions that provide substantial performance improvements over static methods.

Optimal Smoothing for Finite State Hidden Reciprocal Processes

This technical note addresses modelling and estimation of a class of finite state random processes called hidden reciprocal chains (HRC). A hidden reciprocal chain consists of a finite state reciprocal process, together with an observation process conditioned on the reciprocal process much as in the case of a hidden Markov model (HMM). The key difference between Markov models and reciprocal models is that reciprocal models are non-causal. The technical note presents a characterization of a HRC by a finite set of hidden Markov bridges, which are HMMs with the final state fixed. The technical note then uses this characterization to derive the optimal fixed interval smoother for a HRC. Performance of linear and optimal smoothers derived for both HMM and HRC are compared (using simulations) for a class of HRC derived from underlying Markov transitions. These experiments suggest that, not surprisingly, the performance of the optimal HMM and HRC smoothers are signifcantly better than their linear counterparts, and that some performance improvement is obtained using the HRC smoothers compared to the HMM smoothers. The technical note concludes by mentioning some ongoing and future work which exploits this new Markov bridge characterization of a HRC.

Comprehensive Utilization of Temporal and Spatial Domain Outlier Detection Methods for Mobile Terrestrial LiDAR Data

Terrestrial LiDAR provides many disciplines with an effective and efficient means of producing realistic three-dimensional models of real world objects. With the advent of mobile terrestrial LiDAR, this ability has been expanded to include the rapid collection of three-dimensional models of large urban scenes. For all its usefulness, it does have drawbacks. One of the major problems faced by the LiDAR industry today is the automatic removal of outlying data points from LiDAR point clouds. This paper discusses the development and combined implementation of two methods of performing outlier detection in georeferenced point clouds. These methods made use of the raw data available from most time-of-flight mobile terrestrial LiDAR scanners in both the temporal and spatial domains. The first method involved a moving fixed interval smoother derived from the well-known position velocity acceleration Kalman Filter. The second method fitted a quadratic curved surface to sections of LiDAR data. The combined use of these routines is discussed through examples with real LiDAR data.

Exploring the long-term and interannual variability of biogeochemical variables in coastal areas by means of a data assimilation approach

Dynamic Harmonic Regression (DHR) models are applied here to the investigation of the interannual changes in the trend and seasonality of biogeochemical variables monitored in coastal areas. A DHR model can be regarded as a time-series component model, where the phases and amplitudes of the seasonal component, as well as the trend, are parameters that vary with time, reflecting relevant changes in the evolution of the biogeochemical variables. The model parameters and their confidence bounds are estimated by data assimilation algorithms, i.e. the Kalman filter and the Fixed Interval smoother. The DHR model structure is here identified by a preliminary spectral analysis and a subsequent minimization of the Bayesian Information Criterion, thus avoiding subjective choices of the frequencies in the seasonal component. The methodology was applied to the investigation of the long-term and interannual variability of ammonia, nitrate, orthophosphate and chlorophyll-a monitored monthly in the lagoon of Venice (Italy) during the years 1986–2008. It was found that the long-term evolutions of the biogeochemical variables were characterized by non-linear patterns and by statistically significant changes in the trend. The seasonal cycles of all the variables were characterized by a marked interannual variability. In particular, the changes in the seasonality of chlorophyll and nitrate were significantly related to the changes in the seasonality of water temperature at the study site and of nutrient concentrations in river discharges, respectively. These results indicate that the methodology could be a sound alternative to more traditional approaches for investigating the impacts of changes in environmental and anthropogenic forcings on the evolution of biogeochemical variables in coastal areas.

Extraction of interannual trends in seasonal events for ecological time series

The statistical analysis of environmental monitoring data is an important issue in detecting year‐to‐year changes in levels and timings of important ecological events. In many cases, this trend detection must explicitly view interannual changes from the context of an evolving seasonal cycle. This study analyses weekly sampling data from a long‐term ocean monitoring program near Halifax, Nova Scotia, Canada. A state space model of evolving seasonality with a quadratic trend is fit to these time series to extract the signal from the noisy and irregularly sampled data. The procedure uses Kalman filter innovations to estimate model parameters. A fixed interval smoother is then applied to estimate the system state. The resultant state estimates are subjected to a trend analysis carried out with respect to key ecological events: the level and timing of the peak, trough, spring, and fall abundances. These events are identified using derivative information, followed by a regression‐based trend analysis. The analysis found a number of significant linear trends in the biogeochemical variables considered. More generally, the approach used here is suitable for use with monitoring data exhibiting a unimodal seasonal signal with noise and missing values.

Robust ANCOVA using a smoother with bootstrap bagging

Many robust analogs of the classic analysis of covariance (ANCOVA) method have been proposed, some of which are based on some type of regression smoother. A method that first appeared in this journal, which is relatively simple and performs well in simulations, is based on a running interval smoother combined with comparing medians or 20% trimmed means. It makes no parametric assumption about the regression lines and does not assume that the regression lines are parallel. A possible way of improving the efficiency of the running interval smoother is to use bootstrap bagging and a minor goal here is to report some results supporting this approach. The major goal is to consider how ANCOVA might be performed when bootstrap bagging is used. Simple extensions of extant approaches that use some type of bootstrap method were found to be unsatisfactory. However, a basic percentile bootstrap method was found to perform well in simulations. And a reanalysis of data dealing with teachers' expectations about the cognitive ability of students illustrates that bootstrap bagging can make a practical difference.

Efficiency of the California electricity reserves market

AbstractWe test the efficiency of the California electricity reserves market by examining systematic differences between its day‐ and hour‐ahead prices. We uncover significant day‐ahead premia, which we attribute to market design characteristics. On the demand side, the market design established a principal–agent relationship between the markets' buyers (principal) and their supervisory authority (agent). The agent had very limited incentives to shift reserve purchases to the lower priced hour‐ahead markets. On the supply side, the market design raised substantial entry barriers by precluding purely speculative trading and by introducing a complicated code of conduct that induced uncertainty about which actions were subject to regulatory scrutiny. We use a high‐dimensional vector moving average model to estimate the premia and conduct correct inferences. To obtain exact maximum likelihood estimates of the model, we develop a new EM algorithm that seamlessly incorporates missing data and applies directly to general moving average time series models. Our algorithm uses only analytical expressions: the Kalman filter and a fixed interval smoother in the E step and least squares‐type regressions in the M step. Copyright © 2007 John Wiley & Sons, Ltd.

Robust ANCOVA: Some Small-sample Results when there are Multiple Groups and Multiple Covariates

Numerous methods have been proposed for dealing with the serious practical problems associated with the conventional analysis of covariance method, with an emphasis on comparing two groups when there is a single covariate. Recently, Wilcox (2005a: section 11.8.2) outlined a method for handling multiple covariates that allows nonlinearity and heteroscedasticity. The method is readily extended to multiple groups, but nothing is known about its small-sample properties. This paper compares three variations of the method, each method based on one of three measures of location: means, medians and 20% trimmed means. The methods based on a 20% trimmed mean or median are found to avoid Type I error probabilities well above the nominal level, but the method based on medians can be too conservative in various situations; using a 20% trimmed mean gave the best results in terms of Type I errors. The methods are based in part on a running interval smoother approximation of the regression surface. Included are comments on required sample sizes that are relevant to the so-called curse of dimensionality.

A Knowledge Discovery from POS Data using State Space Models An Analysis of Change in Price Elasticities by New Product's Entry to Market

The number of competing-brands changes by new product's entry. The new product introduction is endemic among consumer packaged goods firm and is an integral component of their marketing strategy. As a new product's entry affects markets, there is a pressing need to develop market response model that can adapt to such changes. In this paper, we develop a dynamic model that capture the underlying evolution of the buying behavior associated with the new product. This extends an application of a dynamic linear model, which is used by a number of time series analyses, by allowing the observed dimension to change at some point in time. Our model copes with a problem that dynamic environments entail: changes in parameter over time and changes in the observed dimension. We formulate the model with framework of a state space model. We realize an estimation of the model using modified Kalman filter/fixed interval smoother. We find that new product's entry (1) decreases brand differentiation for existing brands, as indicated by decreasing difference between cross-price elasticities; (2) decreases commodity power for existing brands, as indicated by decreasing trend; and (3) decreases the effect of discount for existing brands, as indicated by a decrease in the magnitude of own-brand price elasticities. The proposed framework is directly applicable to other fields in which the observed dimension might be change, such as economic, bioinformatics, and so forth.

Confidence intervals for prediction intervals

When working with a single random variable, the simplest and most obvious approach when estimating a 1 − γ prediction interval, is to estimate the γ/2 and 1 − γ/2 quantiles. The paper compares the small-sample properties of several methods aimed at estimating an interval that contains the 1 − γ prediction interval with probability 1 − α. In effect, the goal is to compute a 1 − α confidence interval for the true 1 − γ prediction interval. The only successful method when the sample size is small is based in part on an adaptive kernel estimate of the underlying density. Some simulation results are reported on how an extension to non-parametric regression performs, based on a so-called running interval smoother.

Estimating the conditional variance of Y, given X, in a simple regression model

Consider the regression model . In a variety of situations, an estimate of VAR (Y | X) = λ (X) is needed. The paper compares the small-sample accuracy of five estimators of λ (X). The results suggest that the optimal estimator is a somewhat complex function of the underlying distributions. In terms of mean squared error, one of the estimators, which is based in part on a non-robust version of Cleveland's smoother, performed about as well as a bagged version of the so-called running interval smoother, but the running interval smoother was found to be preferable in terms of bias. A modification of Cleveland's smoother, stemming from Ruppert et al. (1997), achieves its intended goal of reducing bias when the error term is homoscedastic, but under heteroscedasticity, bias can be high, and in terms of mean squared error it does not compete well with the kernel method considered in the paper. When ε has a heavy-tailed distribution, a robust version of Cleveland's smoother performed particularly well except in some situations where X has a heavy-tailed distribution as well. A negative feature of using Cleveland's robust smoother is relatively high bias, and when there is heteroscedasticity and X has a heavy-tailed distribution, a kernel-type method and the running interval smoother give superior results in terms of both mean squared error and bias.

ENHANCING ARX-MODEL BASED MPC BY KALMAN FILTER AND SMOOTHER

An approach to enhancing a model-based predictive controller by Kalman filter is proposed. The controller uses an ARX process model and the structure of the controller is assumed fixed; some of its internal variables – past values of controlled variables (output history) are accessible and can be modified to achieve better performance in disturbance attenuation and noise rejection. We present an algorithm of updating the output history using Kalman filter to achieve predictions equivalent to those of the state-space model, thus overcoming the limitations of the ARX predictor. Interesting relations of this algorithm to Kalman interval smoother are given.

A statistical method for the robust detection of interannual changes in plankton abundance: analysis of monitoring data from the Bay of Fundy, Canada

Plankton abundance time series were analysed with an emphasis on the detection of interannual variability. These data covered the period 1988-1999 and were collected in the western Bay of Fundy, Canada as part of an ongoing regional monitoring program. The abundance observations considered here were obtained from water samples at a single station (44°59.57'N, 66° 44.36' W) and at four depths (0, 10, 25 and 50 m). The analysis was based on log-transformed abundance of the taxonomic groups diatoms, dinoflagellates and zooplankton. The time-varying abundance level and its error variance were estimated using a statistical time series method designed for the identification of interannual variability using irregularly sampled and noisy data. To this end, plankton abundance measurements were fitted to a cyclic model using a Kalman filter and associated fixed interval smoother. Maximum likelihood procedures were used to determine all unknown system parameters. The model provided a good fit to these data and allowed identification of year to year changes in the timing and magnitude of the annual abundance cycle. The greatest interannual variability was found in the dinoflagellates and diatoms, with only slight changes in the zooplankton. It was shown that while the annual cycle is readily determined from the observations, interannual variations were near the detection limit. For much of the study period, plankton abundance was not statistically distinguishable from a fixed and repeating mean annual cycle at the 90% confidence level. However, during many time periods dinoflagellates and diatoms, and to a lesser extent zooplankton, exhibited significant interannual variations in abundance. A retrospective analysis of the monitoring program suggested that to achieve robust detection of interannual abundance changes, the variability associated with the water sample based point measurements must be decreased, either through replication, more frequent sampling, or alternative sampling methodologies.

오프라인 항법을 위한 비선형 고정구간 스무더 설계

We propose a new type of nonlinear fixed interval smoother to which an existing nonlinear smoother is modified. The nonlinear smoother is derived from two-filter formulas. For the backward filter. the propagation and the update equation of error states are derived. In particular, the modified update equation of the backward filter uses the estimated error terms from the forward filter. Data fusion algorithm, which combines the forward filter result and the backward filter result, is altered into the compatible form with the new type of the backward filter. The proposed algorithm is more efficient than the existing one because propagation in backward filter is very simple from the implementation point of view. We apply the proposed nonlinear smoothing algorithm to off-line navigation system and show the proposed algorithm estimates position, and altitude fairly well through the computer simulation.

Scale-recursive assimilation of precipitation data

This paper presents a new statistical method for assimilating precipitation data from different sensors operating over a range of scales. The technique is based on a scale-recursive estimation algorithm which is computationally efficient and able to account for the nested spatial structure of precipitation fields. The version of the algorithm described here relies on a static multiplicative cascade model which relates rainrates at different scales. Bayesian estimation techniques are used to condition rainrate estimates on measurements. The conditioning process is carried out recursively in two sweeps: first from fine to coarse scales and then from coarse to fine scales. The complete estimation algorithm is similar to a fixed interval smoother although it processes data over scale rather than time. We use this algorithm to assimilate radar and satellite microwave data collected during the tropical ocean–global atmosphere coupled ocean–atmosphere response experiment (TOGA-COARE). The resulting rainrate estimates reproduce withheld radar measurements to within the level of accuracy predicted by the assimilation algorithm.