Least-squares Prediction Research Articles

A Transferable Thruster Fault Diagnosis Approach for Autonomous Underwater Vehicle under Different Working Conditions with Insufficient Labeled Training Data

Existing thruster fault diagnosis methods for AUV (autonomous underwater vehicle) usually need sufficient labeled training data. However, it is unrealistic to get sufficient labeled training data for each working condition in practice. Based on this challenge, a transferable thruster fault diagnosis approach is proposed. In the approach, an IPSE (instantaneous power spectrum entropy) and a STNED (signal-to-noise energy difference) are added to SPWVD (smoothed pseudo Wigner-Ville distribution) to identify time and frequency boundaries of the local region in the time-frequency power spectrum caused by thruster fault, forming a TFE (time-frequency energy) method for feature extraction. In addition, the RCQFFV (relative change quantity of the fault feature value), an MSN (multiple scale normalization) and a LSP (least square prediction) are added to SVDD (support vector data description) to align distributions of fault samples, contributing a TSVDD (transferable SVDD) for classification of fault samples. The experimental results of a prototype AUV indicate that the fault feature is monotonic to the percentage of thrust loss for the proposed TFE but not for the SPWVD. The TSVDD has a higher overall classification accuracy in comparison to conventional SVDD under working conditions with no labeled training data.

On Optimal Correlation-Based Prediction

This note examines, at the population-level, the approach of obtaining predictors of a random variable Y, given the joint distribution of , by maximizing the mapping for a given correlation function . Commencing with Pearson’s correlation function, the class of such predictors is uncountably infinite. The least-squares predictor is an element of this class obtained by equating the expectations of Y and to be equal and the variances of and to be also equal. On the other hand, replacing the second condition by the equality of the variances of Y and , a natural requirement for some calibration problems, the unique predictor that is obtained has the maximum value of Lin’s (1989) concordance correlation coefficient (CCC) with Y among all predictors. Since the CCC measures the degree of agreement, the new predictor is called the maximal agreement predictor. These predictors are illustrated for three special distributions: the multivariate normal distribution; the exponential distribution, conditional on covariates; and the Dirichlet distribution. The exponential distribution is relevant in survival analysis or in reliability settings, while the Dirichlet distribution is relevant for compositional data.

Distributed Fusion Estimation in Network Systems Subject to Random Delays and Deception Attacks

This paper focuses on the distributed fusion estimation problem in which a signal transmitted over wireless sensor networks is subject to deception attacks and random delays. We assume that each sensor can suffer attacks that may corrupt and/or modify the output measurements. In addition, communication failures between sensors and their local processors can delay the receipt of processed measurements. The randomness of attacks and transmission delays is modelled by different Bernoulli random variables with known probabilities of success. According to these characteristics of the sensor networks and assuming that the measurement noises are cross-correlated at the same time step between sensors and are also correlated with the signal at the same and subsequent time steps, we derive a fusion estimation algorithm, including prediction and filtering, using the distributed fusion method. First, for each sensor, the local least-squares linear prediction and filtering algorithm are derived, using a covariance-based approach. Then, the distributed fusion predictor and the corresponding filter are obtained as the matrix-weighted linear combination of corresponding local estimators, checking that the mean squared error is minimised. A simulation example is then given to illustrate the effectiveness of the proposed algorithms.

Synthetic aperture radar phase unwrapping using region-growing with polynomial-based phase prediction

Phase unwrapping for interferometric synthetic aperture radar (InSAR) remains a challenge due to the presence of speckle noise and temporal decorrelation in many interferograms. This paper proposes a polynomial-based region-growing phase unwrapping (PBRGPU) approach that is built on the region-growing phase unwrapping (RGPU) approach in Xu and Cumming (Xu and Cumming. 1996. A region growing algorithm for insar phase unwrapping. IGARSS 96. International Geoscience and Remote Sensing Symposium. 31–31 May 1996. Lincoln, NE, USA. doi: 10.1109/igarss.1996.516883 ). The proposed approach iteratively performs phase unwrapping at the edges of multiple seeded regions using a least-squares polynomial phase prediction, which allows for the use of statistically rigorous quality assurance to remove low quality pixels from further processing. Here, a user-specified statistical confidence interval is more intuitive to users than the threshold parameters used by other algorithms. The proposed approach is currently the only phase unwrapping approach to take this strategy with its quality assurance. The proposed approach was found to improve upon the solution quality of the RGPU approach, in some cases achieving a tenfold decrease in root-mean-square error for simulated data. The PBRGPU approach performed well when applied to RADARSAT-2 data collected over Polar Bear Provincial Park (Ontario, Canada). The PBRGPU solutions were consistently on par with or superior to those generated by SNAPHU in terms of accuracy. While the PBRGPU approach does lag behind SNAPHU in terms of the domain of the solution, with SNAPHU unwrapping a significantly larger portion of the interferogram in all test cases, this issue could readily be mitigated through post-processing of the unwrapped interferogram. The proposed approach provides a solid foundation for region-growing algorithms that adapt to local noise levels and integrate all available information rather than relying on preprocessing strategies.

The New AFRGDB_V2.2 Gravity Database for Africa

The primary task of the IAG Sub-Commission on Gravity and Geoid in Africa is the development of the vertical reference surface (the geoid) for the entire African continent. For the practical solution of this boundary value problem, the available, arbitrarily distributed boundary data (gravity values) must be interpolated onto a regular grid for numerical reasons. In this paper it is explained in detail how to create this grid from the irregularly distributed point-gravity data. It is worth mentioning that this gravity database is not only used for geoid computation; it is also a stand-alone product used in earth sciences, as it reflects interesting geophysical signals. The gravity data available in this project are land and shipborne point gravity values as well as altimetry-derived gravity anomaly data. One challenge of preparing the homogeneous grid of gravity anomalies is caused by the inhomogeneous distribution of the observations and a lot of data gaps, especially on land. At these data gaps, gravity anomalies are provided on a so-called underlying grid from the GOCE DIR_R5 global reference model. One challenge in the framework of the least-squares prediction technique used is the determination of an empirical covariance function representing the behaviour of the irregularly distributed data points and the individual weights of the land, shipborne, and altimetry data and the underlying grid entering the process. A sophisticated filtering of the available gravity data is carried out to meet this challenge. The preprocessed data from the remove step are predicted to an equiangular $$5^{'} \times 5^{'}$$ grid. Finally, a consistent restore step leads to the AFRGDB_V2.2 gravity database. The precision of the developed gravity database has been studied to assess the quality of the new product. The new AFRGDB_V2.2 gravity database is compared to the preceding one (AFRGDB_V2.0), which was generated using the window remove-restore technique.

Nondestructive determination of lignin content in Korla fragrant pear based on near-infrared spectroscopy

The lignin content is a key index affecting the quality of Korla fragrant pear. This study applied a method of near-infrared diffuse reflectance spectroscopy combined with chemometric method to establish a predictive model of lignin content. Among them, moving average, baseline, standard normal variate transformations and multiplicative scatter correction were used to preprocess the collected near-infrared spectra. then, the backward interval partial least-squares, synergy interval partial least squares and uninformative variable elimination algorithms were used to select characteristic wavelengths from the whole spectral range to establish a partial least-squares prediction model of lignin content. The partial least-squares model based on uninformative variable elimination selected characteristic wavelengths was simplified, and the prediction of lignin content in Korla pear was more accurate. Multiple determination coefficient values, standard prediction errors and residual prediction errors for prediction were 0.87, 1.36 and 2.03%, respectively. Compared with partial least squares based on the whole spectral range and partial least squares based on Uninformative variable elimination selection, the number of characteristic wavelength variables was reduced from 289 to 51, thereby improving the prediction accuracy of the model. The experimental results showed that the uninformative variable elimination by partial least-squares model was the best model. The combination of near-infrared spectroscopy and uninformative variable elimination optimization can effectively determine the lignin content in Korla fragrant pear. The near-infrared diffuse reflectance spectroscopy proved to be a good tool for nondestructive determination of lignin content in Korla fragrant pear. The selection of characteristic wavelengths and appropriate pretreatment methods can improve the accuracy of near-infrared spectroscopy in actual detection.

An improved algorithm for target trajectory prediction in the active protection system based on converted measurement Kalman filter

Fast and accurate prediction of the trajectory is the prerequisite for the successful interception of the incoming target by the active protection system (APS) of armoured vehicles. The traditional least-squares algorithm is susceptible to large errors in the initial stage of the tracking process, and the prediction of interception points converges slowly. This paper proposes an interception point prediction algorithm that combines the Kalman filter and least-squares estimation. By dynamically determining the convergence of the least-squares prediction, a converted measurement Kalman filter is used in the initial tracking stage to obtain higher prediction accuracy of the interception point. Simulations are performed in the scenario of the interception process of the APS. The results prove that the algorithm can effectively accelerate the convergence of the interception point prediction process.

Precipitation Atlas for Germany (GePrA)

A new approach for modeling daily precipitation (RR) at very high spatial resolution (25 m × 25 m) was introduced. It was used to develop the Precipitation Atlas for Germany (GePrA). GePrA is based on 2357 RR time series measured in the period 1981–2018. It provides monthly percentiles (p) of the large-scale RR patterns which were mapped by a thin plate spline interpolation (TPS). A least-squares boosting (LSBoost) approach and orographic predictor variables (PV) were applied to integrate the small-scale precipitation variability in GePrA. Then, a Weibull distribution (Wei) was fitted to RRp. It was found that the mean monthly sum of RR ( R R ¯ s u m ) is highest in July (84 mm) and lowest in April (49 mm). A great dependency of RR on the elevation (ε) was found and quantified. Model validation at 425 stations showed a mean coefficient of determination (R2) of 0.80 and a mean absolute error (MAE) of less than 10 mm in all months. The high spatial resolution, including the effects of the local orography, make GePrA a valuable tool for various applications. Since GePrA does not only describe R R ¯ s u m , but also the entire monthly precipitation distributions, the results of this study enable the seasonal differentiation between dry and wet period at small scales.

Suitable gravity interpolation technique for large data gaps in Africa

The gravity database for the IAG African Geoid Project contains significantly large data gaps. These large data gaps affect the interpolation precision of the reduced gravity anomalies needed for the determination of the gravimetric geoid for Africa. Our aim is to develop a suitable interpolation technique that can be used for a proper gravity interpolation within large data gaps. A gap of 10° × 5° in the latitude and longitude directions, respectively, located at the high lands of Ethiopia has been artificially created within the gravity data set for Africa. The rest of the data set has been used to interpolate the gravity values at the gap points; then a comparison between the interpolated and the actual data values at the artificial data gap has been carried-out to determine the accuracy of the used interpolation technique. The unequal weight least-squares prediction (with the optimum curvature parameter at the origin) with an underlying grid at the gap areas computed by the satellite-only GO CONS GCF 2 DIR R5 model till degree and order 300, has been proposed as the developed interpolation approach. For comparison purpose, the Kriging interpolation technique has also been tested. Both the classical residual terrain modeling reduction and the window technique, suggested earlier by the authors to get rid of the double consideration of the topographic-isostatic masses within the data window in the framework of the remove-restore technique, have been used for the reduction process. A comparison between the data and interpolated values of the gravity at the gap points has been carried out. The results show that the developed interpolation technique gives better interpolation accuracy at the artificial data gap.

Prediction when fitting simple models to high-dimensional data

We study linear subset regression in the context of a high-dimensional linear model. Consider $y=\vartheta +\theta 'z+\epsilon $ with univariate response $y$ and a $d$-vector of random regressors $z$, and a submodel where $y$ is regressed on a set of $p$ explanatory variables that are given by $x=M'z$, for some $d\times p$ matrix $M$. Here, “high-dimensional” means that the number $d$ of available explanatory variables in the overall model is much larger than the number $p$ of variables in the submodel. In this paper, we present Pinsker-type results for prediction of $y$ given $x$. In particular, we show that the mean squared prediction error of the best linear predictor of $y$ given $x$ is close to the mean squared prediction error of the corresponding Bayes predictor $\mathbb{E}[y\|x]$, provided only that $p/\log d$ is small. We also show that the mean squared prediction error of the (feasible) least-squares predictor computed from $n$ independent observations of $(y,x)$ is close to that of the Bayes predictor, provided only that both $p/\log d$ and $p/n$ are small. Our results hold uniformly in the regression parameters and over large collections of distributions for the design variables $z$.

FTIR-PAS coupled to partial least squares for prediction of ash content, volatile matter, fixed carbon and calorific value of coal

Fourier Transform Infrared Photoacoustic Spectroscopy (FT-IR PAS) and multivariate calibration using partial least squares (PLS) has been coupled for the development of predictive models of ash content, volatile matter, fixed carbon and calorific value of coal samples from several mines of Colombia. In the chemometric approach, a novel alternative is proposed to define the complexity and the selection of the models. According to tests and statistical criteria, at a 95% confidence level, the selected models demonstrate their linear character and a true correlation between the reference values and the predicted values. Results provide standard error of cross-validation (SECV) of 1.22 wt%, 0.78 wt%, 1.08 wt% and 0.75 MJ kg−1 predicting ash, volatile matter (VM), fixed carbon (FC) and calorific value, respectively.

Lossless hyperspectral image compression using bimodal conventional recursive least-squares

ABSTRACTHyperspectral image compression is an important task, where the aim is to store or transmit data in an efficient way. Hyperspectral images are mostly captured by a sensor system that includes multiple imaging sensors covering different regions of the electromagnetic spectrum. Misalignment of multiple imaging sensors produces boresight effect, and this problem can degrade band prediction performance noticeably. Another problem is prediction of blurry band images. In order to gain robustness to these problems, bimodal conventional recursive least-squares (B-CRLS) prediction method is proposed for the lossless compression of hyperspectral images. Two prediction modes are defined: spectral and spatio-spectral. B-CRLS method has a two-step process. First, mode selection is carried out for each band. Afterwards, final band image is predicted by using the selected mode, and the residual images are encoded with an arithmetic encoder. The proposed method is compared to adaptive-length CRLS, fixed-length CRLS, and other well-known prediction methods. Experiments have been performed on uncalibrated and calibrated hyperspectral images. Obtained results show that the proposed method achieves competitive compression performance with the state-of-the-art while providing relatively lower-computation times.

A method to improve HEVC lossless coding of volumetric medical images

Medical imaging technology and applications are continuously evolving, dealing with images of increasing spatial and temporal resolutions, which enable more accurate processing, feature analysis and medical diagnosis. However, the increase in resolution also requires a growing amount of data to be stored, processed and exchanged or transmitted through networks. Despite the high coding efficiency achieved by the most recent image and video coding standards in lossy compression, they are not well suited for quality-critical medical image compression where either near-lossless or lossless coding is required. In this paper we propose a method to improve lossless coding of volumetric medical images, such as Magnetic Resonance and Computed Tomography, and medical sequences such as X-ray Angiography images, using the latest standard High Efficiency Video Encoder (HEVC). New pixel-wise prediction techniques are proposed to extend the current HEVC lossless tools, based on Least-Squares Prediction (LSP). Experimental results show a bitrate reduction of over 44%, when compared to DICOM recommended encoders, and 13.8% when compared to standard lossless HEVC, for 8 bpp volumetric images, and over 8% and 4.6%, respectively, for volumetric images using more than 8 bpp.

Heterogeneous Gravity Data Fusion and Gravimetric Quasigeoid Computation in the Coastal Area of China

ABSTRACTDifferent types of gravity observations are available over coastal areas. The main challenge for coastal geoid determination is the proper fusion of heterogeneous gravity data including land, shipborne, airborne, and altimetry-derived gravity data. This paper describes the gravity data fusion and the computation of the gravimetric quasigeoid in the coastal area of mainland China. An iterative procedure of the weighted least-squares prediction based on rectangular harmonic functions is used for merging the land, altimetric, shipborne, and airborne gravity data. Applying the analytical continuation method in Molodensky's theoretic frame, the merged gravity data are then used to determine the gravimetric quasigeoid model by using the generalized Stokes' integral in a remove-compute-restore fashion. The gravimetric quasigeoid model is compared with the height anomalies determined at 662 GPS leveling points over the coastal region of mainland China, where both the geodetic height and the normal height are known. The standard deviations of the differences in the coastal provinces range from 1.8 to 4.4 cm. For the entire computation area, the mean and standard deviation of the differences are 27.9 and 3.9 cm, respectively.

Expected predictive least squares for model selection in covariance structures

Predictive least squares (PLS) using future data to be predicted by current data are defined in covariance structure analysis. The expected predictive least squares (EPLS) obtained by two-fold expectation of PLS are unknown fit indexes. Using the asymptotic biases of weighted least squares given by current data for estimation of EPLS in covariance structures, corrected least square criteria derived similarly to the Takeuchi information criterion are shown to be asymptotically unbiased under arbitrary distributions. Simulations for model selection in exploratory factor analysis show improvements over typical current fit indexes as RMSEA and AIC.

Fast algorithm for least‐squares based image prediction

A new computationally efficient algorithm for two-dimensional sliding-window least-squares prediction is presented in this study. The fast algorithm is based on a recursive update of the Cholesky decomposition. Compared with the state-of-the-art algorithm, the proposed algorithm reduces the computational complexity from O(D3) to O(D2h), where D is the predictor order and h is the height of the prediction patch. The computational improvement is made at the stage of solving the normal equations for which an update algorithm for the Cholesky decomposition of the covariance matrix is proposed. It is shown that a large part of the Cholesky decomposition at location n can be efficiently calculated by performing orthonormal updates on the Cholesky decomposition at n − 1. The computational improvement is made without requiring additional storage space. Extensive experiments using causal and non-causal predictors of varying shapes and sizes have confirmed that the proposed algorithm is consistently faster than the state-of-the-art algorithm and produces identical prediction images. The efficiency of the proposed algorithm is shown to be affected by the order in which pixels are sampled, thus an ordering procedure is proposed to minimise the number of numerical operations.

Lossless compression of hyperspectral images using conventional recursive least-squares predictor with adaptive prediction bands

An efficient lossless compression scheme for hyperspectral images using conventional recursive least-squares (CRLS) predictor with adaptive prediction bands is proposed. The proposed scheme first calculates the preliminary estimates to form the input vector of the CRLS predictor. Then the number of bands used in prediction is adaptively selected by an exhaustive search for the number that minimizes the prediction residual. Finally, after prediction, the prediction residuals are sent to an adaptive arithmetic coder. Experiments on the newer airborne visible/infrared imaging spectrometer (AVIRIS) images in the consultative committee for space data systems (CCSDS) test set show that the proposed scheme yields an average compression performance of 3.29 (bits/pixel) , 5.57 (bits/pixel) , and 2.44 (bits/pixel) on the 16-bit calibrated images, the 16-bit uncalibrated images, and the 12-bit uncalibrated images, respectively. Experimental results demonstrate that the proposed scheme obtains compression results very close to clustered differential pulse code modulation-with-adaptive-prediction-length, which achieves best lossless compression performance for AVIRIS images in the CCSDS test set, and outperforms other current state-of-the-art schemes with relatively low computation complexity.

An extremum-seeking control approach for observer design

Abstract: In this study, we propose to circumvent the difficulties associated with the computation of the observer gain for nonlinear systems by using an extremum-seeking control approach to generate optimal observer gains for a general class of nonlinear systems. This paper proposes a proportional-integral extremum-seeking control (PIESC) technique for the design of nonlinear observers. The PIESC technique is a generalization of the standard perturbation based techniques that provides fast transient performance of the closed-loop system to the optimum equilibrium of a measured objective function. In this application of PIESC, the gain of the nonlinear observer is computed in real-time to minimize the least-squares output prediction error. Two examples are used to demonstrate the effectiveness of this technique.

Comparing the artificial neural network with parcial least squares for prediction of soil organic carbon and pH at different moisture content levels using visible and near-infrared spectroscopy

Visible and near infrared (vis-NIR) spectroscopy is widely used to detect soil properties. The objective of this study is to evaluate the combined effect of moisture content (MC) and the modeling algorithm on prediction of soil organic carbon (SOC) and pH. Partial least squares (PLS) and the Artificial neural network (ANN) for modeling of SOC and pH at different MC levels were compared in terms of efficiency in prediction of regression. A total of 270 soil samples were used. Before spectral measurement, dry soil samples were weighed to determine the amount of water to be added by weight to achieve the specified gravimetric MC levels of 5, 10, 15, 20, and 25 %. A fiber-optic vis-NIR spectrophotometer (350-2500 nm) was used to measure spectra of soil samples in the diffuse reflectance mode. Spectra preprocessing and PLS regression were carried using Unscrambler® software. Statistica® software was used for ANN modeling. The best prediction result for SOC was obtained using the ANN (RMSEP = 0.82 % and RPD = 4.23) for soil samples with 25 % MC. The best prediction results for pH were obtained with PLS for dry soil samples (RMSEP = 0.65 % and RPD = 1.68) and soil samples with 10 % MC (RMSEP = 0.61 % and RPD = 1.71). Whereas the ANN showed better performance for SOC prediction at all MC levels, PLS showed better predictive accuracy of pH at all MC levels except for 25 % MC. Therefore, based on the data set used in the current study, the ANN is recommended for the analyses of SOC at all MC levels, whereas PLS is recommended for the analysis of pH at MC levels below 20 %.

A scaling law for form drag coefficients in incompressible turbulent flows

We present a similarity law for form drag coefficients, which is obtained by a judicious utilization of an energy dissipation equation due to eddy viscosity for incompressible turbulent flow, the steady-state κ–ω turbulence model, and the Kolmogorov turbulence dissipation length scales. It is shown that the form drag coefficients of three geometrically similar vessels subjected to turbulent flows are scaled according to C¯p={c1+c2Re¯−1/3+c3Re¯−1} where (C¯p,Re¯,ci(i=1,2,3)) are the form drag coefficient ratio, the mean flow Reynolds number ratio, and ci are closure coefficients to be determined from existing geometrically similar vessels, respectively. The present theoretical form factor methodology is applied to predict the full scale form factor from the scaled towing tank experiment based on three simulation results, which show improved correlations compared to the empirical least-squares prediction methods.