Sequential Least-squares Method Research Articles

Time-Series InSAR Dynamic Analysis With Robust Sequential Adjustment

Nowadays, SAR instruments such as ESA’s Sentinel-1 constellation, ICEYE’s constellation of small and agile radar satellites, and the upcoming ALOS-4 and NASA/ISRO SAR missions provide new opportunities for near-real-time monitoring of geohazards with enhanced spatiotemporal resolution. Sequential dynamic adjustment model is regarded as an effective way to rapidly update time-series InSAR measurements. However, the accuracy of geophysical parameters of interest estimated from the conventional sequential least squares is greatly sensitive to the anomalous observations and/or anomalous prior parameter information. This letter aims to introduce the robust sequential adjustment method based on the M-estimation principle into near-real-time InSAR deformation monitoring to mitigate the effect of anomalous errors. Using both synthetic and real Sentinel-1 SAR datasets over Echigo plain in Japan, we fully evaluate the performance of the robust sequential estimation approach with respect to unwrapping errors in the SAR data stack. Measurements at 9 GPS stations located in the study area are used to validate the results. We find that the averaged RMSE of robust sequential adjustment is reduced by 15% in comparison with that of the conventional sequential least-squares method.

Noisy Beam Alignment Techniques for Reciprocal MIMO Channels

Future multi-input multi-output (MIMO) wireless communications systems will use beamforming as a first-step towards realizing the capacity requirements necessitated by the exponential increase in data demands. The focus of this work is on beam alignment for time-division duplexing (TDD) systems, for which we propose a number of novel algorithms. These algorithms seek to obtain good estimates of the optimal beamformer/combiner pair (which are the dominant singular vectors of the channel matrix). They are motivated by the power method, an iterative algorithm to determine eigenvalues and eigenvectors through repeated matrix multiplication. In contrast to the basic power method which considers only the most recent iteration and assumes noiseless links, the proposed techniques consider information from all the previous iterations of the algorithm and combine them in different ways. The first technique (Sequential Least-Squares method) sequentially constructs a least-squares estimate of the channel matrix, which is then used to calculate the beamformer/combiner pair estimate. The second technique (Summed Power method) aims to mitigate the effect of noise by using a linear combination of the previously tried beams to calculate the next beam, providing improved performance in the low-SNR regime (typical for mmWave systems) with minimal complexity/feedback overhead. A third technique (Least-Squares Initialized Summed Power method) combines the good performance of the first technique at the high-SNR regime with the low-complexity advantage of the second technique by priming the summed power method with initial estimates from the sequential method.

0247 NEUROCOGNITIVE REHABILITATION –A FOUR-CASE PILOT STUDY

With the advent of probing systems and their integration with machining centers, coordinate metrology-based datum establishment is eliminating the need for precision hard-contact locators in many machining applications. Unfortunately, the coordinate data collected by these systems are often subject to noise in the form of random and biased errors of the workpiece datum features and measurement system. Consequently it is important to use datum-establishment algorithms that are insensitive to noise and that lead to the least measurable machined-feature error.This paper describes a simulation analysis that was carried out to evaluate the performance of three datum-establishment methods: 3–2–1, sequential least-squares (SQLS) and simultaneous least-squares (SMLS). The analysis involved the simulated drilling of three holes in a two set-up process. Simulated coordinate data were obtained from three planar, nominally orthogonal surfaces subject to perpendicularity errors and random roughness errors. Workpiece datum reference frames were fitted to this data using the three methods, the holes were drilled relative to these reference frames, and their position errors were computed relative to an ANSI-Y14.5M-defined reference frame.This analysis demonstrated that the SMLS method results in significantly less hole-position error [0.0173 mm average, 0.0146 mm standard deviation (SD)] than either the 3–2–1 method (0.0943 mm average, 0.0143 mm SD) or the SQLS method (0.0904 mm average, 0.0245 mm SD). This is despite the fact that the datum reference planes (ANSI Y14.5M) used to define these errors are defined sequentially relative to the extrema of the datum features, whereas the SMLS method defines the datum reference planes simultaneously with the purpose of minimizing fitting error.

A New Approach to Sequential Tidal Prediction

Accurate tide prediction is required for safe marine navigation in shallow waters as well as for other marine operations. Traditionally, tide prediction was carried out using the harmonic method, which is based on the identification of the harmonic tidal constituents existing in the tidal record. Unfortunately, however, unless long tidal records are available at the tide gauges, some important tidal constituents may not be identified. This, in turn, deteriorates the accuracy of the tidal prediction. More recently, a sequential least-squares prediction method capable of using relatively short tidal records was developed. This method allows for the modifications and corrections of the original solution of the tidal constituents when new observations and parameters are included. Although it reduces the computation time significantly compared to the batch harmonic method, this method exhibits large residuals particularly when very short tidal records are used. To overcome the limitations of the sequential least-squares method, a neural network-based model is developed for sequentially predicting the tidal heights using tide data series collected at various tide gauges. A modular, three-layer feedforward neural network trained using the back-propagation algorithm is used for this purpose. Tide data from three tide gauges are used to validate the model. A comparison is made between the developed neural network model and the sequential least squares method for tidal prediction. It is shown that the accuracy level of the tidal prediction has improved by a factor of 5 when using the neural network model.

An analysis of the effect of datum-establishment methods on the geometric errors of machined features

With the advent of probing systems and their integration with machining centers, coordinate metrology-based datum establishment is eliminating the need for precision hard-contact locators in many machining applications. Unfortunately, the coordinate data collected by these systems are often subject to noise in the form of random and biased errors of the workpiece datum features and measurement system. Consequently it is important to use datum-establishment algorithms that are insensitive to noise and that lead to the least measurable machined-feature error. This paper describes a simulation analysis that was carried out to evaluate the performance of three datum-establishment methods: 3–2–1, sequential least-squares (SQLS) and simultaneous least-squares (SMLS). The analysis involved the simulated drilling of three holes in a two set-up process. Simulated coordinate data were obtained from three planar, nominally orthogonal surfaces subject to perpendicularity errors and random roughness errors. Workpiece datum reference frames were fitted to this data using the three methods, the holes were drilled relative to these reference frames, and their position errors were computed relative to an ANSI-Y14.5M-defined reference frame. This analysis demonstrated that the SMLS method results in significantly less hole-position error [0.0173 mm average, 0.0146 mm standard deviation (SD)] than either the 3–2–1 method (0.0943 mm average, 0.0143 mm SD) or the SQLS method (0.0904 mm average, 0.0245 mm SD). This is despite the fact that the datum reference planes (ANSI Y14.5M) used to define these errors are defined sequentially relative to the extrema of the datum features, whereas the SMLS method defines the datum reference planes simultaneously with the purpose of minimizing fitting error.

Identification of Coulomb and Viscous Friction in Robot Drives: An Experimental Comparison of Methods

This paper presents an experimental comparison of five methods of identifying friction in robot drives. The methods considered are direct plotting of velocity versus armature voltage, plotting velocity versus armature current, third harmonic estimation, batch least squares and sequential least squares. These methods were implemented on a d.c. servo motor robot drive system to identify Coulomb and viscous friction parameters. It is shown that an asymmetric Coulomb and viscous model properly identifies the frictional torque due to the combined sliding and rolling friction in the motor. Furthermore, although each of the identification methods is shown to be capable of giving reasonable estimates of the frictional coefficients, the plotting of velocity versus armature current is shown to be most suitable for off-line frictional identification and the sequential least-squares method most suitable for on-line identification, particularly when coefficients may change with time.