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Missing data are very common in environmental monitoring activities. Traditional interpolation methods often view the problem from either spatial or temporal perspective and do not make good use of valuable related information, thereby leading to low prediction accuracy. Although many hybrid spatiotemporal interpolation methods combine temporal interpolation methods with spatial interpolation methods and show superiority over other single temporal or spatial interpolation methods, they do not finely treat each missing value in terms of its specific features. In this paper, two dynamic spatiotemporal interpolation (DST) methods, coarse-grained DST (CGDST) and fine-grained DST (FGDST) are proposed by using both temporal and spatial interpolation results. Different from other hybrid spatiotemporal interpolation methods, they create differences in the contribution of temporal and spatial interpolation results and assign them with different weights. Both CGDST and FGDST treat each missing value differently and fill it by considering the reliability of both temporal and spatial interpolation results in terms of the lengths of its column gap and row gap. CGDST treats each missing value in a continuous missing area equally and all missing values have the same lengths of column and row gaps. FGDST goes beyond CGDST and treats each missing value differently based on its temporal distance to the nearest real observed values in both forward and backward directions. To demonstrate their superiority, the experimental datasets were generated randomly to simulate missing values in real life. The results of the extensive experiments showed that FGDST improved by 2.44% ∼ 8.21% in terms of symmetric mean absolute percentage error (SMAPE) compared with the best baseline method. Compared with CGDST, the improvements of FGDST range from 1.05% to 2.87% in terms of SMAPE. Moreover, their superiority is more obvious if there are more continuous missing values in the temporal dimension. [ABSTRACT FROM AUTHOR]

This paper presents a control-based trajectory generation approach for unmanned aerial vehicles (UAVs) under dynamic constraints. It exploits the concept of optimal control to find closed-form differential equations that satisfy any arbitrary dynamic limitation mapped into kinematic constraints. Pontryagin’s Minimum Principle applies to derive a set of differential equations in which the dynamic environment is considered in the constrained Hamiltonian function. In particular, we aim to minimize the L2-norm of the control input avoiding dynamic obstacles, given initial and final boundary conditions. Lastly, this paper proposes a novel interpolation algorithm based on rational functions, referred to as rational recursive smooth trajectory (RRST) method. The method generates an analytic expression that approximates the control inputs, for which no closed-form solutions are in general attainable.

The sea surface height data volume of the future wide-swath two-dimensional (2D) altimetric satellite is thousands of times greater than that of nadir altimetric satellites. The time complexity of the 2D altimetry mapping reaches O(n3). It is challenging to map the global grid products of future 2D altimetric satellites. In this study, to improve the efficiency of global data mapping, a new algorithm called parallel-dynamic interpolation (PA-DI) was designed. Through the use of 2D data segmentation and fine-grained data mosaic methods, the parallel along-track DI processes were accelerated, and a fast and efficient spatial-temporal high-resolution and low-error enhanced mapping method was obtained. As determined from a comparison of the single-threaded DI with the PA-DI, the new algorithm optimized the time complexity from O(n3) to O(n3/KL), which improved the mapping efficiency and achieved the expected results. According to the test results of the observing system simulation experiments, the PA-DI algorithm may provide an efficient and reliable method for future wide-swath 2D altimetric satellite mapping. [ABSTRACT FROM AUTHOR]

In modern agriculture, many advanced automated devices are used on farms. To improve the working effi- ciency of agricultural vehicles, fields are expected to be pre-leveled, because the vehicles work more effectively on a flat field. Leveling a field requires the current field elevation map. Some farmers in Japan have begun to use high-precision real-time kinematic Global Positioning System (RTK-GPS)-based self-steering tractors in the fields. This study uses the RTK-GPS information from a self-steering tractor system to generate a digital elevation model (DEM) especially in mountain regions where the fields are not flat. In addition, all of the information is from the self-steering system with the result that farmers can use the method of this study without additional instruments. However, the GPS receiver sometimes cannot obtain high-quality signals from satellites in mountain regions. Therefore, this study focuses on how to create a high-precision DEM even when a GPS signal is unavailable. It proposes a dynamic interpolation method for generating a DEM. In addition, a test was conducted in a field in a mountain region. The test results show that the dynamic interpolation method can provide an accuracy of less than 0.03 m in the test field for creating a DEM. [ABSTRACT FROM AUTHOR]

As raw sensory data are partial, our visual system extensively fills in missing details, creating enriched percepts based on incomplete bottom-up information. Despite evidence for internally generated representations at early stages of cortical processing, it is not known whether these representations include missing information of dynamically transforming objects. Long-range apparent motion (AM) provides a unique test case because objects in AM can undergo changes both in position and in features. Using fMRI and encoding methods, we found that the "intermediate" orientation of an apparently rotating grating, never presented in the retinal input but interpolated during AM, is reconstructed in population-level, feature-selective tuning responses in the region of early visual cortex (V1) that corresponds to the retinotopic location of the AM path. This neural representation is absent when AM inducers are presented simultaneously and when AM is visually imagined. Our results demonstrate dynamic filling-in in V1 for object features that are interpolated during kinetic transformations. [ABSTRACT FROM AUTHOR]

The behavioral system theory and in particular a result that became known as the "fundamental lemma" give the theoretical foundation for nonparametric representations of linear time-invariant systems based on Hankel matrices constructed from data. These "data-driven" representations led in turn to new system identification, signal processing, and control methods. This paper shows how the approach can be used further on for solving interpolation, extrapolation, and smoothing problems. The solution proposed and the resulting method are general – can deal simultaneously with missing, exact, and noisy data of multivariable systems – and simple—require only the solution of a linear system of equations. In the case of exact data, we provide conditions for existence and uniqueness of solution. In the case of noisy data, we propose an approximation procedure based on ℓ 1 -norm regularization and validate its performance on real-life datasets. The results have application in missing data estimation and trajectory planning. They open a practical computational way of doing system theory and signal processing directly from data without identification of a transfer function or state-space system representation. [ABSTRACT FROM AUTHOR]

Background: Particle tracking passive microrheology relates recorded trajectories of microbeads, embedded in soft samples, to the local mechanical properties of the sample. The method requires intensive numerical data processing and tools allowing control of the calculation errors. Results: We report the development of a software package collecting functions and scripts written in Python for automated and manual data processing, to extract viscoelastic information about the sample using recorded particle trajectories. The resulting program package analyzes the fundamental diffusion characteristics of particle trajectories and calculates the frequency dependent complex shear modulus using methods published in the literature. In order to increase conversion accuracy, segmentwise, double step, range-adaptive fitting and dynamic sampling algorithms are introduced to interpolate the data in a splinelike manner. Conclusions: The presented set of algorithms allows for flexible data processing for particle tracking microrheology. The package presents improved algorithms for mean square displacement estimation, controlling effects of frame loss during recording, and a novel numerical conversion method using segmentwise interpolation, decreasing the conversion error from about 100% to the order of 1%. [ABSTRACT FROM AUTHOR]

This paper investigates a variety of statistical cache-based language models built upon three corpora: English, Lithuanian, and Lithuanian base forms. The impact of the cache size, type of the decay function, including custom corpus derived functions, and interpolation technique (static vs. dynamic) on the perplexity of a language model is studied. The best results are achieved by models consisting of 3 components: standard 3-gram, decaying cache 1-gram and decaying cache 2-gram that are joined together by means of linear interpolation using the technique of dynamic weight update. Such a model led up to 36% and 43% perplexity improvement with respect to the 3-gram baseline for Lithuanian words and Lithuanian word base forms respectively. The best language model of English led up to a 16% perplexity improvement. This suggests that cache-based modeling is of greater utility for the free word order highly inflected languages. [ABSTRACT FROM AUTHOR]

The authors present the implementation and validation of a novel machine tool control mechanism called 3-Dimensional Dynamic Interpolation. The approach, which was described in a previous paper (Oldknow and Yellowley, Int. J. Mach. Tools Manufact., 42 (2003) 1627), allows for the real-time manipulation of the nominal reference trajectory in three orthogonal directions in response to both process and system dynamics. This paper discusses results from the experimental validation of the approach using a Field-Programmable Gate Array based controller and two-axis test stand. [Copyright &y& Elsevier]

Abstract Background Particle tracking passive microrheology relates recorded trajectories of microbeads, embedded in soft samples, to the local mechanical properties of the sample. The method requires intensive numerical data processing and tools allowing control of the calculation errors. Results We report the development of a software package collecting functions and scripts written in Python for automated and manual data processing, to extract viscoelastic information about the sample using recorded particle trajectories. The resulting program package analyzes the fundamental diffusion characteristics of particle trajectories and calculates the frequency dependent complex shear modulus using methods published in the literature. In order to increase conversion accuracy, segmentwise, double step, range-adaptive fitting and dynamic sampling algorithms are introduced to interpolate the data in a splinelike manner. Conclusions The presented set of algorithms allows for flexible data processing for particle tracking microrheology. The package presents improved algorithms for mean square displacement estimation, controlling effects of frame loss during recording, and a novel numerical conversion method using segmentwise interpolation, decreasing the conversion error from about 100% to the order of 1%.

This article presents the dynamic interpolation problem for locomotion systems evolving on a trivial principal bundle Q. Given an ordered set of points in Q , we wish to generate a trajectory which passes through these points by synthesizing suitable controls. The global product structure of the trivial bundle is used to obtain an induced Riemannian product metric on Q. The squared L 2 -norm of the covariant acceleration is considered as the cost function, and its first order variations are taken for generating the trajectories. The nonholonomic constraint is enforced through the local form of the principal connection and the group symmetry is employed for reduction. The explicit form of the Riemannian connection for the trivial bundle is employed to arrive at the extremal of the cost function. The result is applied to generate a trajectory for the generalized Purcell's swimmer - a low Reynolds number microswimming mechanism. [ABSTRACT FROM AUTHOR]