A Multivariate Complexity Analysis of Qualitative Reasoning Problems

Qualitative reasoning is an important subfield of artificial intelligence where one describes relationships with qualitative, rather than numerical, relations. Many such reasoning tasks, e.g., Allen's interval algebra, can be solved in $2^{O(n \cdot \log n)}$ time, but single-exponential running times $2^{O(n)}$ are currently far out of reach. In this paper we consider single-exponential algorithms via a multivariate analysis consisting of a fine-grained parameter $n$ (e.g., the number of variables) and a coarse-grained parameter $k$ expected to be relatively small. We introduce the classes FPE and XE of problems solvable in $f(k) \cdot 2^{O(n)}$, respectively $f(k)^n$, time, and prove several fundamental properties of these classes. We proceed by studying temporal reasoning problems and (1) show that the Partially Ordered Time problem of effective width $k$ is solvable in $16^{kn}$ time and is thus included in XE, and (2) that the network consistency problem for Allen's interval algebra with no interval overlapping with more than $k$ others is solvable in $(2nk)^{2k} \cdot 2^{n}$ time and is included in FPE. Our multivariate approach is in no way limited to these to specific problems and may be a generally useful approach for obtaining single-exponential algorithms

Investigation of a Hybrid Algorithm for Sea Ice Drift Measurements Using Synthetic Aperture Radar Images

Areal matching by phase correlation and feature tracking are two complementary methods used to measure sea ice drift between synthetic aperture radar images. This paper evaluates a new algorithm that combines the two methods. Areal matching is improved by new methods to handle large motions and rotated ice. It is shown that areal rotation can be resolved using a frequency-domain approach. Image segmentation is a prerequisite for feature tracking and achieved by a new method that performs better than Otsu's method for two-component Gaussian mixture distributions. A circular weighted median filter is found to be suitable for the filtering of the motion field. The algorithm is evaluated through a thorough analysis of the response and sensitivity to various algorithm settings. The accuracy of the algorithm varies by up to 50% for one image pair within the studied range of parameter settings, thus indicating the need for a proper initialization of the algorithm

Efficiency of a voluntary speed reduction algorithm for a ship’s great circle sailing

The great-circle is the shortest distance between two points on the surface of the earth. When planning a ship’s sailing route (waypoints and forward speeds) for a specific voyage, the great circle route is commonly considered as a reference route, especially for ocean-crossing seaborne transport. During the planning process, the upcoming sea weather condition is one of the most important factors affecting the ship’s route optimization/planning results. To avoid encountering harsh conditions, conventional routing optimization algorithms, such as Isochrone method and Dynamic Programming method, have been developed/implemented to schedule a ship’s optimal routes by selecting waypoints around the great circle reference route based on the ship’s operational performances at sea. Due to large uncertainties in sea weather forecast that used as inputs of these optimization algorithms, the optimized routes may have worse performances than the traditional great circle sailing. In addition, some shipping companies are still sailing in or making charting contracts based on the great circle routes. Therefore, in this study, a new optimization algorithm is proposed to consider the voluntary speed reduction with optimal speed configuration along the great circle course. The efficiency of this method is investigated by comparing these two methods for optimal route planning with respect to ETA and minimum fuel consumption. A container ship sailing in the North Atlantic with full-scale performance measurements are employed as the case study vessels for the comparison

Benchmark study of five optimization algorithms for weather routing

Safety and energy efficiency are two of the key issues in the maritime transport community. A sail plan system, which combines the concepts of weather routing and voyage optimization, are recognized by the shipping industry as an efficient measure to ensure a ship’s safety, gain more economic benefit, and reduce negative effects on our environment. In such a system, the key component is to develop a proper optimization algorithm to generate potential ship routes between a ship’s departure and destination. In the weather routing market, four routing optimization algorithms are commonly used. They are the so-called modified Isochrone and Isopone methods, dynamic programming, three dimensional dynamic programming, and Dijkstra’s algorithm, respectively. Each optimization algorithm has its own advantages and disadvantages to estimate a ship routing with shortest sailing time or/and minimum fuel consumption. This paper will present a benchmark study that compares these algorithms for routing optimization aiming at minimum fuel consumption. A merchant ship sailing in the North Atlantic with full-scale performance measurements are employed as the case study vessels for the comparison. The ship’s speed/power performance is based on the ISO2015 methods combined with the measurement data. It is expected to demonstrate the pros and cons of different algorithms for the ship’s sail planning

Direct comparison of sea surface velocity estimated from Sentinel-1 and TanDEM-X SAR data

This paper presents the first direct comparison of the sea surface radial velocity (RVL) derived from the two satellite SAR systems Sentinel-1 and TanDEM-X, operating at different frequencies and imaging modes. The RVL is derived from the Doppler centroid (Dc) provided in the Sentinel-1 OCN product and from the along-track interferometric phase of the TanDEM-X. The comparison is carried out using opportunistic acquisitions, collocated in space and time, over three different sites. First, it is observed that the RVL derived from both satellites is biased, thus calibration is applied using the land as a reference. The comparison shows that the correlation and the mean RVL bias between the two datasets depend on the differences in acquisition time, incidence angle and azimuth angle, and on wind and current speed and direction. It is found that, given a time difference of < 20 min, the spatial correlation coefficient is relatively high (between 0.7 and 0.93), which indicates that the two SAR systems observe similar sea surface current fields. The spatial correlation degrades primarily due to increasing time difference and decreasing current magnitudes. The mean RVL bias increases primarily with the radial wind speed, which suggests that the RVL bias is mainly due to the wave-induced Doppler shift. This study shows that under certain conditions, i.e. similar acquisition geometry and short time delay, a good agreement between the two independently derived RVL is achieved. This encourages a synergistic use of the sea surface velocity estimated from different C- and X-band SAR systems

X-Band Interferometric SAR Observations of Baltic Fast Ice

Detailed mapping of fast-ice deformation can be used to characterize the rheological behavior of fast ice and subsequently improve sea ice modeling. This study uses interferometric synthetic aperture radar to map fast-ice deformation with unprecedented spatial resolution (meter range) and sensitivity (cm-mm range). Two interferometric acquisitions, each with a temporal baseline of 24 h, were performed by the X-band SAR satellite constellation Cosmo-SkyMed over the northeast Bay of Bothnia in the middle of the 2012 ice season. The first interferogram shows deformation of the fast ice due to force from impinging drift ice, and the normal strain within the fast ice is measured. Complementary intensity correlation measurements reveal a slow movement of the drift ice toward the fast ice. The second interferogram exhibits a low fringe rate over the fast ice with fringes being aligned along the coastline. Deformation appears to be stronger around leads, skerries, and grounded ice ridges. It is also observed that the coherence images provide information that is complementary to the information in the backscatter images

Sensitivity of radar altimeterwaveform to changes in sea ice type at resolution of synthetic aperture radar

Radar altimetry in the context of sea ice has mostly been exploited to retrieve basin-scale information about sea ice thickness. In this paper, we investigate the sensitivity of altimetric waveforms to small-scale changes (a few hundred meters to about 10 km) of the sea ice surface. Near-coincidental synthetic aperture radar (SAR) imagery and CryoSat-2 altimetric data in the Beaufort Sea are used to identify and study the spatial evolution of altimeter waveforms over these features. Open water and thin ice features are easily identified because of their high peak power waveforms. Thicker ice features such as ridges and multiyear ice floes of a few hundred meters cause a response in the waveform. However, these changes are not reflected in freeboard estimates. Retrieval of robust freeboard estimates requires homogeneous floes in the order of 10 km along-track and a few kilometers to both sides across-track. We conclude that the combination of SAR imagery and altimeter data could improve the local sea ice picture by extending spatially scarce freeboard estimates to regions of similar SAR signature

Measurements of Sea Surface Currents in the Baltic Sea Region Using Spaceborne Along-Track InSAR

The main challenging problems in ocean current retrieval from along-track interferometric (ATI)-synthetic aperture radar (SAR) are phase calibration and wave bias removal. In this paper, a method based on differential InSAR (DInSAR) technique for correcting the phase offset and its variation is proposed. The wave bias removal is assessed using two different Doppler models and two different wind sources. In addition to the wind provided by an atmospheric model, the wind speed used for wave correction in this work is extracted from the calibrated SAR backscatter. This demonstrates that current retrieval from ATI-SAR can be completed independently of atmospheric models. The retrieved currents, from four TanDEM-X (TDX) acquisitions over the 6resund channel in the Baltic Sea, are compared to a regional ocean circulation model. It is shown that by applying the proposed phase correction and wave bias removal, a good agreement in spatial variation and current direction is achieved. The residual bias, between the ocean model and the current retrievals, varies between 0.013 and 0.3 m/s depending on the Doppler model and wind source used for wave correction. This paper shows that using SAR as a source of wind speed reduces the bias and root-mean-squared-error (RMSE) of the retrieved currents by 20% and 15%, respectively. Finally, the sensitivity of the sea current retrieval to Doppler model and wind errors are discussed

Empirical Relationship Between the Doppler Centroid Derived From X-Band Spaceborne InSAR Data and Wind Vectors

One of the challenges in ocean surface current retrieval from synthetic aperture radar (SAR) data is the estimation and removal of the wave-induced Doppler centroid (DC). This article demonstrates empirically the relationship between the dc derived from spaceborne X-band InSAR data and the ocean surface wind and waves. In this study, we analyzed over 300 TanDEM-X image pairs. It is found that the general characteristics of the estimated dc follow the theoretically expected variation with incidence angle, wind speed, and wind direction. An empirical geophysical model function (GMF) is fit to the estimated dc and compared to existing models and previous experiments. Our GMF is in good agreement (within 0.2 m/s) with other models and data sets. It is found that the wind-induced Doppler velocity contributes to the total Doppler velocity with about 15% of the radial wind speed. This is much larger than the sum of the contributions from the Bragg waves (~0.2 m/s) and the wind-induced drift current (~3% of wind speed). This indicates a significant (dominant) contribution of the long wind waves to the SAR dc. Moreover, analysis of dual-polarized data shows that the backscatter polarization ratio (PR=σ⁰VV/σ⁰HH) and the dc polarization difference (PD=|dcVV|-|dcHH|) are systematically larger than 1 and smaller than 0 Hz, respectively, and both increase in magnitude with incidence angle. The estimated PR and PD are compared to other theoretical and empirical models. The Bragg scattering theory-based (pure Bragg and composite surface) models overestimate both PR and PD, suggesting that other scattering mechanisms, e.g., wave breaking, are involved. In general, it is found that empirical models are more consistent with both backscatter and Doppler data than theory-based models. This motivates a further improvement of SAR dc GMFs