Flight Track Research Articles

TrackMatcher – a tool for finding intercepts in tracks of geographical positions

Abstract. Working with measurement data in atmospheric science often necessitates the co-location of observations from instruments or platforms at different locations with different geographical and/or temporal data coverage. The varying complexity and abundance of the different data sets demand a consolidation of the observations. This paper presents a tool for (i) finding temporally and spatially resolved intersections between two- or three-dimensional geographical tracks (trajectories) and (ii) extracting observations and other derived parameters in the vicinity of intersections to achieve the optimal combination of various data sets and measurement techniques. The TrackMatcher tool has been designed specifically for matching height-resolved remote sensing observations along the ground track of a satellite with position data of aircraft (flight tracks) and clouds (cloud tracks) and is intended to be an extension for ships (ship tracks) and air parcels (forward and backward trajectories). The open-source algorithm is written in the Julia programming language. The core of the matching algorithm consist of interpolating tracks of different objects with a piecewise cubic Hermite interpolating polynomial with the subsequent identification of an intercept point by minimising the norm between the different track point coordinate pairs. The functionality wrapped around the two steps allows for the application of the TrackMatcher tool to a wide range of scenarios. Here, we present three examples of matching satellite tracks with the position of individual aircraft and clouds that demonstrate the usefulness of TrackMatcher for application in atmospheric science.

Controlling a quadrotor UAV by means of a fractional nested saturation control

In this paper, a fractional nonlinear control strategy based on the nested saturations technique and the Caputo-Fabrizio derivative for a quadrotor aircraft, to maintain desired position and orientation in stationary flight and trajectory tracking tasks, is proposed and developed. In addition, the dynamic model is obtained by using the Euler–Lagrange formulation, and then it is generalized to an arbitrary order through the Caputo-Fabrizio derivative. The traditional nonlinear control based on the nested saturation technique is also developed and implemented on the quadrotor for comparison purposes between both control schemes. Numerical simulations demonstrated the superiority of the proposed control strategy for stabilizing the quadrotor at hover and reaching the desired position and orientation, over its integer-order counterpart. In addition, three additional desired trajectories are considered, keeping the same gains and orders, to demonstrate the robustness of the proposed control scheme under different operating conditions. In this sense, our controller presents significant performance improvements, which were validated through system simulations. Our proposed control system and its traditional counterpart were tuned experimentally using the response of the system to a desired trajectory.

Maneuvering target state estimation based on separate modeling of target trajectory shape and dynamic characteristics

The state estimation of a maneuvering target, of which the trajectory shape is independent on dynamic characteristics, is studied. The conventional motion models in Cartesian coordinates imply that the trajectory of a target is completely determined by its dynamic characteristics. However, this is not true in the applications of road-target, sea-route-target or flight route-target tracking, where target trajectory shape is uncoupled with target velocity properties. In this paper, a new estimation algorithm based on separate modeling of target trajectory shape and dynamic characteristics is proposed. The trajectory of a target over a sliding window is described by a linear function of the arc length. To determine the unknown target trajectory, an augmented system is derived by denoting the unknown coefficients of the function as states in mileage coordinates. At every estimation cycle except the first one, the interaction (mixing) stage of the proposed algorithm starts from the latest estimated base state and a recalculated parameter vector, which is determined by the least squares (LS). Numerical experiments are conducted to assess the performance of the proposed algorithm. Simulation results show that the proposed algorithm can achieve better performance than the conventional coupled model-based algorithms in the presence of target maneuvers.

Can Decision Theory Help End-Users Take the Appropriate Action in an Emergency?

Abstract Making decisions about the appropriate action to take when presented with uncertain information is difficult, particularly in an emergency response situation. Decision-makers can be influenced by factors such as how information is framed, their risk sensitivity, and the impact of false alarms. Uncertainty arising from limited knowledge of the current state or future outcome of an event is unavoidable when making decisions. However, there is no universally agreed method on the design and presentation of uncertainty information. The aim of this article is to demonstrate that decision theory can be applied to an ensemble of plausible realizations of a situation to build a transparent framework that can then be used to determine the optimal action by assigning losses to different decision outcomes. The optimal action is then visualized, enabling the uncertainty information to be presented in a condensed manner suitable for decision-makers. The losses are adaptable depending on the hazard and the individual operational model of the decision-maker. To illustrate this approach, decision theory will be applied to an ensemble of volcanic ash simulations used for the purpose of airline flight planning, focusing on the 2019 eruption of Russian volcano Raikoke. Three idealized scenarios are constructed to show the impact of different loss models on the optimal action. In all cases, applying decision theory can significantly alter the regions, and therefore potential flight tracks, identified as potentially hazardous. Thus, we show that different end-users would and should make different decisions when presented with the same probabilistic information based on their individual user requirements.

Assessing potential conflicts between offshore wind farms and migration patterns of a threatened shorebird species

AbstractInstallation of offshore wind farms (OWFs) is becoming increasingly important to ensure a reduction in greenhouse gas emissions; however, OWFs also pose a threat to migrating birds and other wildlife. Informed marine spatial planning is therefore crucial, but individual‐based high‐resolution data on bird migration across the sea are currently lacking. We equipped 51 individuals of the near threatened Eurasian curlew Numenius arquata with GPS tags (118 flight tracks) across multiple years and countries to assess their four‐dimensional migration routes across the Baltic Sea (i.e. flight tracks, altitudes, phenology and diurnal patterns), to inform collision‐risk models and assess potential conflicts with current and future OWFs. Despite a broad‐front migration, we identified core migration areas in the south‐western Baltic Sea (and adjacent mainland), largely overlapping with already operating OWFs. Generalized linear models based on a resampling procedure to overcome autocorrelation of tracking data showed that flight altitudes across the sea and during autumn (median: 60 m) were significantly lower than those across land (median: 335 m) and during spring (median across sea: 150; median across land: 576 m). Across the sea, curlews spent 74.8% and 62.2% of their migration times below 300 m during autumn and spring, respectively, indicating a potentially high collision risk with OWFs. The mean flight speed was 56.3 km/h (±20.3 km/h). Migration intensity was highest at night over a 10‐day period during April, suggesting that restricted turbine operation for several days might be a possible management measure. Our study showed that, even for broad‐front migrants, it is possible to identify particularly sensitive sea areas deserving special protection enabling a sound marine spatial planning. This is a crucial finding also for various other shorebirds on the East Atlantic Flyway. Further studies are needed to assess the behavioural reactions of migrating birds with respect to OWFs using high‐resolution tracking data.

Tracking flight control of UAV based on multiple regions pole assignment method

This paper presents a tracking control problem for an unmanned aerial vehicle (UAV) using a multiple regions pole assignment method. To obtain the UAV control gains under the regional pole assignment method, the traditional robust control approach is to construct a closed-loop system and a specific linear matrix inequality (LMI) region in a complex plane, all poles in the system are configured in this specific region by solving LMI. Since the given LMI region is fixed with a large scale, further constraints on the LMI region can make poles configuring in a more appropriate position to obtain better control effects. Hence, based on the UAV tracking control problem, a multiple regions pole assignment method is proposed in this paper. By designing multiple LMI regions and a novel solving algorithm for pole assignment, the optimized tracking control scheme can be obtained. A practical example of quadrotor UAV tracking is given to illustrate the effectiveness of the proposed method.

Artificial Potential Field-Based Multi-UAV Formation Control and Target Tracking

To simultaneously achieve space formation flight and target tracking of multiple unmanned aerial vehicles (UAVs) and solve the rotation buffeting problem of the UAV, a robust formation control and target tracking algorithm is proposed. The artificial potential function consisting of formation control term and target tracking term is established, and its convergence is proved. The sliding mode control method with the saturation function is established, and a sufficient condition for sliding mode to occur is analysed. Finally, the numerical simulation is conducted for the proposed algorithm, and the simulation result is analysed. The results show that the proposed algorithm can quickly achieve the formation flight and target tracking of multi-UAVs and improve the tracking performance; meanwhile, it can effectively weaken the rotation buffeting and improve the robustness.

Adaptive proportional integral derivative deep feedforward network for quadrotor trajectory-tracking flight control

<span>When the controlled system is subject to parameter variations and external disturbances, a fixed-parameter proportional integral derivative (PID) controller cannot ensure its stabilization. In this case, its control requires online parameter adjustment. Specifically, as the quadrotor is a multi-input multi-output, nonlinear, and underactuated system, robust control is necessary to ensure efficient trajectory tracking flights. In this paper, an adaptive proportional integral derivative (APID) controller is proposed to control the quadrotor systems. This APID-based control strategy uses a two hidden layer deep feedforward network (DFN), where the one-step secant algorithm is chosen for initializing the DFN parameters. All the design steps of the proposed adaptive controller are described. The multidimensional particle swarm optimization (PSO) algorithm is used for tuning the DFN parameters. Then, using two simulation efficiency tests, a comparison between the proposed PSO-based APID-DFN, the (non-optimized) APID-DFN, the feedforward network APID, and the fixed-parameter PID controllers proves much efficiency of the proposed adaptive controller. The results illustrate that the proposed PSO-based APID-DFN controller can ensure good quadrotor system stabilization and achieve minimum overshoot and faster convergence speed for all quadrotor motions. Thus, the proposed control strategy could be considered an additional intelligent method-based adaptive control for unmanned aerial vehicles.</span>

Remote sensing of seawater optical properties and the subsurface phytoplankton layer in coastal waters using an airborne multiwavelength polarimetric ocean lidar.

The vertical profiles of the seawater optical properties and subsurface phytoplankton layer observed during an airborne lidar flight experiment carried out on 29 January 2021 in the coastal waters near Qionghai city were studied. We employed a hybrid inversion model combining the Klett and perturbation retrieval methods to estimate the seawater optical properties, while the vertical subsurface phytoplankton layer profiles were obtained by an adaptive evaluation. The airborne lidar data preprocessing scheme and inversion of the seawater optical properties were described in detail, and the effects of water environment parameters on the airborne lidar detection performance in coastal waters were discussed. The obtained seawater optical properties and phytoplankton layer profiles exhibit characteristic spatiotemporal distributions. The vertical stratification of seawater optical properties along a flight track from 19.19°N to 19.27°N is more pronounced than that from 19.27°N to 19.31°N. The subsurface phytoplankton layer appears along the flight track at water depths of 5-14 m with a thickness of 2-8.3 m. The high concentrations of chlorophyll, colored dissolved organic matter (CDOM), and suspended particulate matter (SPM) in coastal waters are the main factors leading to the shallower detection depth for airborne lidar. A 532 nm laser emission wavelength is more suitable than 486 nm for investigating coastal waters. The 532 nm receiving channel with 25 mrad receiving field of view achieves a better detection performance than that with 6 mrad. These results indicate that lidar technology has great potential for the wide-range and long-term monitoring of coastal waters.

Study on Numerical Algorithm of the N-S Equation for Multi-Body Flows around Irregular Disintegrations in Near Space

There has been a concern that the accurate numerical simulation of multi-body flow, which is caused by the multiple disintegrations of expired spacecraft re-entering into the near space, has a critical bottleneck impact on the falling area of the disintegrated debris. To solve this problem, an O-type grid topology method has been designed for the multi-body flow field of irregular debris formed by multiple disintegrations in near space, and a finite-volume implicit numerical scheme has been constructed for the Navier-Stokes equations to solve the aerodynamic interference characteristics of irregular multi-body flow, and further the N-S equation numerical algorithm has been established for the irregular multi-body flows in near space. The reliability of the method has been verified by the comparison of the present computation and the experiment of the low-density wind tunnel for the two-body flow of sphere, cylinder and square scripts. The objects of this study are from the multiple disintegrations of the Tiangong-1 spacecraft during uncontrolled re-entry into the atmosphere, including propelling cylinders and low-temperature lock cabinets. A series of simulations of multi-body flow mechanisms around different combinations have been carried out with varied shapes and spacing. As a result, it is found that when the distance of irregular debris (e.g., two propelling cylinders) in the near space is in the range of Δy < 3D or Δx < D, there is an obvious multi-body interference between debris, and the flow characteristics are obviously changed. When the distance between the debris in near space reaches a certain level, the influence of mutual interference can be ignored. For example, when the y-direction distance between multiple bodies is greater than 3D, the flow interference tends to be small and can be ignored, and we can regard them as two separate pieces to be carried out by the numerical prediction of flight track and falling area in engineering application. The results provide a practical design criterion for the integrated simulation platform which is used to simulate the multi-physics complex aerodynamics of space vehicles from the free-molecule flow of the outer space to the near-ground continuum flow.

Change of community noise and noise impact with changes in air-taxi fleet compostitions over a longer period of time

Generic air vehicles are helping to understand effects specifically related to urban air mobility (UAM) noise. Air corridors were already studied, managing complex air-taxi traffic to reduce population's exposure to higher or critical noise levels in the vicinity of a highly frequented flight paths. The results still depend on fleet compositions, which may change over shorter or longer periods because future UAM carriers can select from a variety of different air-taxi types, in some cases strongly differing in their noise characteristics. Once an air-taxi-fleet is operated at a certain vertiport, its composition may not remain the same after one month or even after one year. This study is evaluating a long-term effect with changing fleets operated on the same flight paths in the same air corridor. Besides usual noise metrics like DNL, the results provide also a first insight how metrics like the dose-response may be affected over a longer period of time. 25 acoustically diverse air-taxis were distributed inside an 8 km wide air corridor, carrying 165 single flight tracks at 5 flight levels. Approximately 60,200 movements were simulated representing short-term effects, ten times more for mid-term scenarios, and finally a large number of 1,505,000 for the long-term study.

High speed visual insect swarm tracker (Hi-VISTA) used to identify the effects of confinement on individual insect flight

Individual insects flying in crowded assemblies perform complex aerial maneuvers by sensing and feeding back neighbor measurements to small changes in their wing motions. To understand the individual feedback rules that permit these fast, adaptive behaviors in group flight, both experimental preparations inducing crowded flight and high-speed tracking systems capable of tracking both body motions and more subtle wing motion changes for multiple insects in simultaneous flight are needed. This measurement capability extends tracking beyond the previous focus on individual insects to multiple insects. This paper describes an experimental preparation that induces crowded insect flight in more naturalistic conditions (a laboratory-outdoor transition tunnel) and directly compares the resulting flight performance to traditional flight enclosures. Measurements are made possible via the introduction of a multi-agent high speed insect tracker called Hi-VISTA, which provides a capability to track wing and body motions of multiple insects using high speed cameras (9000–12 500 fps). Processing steps consist of automatic background identification, data association, hull reconstruction, segmentation, and feature measurement. To improve the biological relevance of laboratory experiments and develop a platform for interaction studies, this paper applies the Hi-VISTA measurement system to Apis mellifera foragers habituated to transit flights through the transparent transition environment. Binary statistical analysis (Welch’s t-test, Cohen’s d effect size) of 95 flight trajectories is presented, quantifying the differences between flights in an unobstructed environment and in a confined tunnel volume. The results indicate that body pitch angle, heading rate, flapping frequency, and vertical speed (heave) are each affected by confinement, and other flight variables show minor or statistically insignificant changes. These results form a baseline as swarm tracking and analysis begins to isolate the effects of neighbors from environmental enclosures, and improve the connection of high speed insect laboratory experiments to outdoor field experiments.

Initiatives for Wireless Channel Sounding Standards in IEEE [Standards

The synthetic aperture is a signal processing technique that collects signal samples across a spatial volume and generates a huge database that helps solve a wide array of problems. For example, a synthetic aperture radar (SAR) synthesizes the motion of a long antenna by combining received signals as it moves along a flight track and provides data with finer spatial resolution that help create 2D images and the 3D reconstruction of objects. Recently, the synthetic aperture has also applied to wireless channel sounding and the over-the-air calibration of wireless devices <xref ref-type="bibr" rid="ref1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1]</xref> .

Large-eddy simulation of airborne wind energy farms

Abstract. The future utility-scale deployment of airborne wind energy technologies requires the development of large-scale multi-megawatt systems. This study aims at quantifying the interaction between the atmospheric boundary layer (ABL) and large-scale airborne wind energy systems operating in a farm. To that end, we present a virtual flight simulator combining large-eddy simulations to simulate turbulent flow conditions and optimal control techniques for flight path generation and tracking. The two-way coupling between flow and system dynamics is achieved by implementing an actuator sector method that we pair to a model predictive controller. In this study, we consider ground-based power generation pumping-mode AWE systems (lift-mode AWES) and on-board power generation AWE systems (drag-mode AWES). The aircraft have wingspans of approximately 60 m and fly large loops of approximately 200 m diameter centred at 200 m altitude. For the lift-mode AWES, we additionally investigate different reel-out strategies to reduce the interaction between the tethered wing and its own wake. Further, we investigate AWE parks consisting of 25 systems organised in five rows of five systems. For both lift- and drag-mode archetypes, we consider a moderate park layout with a power density of 10 MW km−2 achieved at a rated wind speed of 12 m s−1. For the drag-mode AWES, an additional park with denser layout and power density of 28 MW km−2 is also considered. The model predictive controller achieves very satisfactory flight path tracking despite the AWE systems operating in fully waked, turbulent flow conditions. Furthermore, we observe significant wake effects for the utility-scale AWE systems considered in the study. Wake-induced performance losses increase gradually through the downstream rows of systems and reach up to 17 % in the last row of the lift-mode AWE park and up to 25 % and 45 % in the last rows of the moderate and dense-drag-mode AWE parks respectively. For an operation period of 60 min at a below-rated reference wind speed of 10 m s−1, the lift-mode AWE park generates about 84.4 MW of power, corresponding to 82.5 % of the power yield expected when AWE systems operate ideally and interaction with the ABL is negligible. For the drag-mode AWE parks, the moderate and dense layouts generate about 86.0 and 72.9 MW of power respectively corresponding to 89.2 % and 75.6 % of the ideal power yield.

Mixed analysis-synthesis approach for estimating airport noise from civil air traffic

This paper presents an important upgrade of a modelling tool devised by the authors for estimating aircraft noise around civil airports, which is based on a best-practice noise computation method and flight tracking data collected from the Internet and complemented by datasets of aircraft models, runways, and terrain elevation. Targeting more accurate noise predictions , the upgraded model introduces reasoned degrees of freedom in the standard flight procedures, and the tracked altitudes and speeds of each flight event are used to fit these modified procedures, which leads to an original mixed analysis-synthesis approach. Additional improvements include better runway assignment and consideration of actual weather conditions. Comparison of July 2019 results with official data for Heathrow, Gatwick and Schiphol airports shows an improved noise prediction, with an average underestimation lowered to 1.5 dB(A) for exposure-based metrics. Therefore, this upgraded modelling tool can be a reliable support to civil aviation authorities and policy-makers.

Meteorological Conditions That Promote Persistent Contrails

Climate-impacting contrails need ice (super-)saturation to persist longer than a few minutes. However, this simple criterion cannot be easily applied for the prediction of persistent contrails. The current weather forecast models, which lack humidity data for assimilation in the upper troposphere, have difficulties coping with the enormous variability and sharp gradients in the relative humidity field. Thus, ice supersaturation, which is an extremal state of relative humidity, is hard to forecast at a precise location and time to allow contrail-avoiding flight routing. In this paper, we investigate the possibility of using dynamical proxy variables for improved contrail prediction. This idea is guided by the fact that the probability of ice supersaturation differs in different dynamical regimes. Therefore, we determine probability distributions of temperature, water vapour concentration, vertical velocity, divergence, relative and potential vorticity, geopotential height, and lapse rate conditioned on three situations: (a) contrail persistence not possible; (b) contrail persistence possible; and (c) strongly warming persistent contrails possible. While the atmospheric variables are taken from reanalysis data, the conditions (a–c) are based on airborne measurement data and radiation quantities from the reanalysis. It turns out that the vorticity variables, and in particular geopotential and lapse rate, show quite distinct conditional probabilities, suggesting a possibility to base an improved forecast of persistent contrails not only on the traditional quantities of temperature and relative humidity, but on these dynamical proxies as well. Furthermore, we show the existence of long flight tracks with the formation of strongly warming contrails, which are probably embedded in larger ice-supersaturated regions with conditions that foster such contrails. For forecasting purposes, this is a beneficial property since the humidity forecast is easier on large, rather than small, spatial scales.

Aircraft noise and environmental equity in Montréal: A comparison of noise indicators and an analysis of the impacts of COVID-19.

From an environmental equity perspective, the aim of this paper is twofold. First, we want to verify to what extent vulnerable population groups resided in areas exposed to high levels of aircraft noise before and during the COVID-19 pandemic (2019 and 2020) in the Montréal census metropolitan area. Second, we want to identify whether the use of an aircraft noise indicator rather than another generates significant variations in the results and consequently in terms of affected areas and populations.With the IMPACT web-application, we model aircraft noise contours from three cumulative (Lden, Ldn, Laeq,24h) and a single-event (LAmax) metrics. The model’s input data are retrieved by a website for flight tracking. Next, four variables are extracted from the 2016 Statistics Canada census at a fine scale level (dissemination areas): that is, the percentages of low-income individuals, visible minorities, children under 15 years old, and individuals aged 65 and over.The results show a significant drop in population exposed to aircraft noise in 2020 compared to 2019. In addition, the estimates of populations impacted by aircraft noise differ from one indicator to the next. The logistic regression models indicate that the inequities are inconsistent between cumulative and single-event metrics.

Quantification and mitigation of the instrument effects and uncertainties of the airborne limb imaging FTIR GLORIA

Abstract. The Gimballed Limb Observer for Radiance Imaging of the Atmosphere (GLORIA) is an infrared imaging FTS (Fourier transform spectrometer) with a 2-D infrared detector that is operated on two high-flying research aircraft. It has flown on eight campaigns and measured along more than 300 000 km of flight track. This paper details our instrument calibration and characterization efforts, which, in particular, almost exclusively leverage in-flight data. First, we present the framework of our new calibration scheme, which uses information from all three available calibration sources (two blackbodies and upward-pointing “deep space” measurements). Part of this scheme is a new algorithm for correcting the erratically changing nonlinearity of a subset of detector pixels and the identification of the remaining bad pixels. Using this new calibration, we derive a 1σ bound of 1 % on the instrument gain error and a bound of 30 nW cm−2 sr−1 cm on the instrument offset error. We show how we can examine the noise and spectral accuracy for all measured atmospheric spectra and derive a spectral accuracy of 5 ppm on average. All these errors are compliant with the initial instrument requirements. We also discuss, for the first time, the pointing system of the GLORIA instrument. Combining laboratory calibration efforts with the measurement of astronomical bodies during the flight, we can achieve a pointing accuracy of 0.032∘, which corresponds to one detector pixel. The paper concludes with a brief study of how these newly characterized instrument parameters affect temperature and ozone retrievals. We find that the pointing uncertainty and, to a lesser extent, the instrument gain uncertainty are the main contributors to the error in the result.

A practical approach with drones, smartphones, and tracking tags for potential real-time animal tracking.

Drones are increasingly used for fauna monitoring and wildlife tracking; however, their application for wildlife tracking is restricted by developing such systems. Here we explore the potential of drones for wildlife tracking using an off-the-shelf system that is easy to use by non-specialists consisting of a multirotor drone, smartphones, and commercial tracking devices via Bluetooth and Ultra-Wide Band (UWB). We present the system configuration, explore the operational parameters that can affect detection capabilities, and test the effectiveness of the system for locating targets by simulating target animals in savanna and forest environments. The self-contained tracking system was built without hardware or software customization. In 40 tracking flights carried out in the Brazilian Cerrado, we obtained a detection rate of 90% in savanna and 40% in forest areas. Tests for targets in movement (N = 20), the detection rates were 90% in the savanna and 30% in the forest areas. The spatial accuracy obtained by the system was 14.61 m, being significantly more accurate in savanna ( = 10.53) than in forest areas ( = 13.06). This approach to wildlife tracking facilitates the use of drones by non-specialists at an affordable cost for conservation projects with limited resources. The reduced size of the tags, the long battery life, and the lower cost compared to GPS-tags open up a range of opportunities for animal tracking.

Comparison of DVB-T Passive Radar Simulated and Measured Bistatic RCS Values for a Pilatus PC-12 Aircraft.

Passive radar is a technology that has huge potential for airspace monitoring, taking advantage of existing transmissions. However, to predict whether particular targets can be measured in a particular scenario, it is necessary to be able to model the received signal. In this paper, we present the results of a campaign in which a Pilatus PC-12 single-engine aircraft was measured with a passive radar system relying on DVB-T transmission from a single transmitter. We then present our work to simulate the bistatic RCS of the aircraft along its flight track, using both the method of moments and the shooting and bouncing ray solvers, assess the uncertainty in the simulations, and compare against the measurements. We find that our simulated RCS values are useful in predicting whether or not detection occurs. However, we see poor agreement between simulated and measured RCS values where measurements are available, which we attribute primarily to the difficulties in extracting RCS measurements from the data and to unmodeled transmission and received path effects.