V-Spline: An Adaptive Smoothing Spline for Trajectory Reconstruction.

Trajectory reconstruction is the process of inferring the path of a moving object between successive observations. In this paper, we propose a smoothing spline-which we name the V-spline-that incorporates position and velocity information and a penalty term that controls acceleration. We introduce an adaptive V-spline designed to control the impact of irregularly sampled observations and noisy velocity measurements. A cross-validation scheme for estimating the V-spline parameters is proposed, and, in simulation studies, the V-spline shows superior performance to existing methods. Finally, an application of the V-spline to vehicle trajectory reconstruction in two dimensions is given, in which the penalty term is allowed to further depend on known operational characteristics of the vehicle.

Estimating Position from Millisecond Samples of GPS Signals (the "FastFix" Algorithm).

A new approach to GPS positioning is described in which the post-processing of ultra-short sequences of captured GPS signal data can produce an estimate of receiver location. The algorithm, called 'FastFix', needs only 2-4 ms of stored L1-band data sampled at ∼16 MHz. The algorithm uses a least-squares optimization to estimate receiver position and GPS time from measurements of the relative codephase, and Doppler-shift of GNSS satellite signals. A practical application of this algorithm is demonstrated in a small, lightweight, low-power tracking tag that periodically wakes-up, records and stores 4 ms of GPS L1-band signal and returns to a low-power state-reducing power requirements by a factor of ∼10,000 compared to typical GPS devices. Stationary device testing shows a median error of 27.7 m with a small patch antenna. Results from deployment of this tag on adult Royal Albatross show excellent performance, demonstrating lightweight, solar-powered, long-term tracking of these remarkable birds. This work was performed on the GPS system; however, the algorithm is applicable to other GNSS systems.

Comparison of Enhanced Noise Model Performance Based on Analysis of Civilian GPS Data.

We recorded the time series of location data from stationary, single-frequency (L1) GPS positioning systems at a variety of geographic locations. The empirical autocorrelation function of these data shows significant temporal correlations. The Gaussian white noise model, widely used in sensor-fusion algorithms, does not account for the observed autocorrelations and has an artificially large variance. Noise-model analysis-using Akaike's Information Criterion-favours alternative models, such as an Ornstein-Uhlenbeck or an autoregressive process. We suggest that incorporating a suitable enhanced noise model into applications (e.g., Kalman Filters) that rely on GPS position estimates will improve performance. This provides an alternative to explicitly modelling possible sources of correlation (e.g., multipath, shadowing, or other second-order physical phenomena).

Improving Real-Time Position Estimation Using Correlated Noise Models.

We provide algorithms for inferring GPS (Global Positioning System) location and for quantifying the uncertainty of this estimate in real time. The algorithms are tested on GPS data from locations in the Southern Hemisphere at four significantly different latitudes. In order to rank the algorithms, we use the so-called log-score rule. The best algorithm uses an Ornstein-Uhlenbeck (OU) noise model and is built on an enhanced Kalman Filter (KF). The noise model is capable of capturing the observed autocorrelated process noise in the altitude, latitude and longitude recordings. This model outperforms a KF that assumes a Gaussian noise model, which under-reports the position uncertainties. We also found that the dilution-of-precision parameters, automatically reported by the GPS receiver at no additional cost, do not help significantly in the uncertainty quantification of the GPS positioning. A non-learning method using the actual position measurements and employing a constant uncertainty does not even converge to the correct position. Inference with the enhanced noise model is suitable for embedded computing and capable of achieving real-time position inference, can quantify uncertainty and be extended to incorporate complementary sensor recordings, e.g., from an accelerometer or from a magnetometer, in order to improve accuracy. The algorithm corresponding to the augmented-state unscented KF method suggests a computational cost of O(dx2dt), where dx is the dimension of the augmented state-vector and dt is an adjustable, design-dependent parameter corresponding to the length of "past values" one wishes to keep for re-evaluation of the model from time to time. The provided algorithm assumes dt=1. Hence, the algorithm is likely to be suitable for sensor fusion applications.

Nature's Wind Turbines: The Measured Aerodynamic Efficiency of Spinning Seeds Approaches Theoretical Limits.

This paper describe a procedure to measure experimentally the power coefficient, Cp, of winged seeds, and apply this technique to seeds from the Norway maple (Acer platanoides). We measure Cp=56.9±2% at a tip speed ratio of 3.21±0.06. Our results are in agreement with previously published CFD simulations that indicate that these seeds-operating in low-Reynolds number conditions-approach the Betz limit (Cp=59.3%) the maximum possible efficiency for a wind turbine. In addition, this result is not consistent with the recent theoretical work of Okulov & Sørensen, which suggests that a single-bladed turbine with a tip-speed ratio of 3.2 can achieve a power efficiency of no more than 30%.

Optimal nonlinear filtering using the finite-volume method.

Optimal sequential inference, or filtering, for the state of a deterministic dynamical system requires simulation of the Frobenius-Perron operator, that can be formulated as the solution of a continuity equation. For low-dimensional, smooth systems, the finite-volume numerical method provides a solution that conserves probability and gives estimates that converge to the optimal continuous-time values, while a Courant-Friedrichs-Lewy-type condition assures that intermediate discretized solutions remain positive density functions. This method is demonstrated in an example of nonlinear filtering for the state of a simple pendulum, with comparison to results using the unscented Kalman filter, and for a case where rank-deficient observations lead to multimodal probability distributions.

A video-based movement analysis system to quantify behavioral stress responses of fish.

Behavioral alterations can be measured as endpoints for sublethal toxicity, and serve as a tool for environmental risk assessment and analysis of toxicological impact. Numerous technical and biological factors have made sublethal effects on fish behavior difficult to quantify. In order to investigate stress- and contaminant-induced behavioral alterations, a video analysis system was designed by our laboratory. With this system up to 12 fish may be individually housed in 20 L exposure arenas and automatically videotaped at multiple and discrete intervals during an experimental period. Analog video data can then digitized, converted into x,y coordinates, and finally transformed into relevant behavioral endpoints using software designed for tracking fish movement combined with specific algorithms. These endpoints include velocity, total distance traveled, angular change, percent movement, space utilization, and fractal dimension (path complexity). Data from fish exposed to a reference toxicant, MS222, and simulation experiments, are presented to exemplify alterations in fish behavior associated with exposure, and accuracy and precision, respectively. The system provides flexibility to analyze any observed movement behavior, is remotely controlled, and can be transportable. These movement analyses can be used to identify characteristic behavioral responses to a variety of environmentally-relevant stressors, and assist in risk assessment and the development of more sensitive lowest observable effect level and no observable effect level for sentinel species.