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).

Dataset License: BY-NC-ND

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.

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.