Modeling and decision making in spatio-temporal processes for environmental surveillance

Abstract

I. MOTIVATION AND METHODOLOGYA broad class of environmental monitoring applications, including meteorology and climatology, epidemiology, ecology, demography, forestry, fishery and others, require distributed sensing capabilities [1] due to the dynamics exhibited in both space and time. Understanding and modeling such complex space time dynamics with only static sensors would require an impractically large number of sensors to be distributed across the complete spatial extent of the observed environment. Mobile robots equipped with sensors offer an alternative to a network of static sensing elements for high spatial coverage but at the cost of increased delay (sampling latency). Several path planning approaches have been proposed in the literature to adaptively sample the environment to reduce the latency while still providing high fidelity sampling [2]- [5].At the core of each path planning approach is a model representing the space-time dependencies. Learning such complex and non-deterministic spatio-temporal dynamics, for accurate predictions, is challenging. A typical modeling procedure adopted in the field of environmental science is to manually specify partial differential equations governing the behavior of the observed phenomena [6]. This, however, relies on experts and usually requires time consuming validation experiments [7].In this work we consider a machine learning approach to the problem where a spatio-temporal Gaussian process model is learned through an optimization procedure. The model is then used for path planning. We propose a path planning method in continuous domain that can exploit the Gaussian Process based modeling to guide informative sensing. Our proposed greedy path planning algorithm uses information gain as the objective function. We assume that X t = (s 1 ; t 1 ), . . . , (s N ; t N ) be the training set of N observation locations, available to learn the hyper-parameters of the covariance function. With the learned hyper-parameters, the trained model is used for testing on the spatio-temporal dataset. We define a timestep to be an instance of the environment during which the observed phenomena is assumed to be static.A major difficulty for modeling spatio-temporal stochastic processes with GPs is the definition of a valid covariance function that can accurately account for space-time dependencies. We study a generic approach for creating several classes of valid non-stationary, spatio-temporal GP models. After learning the parameters associated with the corresponding covariance model, path planning is performed in continuous domain, incrementally adding new data points to the model. We present extensive empirical evaluation comparing several classes of GP models using different real world sensing datasets. We validate the proposed methodology of model learning and path planning using a Networked Info Mechanical System (NIMS, a tethered robotic system). A detailed presentation of this study was published in the proceedings of ICRA 2010.

Lifelong Information-Driven Exploration to Complete and Refine 4-D Spatio-Temporal Maps

“…They achieve this by reasoning about the best times and paths to take. Typically, these algorithms rely on Gaussian Processes [20], [21], [22], which allow the robot to learn patterns in the environment. Other approaches represent the dynamics of the environment states based on the assumption that some of the environment variations observed are caused by routines performed by humans [23].…”

Spatial Gaussian Process Regression With Mobile Sensor Networks

“…Now we are in a position to deduce the DGPR from the SGPR in (16). Given the neighbor set definitions and the compactly supported covariance function in (20), the following results are obtained.…”

“…The Kriged Kalman filter and swarm control were used in [15] to reconstruct spatiotemporal functions. In [16], several nonseparable spatiotemporal covariance functions were proposed for modeling spatiotemporal functions.…”

Learning navigational maps by observing human motion patterns

“…2 thus eliminating the computational bottleneck during online use. Additional observation locations can be subsumed into K −1 using the matrix inversion lemma and submatrix inversion principle [23].…”