Data

Path and travel time inference from GPS probe vehicle data

Hunter, Timothy
Herring, Ryan
Bayen, Alexandre M.
2009

We consider the problem of estimating real-time traffic conditions from sparse, noisy GPS probe vehicle data. We specifically address arterial roads, which are also known as the secondary road network (highways are considered the primary road network). We consider several estimation problems: historical traffic patterns, real-time traffic conditions, and forecasting future traffic conditions. We assume that the data available for these estimation problems is a small set of sparsely traced vehicle trajectories, which represents a small fraction of the total vehicle flow through the network. We...

Viability-based computation of spatially constrained minimum time trajectories for an autonomous underwater vehicle: implementation and experiments

Tinka, Andrew
Diemer, S.
Bayen, Alexandre M.
2009

A viability algorithm is developed to compute the constrained minimum time function for general dynamical systems. The algorithm is instantiated for a specific dynamics (Dubin's vehicle forced by a flow field) in order to numerically solve the minimum time problem. With the specific dynamics considered, the framework of hybrid systems enables us to solve the problem efficiently. The algorithm is implemented in C using epigraphical techniques to reduce the dimension of the problem. The feasibility of this optimal trajectory algorithm is tested in an experiment with a light autonomous...

Minimal Error Certificates for Detection of Faulty Sensors Using Convex Optimization

Claudel, Christian G.
Nahoum, Matthieu
Bayen, Alexandre M.
2009

This article proposes a new method for sensor fault detection, applicable to systems modeled by conservation laws. The state of the system is modeled by a Hamilton-Jacobi equation, in which the Hamiltonian is uncertain. Using a LaxHopf formula, we show that any local measurement of the state of the system restricts the allowed set of possible values of other local measurements. We derive these constraints explicitly for arbitrary Hamilton-Jacobi equations. We apply this framework to sensor fault detection, and pose the problem finding the minimal possible sensor error (minimal error...

Flatness-Based Control of Open-Channel Flow in an Irrigation Canal Using SCADA [Applications of Control]

Rabbani, Tarek
Munier, Simon
Dorchies, David
Malaterre, Pierre-olivier
Bayen, Alexandre
Litrico, Xavier
2009

This article applied a flatness-based controller to an open channel hydraulic canal. The controller was tested by computer simulation using Saint-Venant equations as well as by real experimentation on the Gignac canal in southern France. The initial model that assumes constant lateral withdrawals is improved to take into account gravitational lateral withdrawals, which vary with the water level. Accounting for gravitational lateral withdrawals decreased the steady-state error from 6.2% (constant lateral withdrawals assumption) to 1% (gravitational lateral withdrawals assumption). The...

Kernel Regression for Travel Time Estimation via Convex Optimization

Blandin, Sébastien
El Ghaoui, Laurent
Bayen, Alexandre
2009

We develop an algorithm aimed at estimating travel time on segments of a road network using a convex optimization framework. Sampled travel time from probe vehicles are assumed to be known and serve as a training set for a machine learning algorithm to provide an optimal estimate of the travel time for all vehicles. A kernel method is introduced to allow for a non-linear relation between the known entry times and the travel times that we want to estimate. To improve the quality of the estimate we minimize the estimation error over a convex combination of known kernels. This problem is...

Kalman Filter Based Estimation of Flow States in Open Channels Using Lagrangian Sensing

Rafiee, Mohammad
Wu, Qingfang
Bayen, Alexandre M.
2009

In this article, we investigate real-time estimation of flow state in open channels using the measurements obtained from Lagrangian sensors (drifters). One-dimensional Shallow Water Equations (SWE), also known as Saint-Venant equations, are used as the mathematical model for the flow. After linearizing and discretizing the PDEs using an explicit linear scheme, we construct a linear state-space model of the flow. The Kalman filter is then used to estimate the states by incorporating the measurements obtained from passive drifters. Drifters which are equipped with GPS receivers move with the...

Quadratic Programming Based Data Assimilation with Passive Drifting Sensors for Shallow Water Flows

Tinka, Andrew
Strub, Issam
Wu, Qingfang
Bayen, Alexandre M.
2009

We present a method for assimilating Lagrangian sensor measurement data into a shallow water equation model. Using our method, the variational data assimilation problem is formulated as a quadratic programming problem with linear constraints. Drifting sensors that gather position and velocity information in the modeled system can then be used to refine the estimate of the initial conditions of the system. A new sensor network hardware platform for gathering flow information is presented. We summarize the results of a field experiment designed to demonstrate the capabilities of our...

Inverse Modeling for Open Boundary Conditions in Channel Network

Wu, Qingfang
Rafiee, Mohammad
Tinka, Andrew
Bayen, Alexandre M.
2009

An inverse modeling problem for systems of networked one dimensional shallow water equations subject to periodic forcing is investigated. The problem is described as a PDE-constrained optimization problem with the objective of minimizing the norm of the difference between the observed variables and model outputs. After linearizing and discretizing the governing equations using an implicit discretization scheme, linear constraints are constructed which leads to a quadratic programming formulation of the state estimation problem. The usefulness of the proposed approach is illustrated with a...

Cyber Attaques Sur des Réseaux d'Eau Gérés par des SCADA

Amin, Saurabh
Litrico, Xavier
Sastry, Shankar
Bayen, Alexandre M.
2010

Using Mobile Phones to Forecast Arterial Traffic through Statistical Learning

Herring, Ryan
Hofleitner, Aude
Amin, Saurabh
Abou Nasr, Tania
Khalek, Amin Abdel
Abbeel, Pieter
Bayen, Alexandre M.
2010

This article introduces the new component of Mobile Millennium dedicated to arterial traffic. Mobile Millennium is a pilot system for collecting, processing and broadcasting real-time traffic conditions through the use of global position system (GPS) equipped smartphones. Two algorithms that use data from GPS equipped smartphones to estimate arterial traffic conditions are presented, analyzed and compared. The algorithms are based on Logistic Regression and Spatio-Temporal Auto Regressive Moving Average (STARMA), respectively. Each algorithm contains a learning component, which...