Handbook on Array Processing and Sensor Networks

CHAPTER 27

Biochemical Transport Modeling, Estimation, and Detection in Realistic Environments

Mathias Ortner Arye Nehorai

Department of Electrical and Systems Engineering, Washington University, St. Louis, Missouri

27.1 INTRODUCTION

New Numerical Approach We present¹ in this chapter a new approach for computing and using a numerical forward physical dispersion model relating the source to the measurements given by an array of biochemical sensors in realistic environments. The approach presented here provides a modeling framework that accounts for complex geometries and allows full use of software-simulated random wind turbulence. The key point of our approach is that we decouple the “fluid simulation” part from the “transport compution.” In particular, we show on a simple but realistic example how to incorporate numerical simulations including random effects. The approach we propose is generic enough to incorporate additional random effects, including chemical reactions, temperature effects, and radioactive decaying. The Monte Carlo approach we employ is based on a Feynman–Kac representation and therefore does not require solving the problem on the entire domain but only at the sensor positions. The required computational time is thereby limited.

Illustrating Example: Monitoring Biochemical Events We take monitoring biological or chemical events as an illustrating example. The ...