Stable arrangements of mobile sensors for sampling physical fields

Abstract

Abstract-Today's wireless sensor nodes can be easily attached to mobile platforms such as robots, cars and cell phones enabling pervasive sensing of physical fields (say of temperature, vibrations, air quality and chemicals). We address the sensor arrangement problem, i.e. when and where sensors should take samples to obtain a good estimate of a field using mobile sensors. In particular, we focus on incidentally mobile sensors that move passively under the influence of the environment (e.g. sensors attached to floating buoys, cars and smartphones carried by humans). We model the field as a linear combination of known basis functions. Given the samples, we use a linear estimator to find unknown coefficients of the basis functions. We formulate the sensor arrangement problem as one of finding suitably characterized classes of sensor arrangements that lead to a stable reconstruction of the field. We consider a family of multidimensional

Efficient Parametric Signal Estimation From Samples With Location Errors

“…Since for a general choice of basis functions, no closed form solution exists to the likelihood function given by (8), a numerical method is needed to approximate (8). This numerical approximation is a precursor for either obtaining the CRB or implementing an EM approximation to the ML estimator (9) as discussed in [20].…”

“…This numerical approximation is a precursor for either obtaining the CRB or implementing an EM approximation to the ML estimator (9) as discussed in [20]. In this section we first discuss techniques and issues involved in obtaining an approximation to (8). On the basis of our numerical approximation scheme we then present an approximation to the CRB and an EM algorithm for ML estimation.…”

“…We use Gram-Schmidt orthonormalization [8] to generate 11 orthonormal basis functions φ k (x)'s and call it the set of trigonometric basis functions. Similarly, we create an orthonormal set of 10 polynomial basis functions from ψ k (x) = x k ∀k = 0 to 9.…”

“…One key application of such mobile WSNs is to reconstruct a spatiotemporal field such as temperature or chemical concentration. Several approaches have been explored in the literature for reconstructing such fields in the presence of measurement/modeling errors [4]- [8].…”