An Ensemble Smoother with Error Estimates

A smoother introduced earlier by van Leeuwen and Evensen is applied to a problem in which real obser vations are used in an area with strongly nonlinear dynamics. The derivation is new , but it resembles an earlier derivation by van Leeuwen and Evensen. Again a Bayesian view is taken in which the prior probability density of the model and the probability density of the obser vations are combined to for m a posterior density . The mean and the covariance of this density give the variance-minimizing model evolution and its errors. The assumption is made that the prior probability density is a Gaussian, leading to a linear update equation. Critical evaluation shows when the assumption is justified. This also sheds light on why Kalman filters, in which the same ap- proximation is made, work for nonlinear models. By reference to the derivation, the impact of model and obser vational biases on the equations is discussed, and it is shown that Bayes’ s for mulation can still be used. A practical advantage of the ensemble smoother is that no adjoint equations have to be integrated and that error estimates are easily obtained. The present application shows that for process studies a smoother will give superior results compared to a filter , not only owing to the smooth transitions at obser vation points, but also because the origin of features can be followed back in time. Also its preference over a strong-constraint method is highlighted. Further more, it is argued that the proposed smoother is more efficient than gradient descent methods or than the representer method when error estimates are taken into account

Cross layer based protocols for energy aware and critical data delivery related applications using wireless sensor networks

Wireless Sensor Networks (WSNs) have been an exciting topic in recent years. The services offered by a WSN can be classified into three major categories: monitoring, alerting, and information on demand. WSNs have been used for a variety of applications related to the environment (agriculture, water and forest fire detection), the military, buildings, health (elderly people and home monitoring), disaster relief, and area or industrial monitoring. In most WSNs tasks like processing the sensed data, making decisions and generating emergency messages are carried out by a remote server, hence the need for efficient means of transferring data across the network. Because of the range of applications and types of WSN there is a need for different kinds of MAC and routing protocols in order to guarantee delivery of data from the source nodes to the server (or sink). In order to minimize energy consumption and increase performance in areas such as reliability of data delivery, extensive research has been conducted and documented in the literature on designing energy efficient protocols for each individual layer. The most common way to conserve energy in WSNs involves using the MAC layer to put the transceiver and the processor of the sensor node into a low power, sleep state when they are not being used. Hence the energy wasted due to collisions, overhearing and idle listening is reduced. As a result of this strategy for saving energy, the routing protocols need new solutions that take into account the sleep state of some nodes, and which also enable the lifetime of the entire network to be increased by distributing energy usage between nodes over time. This could mean that a combined MAC and routing protocol could significantly improve WSNs because the interaction between the MAC and network layers lets nodes be active at the same time in order to deal with data transmission. In the research presented in this thesis, a cross-layer protocol based on MAC and routing protocols was designed in order to improve the capability of WSNs for a range of different applications. Simulation results, based on a range of realistic scenarios, show that these new protocols improve WSNs by reducing their energy consumption as well as enabling them to support mobile nodes, where necessary. A number of conference and journal papers have been published to disseminate these results for a range of applications.