We propose a sensor placement method for spatio-temporal field estimation based on a kriged Kalman filter (KKF) using a network of static or mobile sensors. The developed framework dynamically designs the optimal constellation to place the sensors. We combine the estimation error (for the stationary as well as non-stationary component of the field) minimization problem with a sparsity-enforcing penalty to design the optimal sensor constellation in an economic manner. The developed sensor placement method can be directly used for a general class of covariance matrices (ill-conditioned or well-conditioned) modelling the spatial variability of the stationary component of the field, which acts as a correlated observation noise, while estimating the non-stationary component of the field. Finally, a KKF estimator is used to estimate the field using the measurements from the selected sensing locations. Numerical results are provided to exhibit the feasibility of the proposed dynamic sensor placement followed by the KKF estimation method.

Reliable prediction and monitoring of dynamically changing environments are essential for a safer and healthier society. Sensor networks play a significant role in fulfilling this task. The two fundamental aspects of environmental sensor networks (ESNs) include the need for accuracy as well as low-complexity and energy efficient sensing modalities. One of the wonted challenges of ESNs is high resolution environment monitoring in the presence of sensing overheads (such as number of sensors, battery life, maintenance). Limiting the number of sensing resources yet still guarantee a desired resolution of the unknown environmental field necessitates resource-efficient sensing framework. On the other hand, the physical behavior of many environmental fields can be predicted using statistical models. Cognizance of the physical properties of environmental fields motivates opportunistic sensor placement to dynamically monitor the environment. In this thesis, we present signal processing methods for resource-efficient environment monitoring exploiting the physical properties of environmental fields. We mainly focus on a general class of environmental fields that obey standard physical properties (such as diffusion, advection) responsible for the spatio-temporal evolution of the field. We first discuss different mathematical representations to link the sensor measurements with the unknown field intensities. Statistical characterizations of different physical properties of environmental fields such as space-time correlation and the dynamics of field propagation are also discussed. A comprehensive environment monitoring framework is presented that encompasses sensor management, measurement accumulation, and field estimation. We propose a spatio-temporal sensor management method which can be applied for stationary as well as non-stationary environmental fields. We formulate a unified optimization framework that provides the number and the most informative sensing locations to deploy sensors guaranteeing a desired estimation accuracy in terms of the mean square error (MSE). The main objective is to implement “sparse-sensing” in an environment monitoring perspective while also achieving a prescribed accuracy. We also propose different strategies to solve the proposed optimization problem for both online and offline applications. We present a practical example of environment monitoring, i.e., dynamic rainfall monitoring using rain-induced attenuation measurements from commercial microwave links. We describe different methods to incorporate some physical properties of rainfall (such as the physics behind the rainfall propagation, spatial effects such as sparsity, correlation etc.) in the dynamic monitoring setup. We also compare the estimation performance of the developed technique with standard estimators such as an extended Kalman filter (EKF). We extend the proposed sparsity-enforcing spatio-temporal sensor management method for a broader class of environmental fields consisting of a combination of both stationary and non-stationary components. We develop an algorithm for sensor placement followed by field estimation using a kriged Kalman filter (KKF), which is used for the estimation of the aforementioned type of field. We also consider the scenario, where the prior physical knowledge regarding the environmental field is either unavailable or inaccurate. In these circumstances, we discuss some methods to estimate the underlying dynamics of the field, i.e., the state/process model using the observed measurements. While estimating the process model, we consider both the scenario, where the true value/ground truth of the field is known as well as the scenario where it is unknown.

In this work, we propose a sparsity-exploiting dynamic rainfall monitoring methodology using rain-induced attenuation measurements from microwave links. To estimate rainfall field intensity dynamically from a limited number of non-linear measurements, we exploit physical properties of the rainfall such as spatial sparsity and non-negativity along with the dynamics of rainfall intensity. We develop a dynamic state estimation algorithm, where the aforementioned spatial properties are utilized as prior information. To exploit spatial sparsity, we use a basis function to tailor the sparse representation of the rainfall intensity. The basis is selected based on some criteria for sparse reconstruction such as orthonormality and mutual coherence. The tuning parameter that controls the sparsity in the spatial rainfall distribution is dynamically updated at every correction step. The developed methodology is applied to dynamically monitor the rainfall field intensity in an area with a specified spatial resolution using less number of simulated non-linear measurements than pixels. The proposed methodology can be generalized for any dynamic field reconstruction, where the limited number of non-linear measurements are field intensities integrated over a linear path.

We develop sparsity-enforcing spatio-temporal sensor management methods for environmental field monitoring applications. Leveraging the space–time stationarity, an environmental field can be estimated with a desired spatio-temporal resolution based on recorded measurements. If the field is non-stationary, it can be monitored dynamically based on the collected measurements and predictions made through a state model, if known a priori. We develop algorithms to implement sparse sensing, i.e., sensing only the most informative locations in space and time for both spatio-temporally stationary and non-stationary field monitoring applications. The selected sensing locations form an underdetermined measurement model which can be used to estimate the field based on the prior knowledge regarding the space–time variability of the field. The task of locating the most informative sensing locations can be performed for both multiple snapshots and a single snapshot based on the availability of prior knowledge (space–time correlation and dynamics) regarding the field, available computing power and the application. Centralized sensor placement problems for the estimation of both stationary and non-stationary fields are formulated as relaxed convex optimization problems, constrained by static or dynamic performance criteria. Finally, an iterative sparsity-enhancing saddle point method is formulated to solve both of these sensor placement problems.