This article introduces a Poisson multi-Bernoulli mixture (PMBM) filter in which the intensities of target birth and undetected targets are grid-based. A simplified version of the Rao-Blackwellized point mass filter is used to predict the intensity of undetected targets and to initialize tracks of targets detected for the first time. The grid approximation can efficiently represents intensities with abrupt changes with relatively few grid points compared to the number of Gaussian components needed in conventional PMBM implementations. This is beneficial in scenarios where the sensors field of view is limited. The proposed method is illustrated in a sensor management setting, where trajectories of sensors with limited fields of view are controlled to search for and track the targets in a region of interest.

The problem of path planning for mobilesensors with the task of target monitoring is considered. A receding horizon optimal control approach based on the information filter is presented, where the limited field of view of the sensor can be modeled by introducing binary variables. The resulting nonlinear mixed integer problem to be solved in each sample, with no apparent tractable solution, is shown to be equivalent to a problem that robustly can be solved to global optimality using off-the-shelf optimization tools.

For a given radar system on an unmanned air vehicle, this work proposes a method to find the optimal tracking rangeand the optimal beamwidth for tracking a maneuvering target.  An inappropriate optimal range or beamwidth is indicative ofthe need for a redesign of the radar system. An extended Kalman filter (EKF) is employed to estimate the state of the target using measurements of the range and bearing from the sensor to the target. The proposed method makes use of an alpha-beta filter to predict the expected tracking performanceof the EKF. Using an assumption of the maximum acceleration of the target, the optimal tracking range (or beamwidth) is determined as the one that minimizes the maximum mean squared error (MMSE) of the position estimates while satisfying a user-defined constraint on the probability of losing track of the target.The applicability of the design method is verified using Monte Carlo simulations.

This paper proposes a method to generate informative trajectories for a mobile sensor that tracks agile targets.The goal is to generate a sensor trajectory that maximizes the tracking performance, captured by a measure of the covariance matrix of the target state estimate. The considered problem is acombination of estimation and control, and is often referred to as informative path planning (IPP). When using nonlinear sensors, the tracking performance depends on the actual measurements, which are naturally unavailable in the planning stage.The planning problem hence becomes a stochastic optimization problem, where the expected tracking performance is used inthe objective function. The main contribution of this work is anapproximation of the problem based on deterministic sampling of the predicted target distribution. This is in contrast to prior work, where only the most likely target trajectory is considered.It is shown that the proposed method greatly improves the ability to track agile targets, compared to a baseline approach.   

Many practical applications, such as search and rescue operations and environmental monitoring, involve the use of mobile sensor platforms. The workload of the sensor operators is becoming overwhelming, as both the number of sensors and their complexity are increasing. This thesis addresses the problem of automating sensor systems to support the operators. This is often referred to as sensor management. By planning trajectories for the sensor platforms and exploiting sensor characteristics, the accuracy of the resulting state estimates can be improved. The considered sensor management problems are formulated in the framework of stochastic optimal control, where prior knowledge, sensor models, and environment models can be incorporated. The core challenge lies in making decisions based on the predicted utility of future measurements.

In the special case of linear Gaussian measurement and motion models, the estimation performance is independent of the actual measurements. This reduces the problem of computing sensing trajectories to a deterministic optimal control problem, for which standard numerical optimization techniques can be applied. A theorem is formulated that makes it possible to reformulate a class of nonconvex optimization problems with matrix-valued variables as convex optimization problems. This theorem is then used to prove that globally optimal sensing trajectories can be computed using off-the-shelf optimization tools. 

As in many other fields, nonlinearities make sensor management problems more complicated. Two approaches are derived to handle the randomness inherent in the nonlinear problem of tracking a maneuvering target using a mobile range-bearing sensor with limited field of view. The first approach uses deterministic sampling to predict several candidates of future target trajectories that are taken into account when planning the sensing trajectory. This significantly increases the tracking performance compared to a conventional approach that neglects the uncertainty in the future target trajectory. The second approach is a method to find the optimal range between the sensor and the target. Given the size of the sensor's field of view and an assumption of the maximum acceleration of the target, the optimal range is determined as the one that minimizes the tracking error while satisfying a user-defined constraint on the probability of losing track of the target.    

While optimization for tracking of a single target may be difficult, planning for jointly maintaining track of discovered targets and searching for yet undetected targets is even more challenging. Conventional approaches are typically based on a traditional tracking method with separate handling of undetected targets. Here, it is shown that the Poisson multi-Bernoulli mixture (PMBM) filter provides a theoretical foundation for a unified search and track method, as it not only provides state estimates of discovered targets, but also maintains an explicit representation of where undetected targets may be located. Furthermore, in an effort to decrease the computational complexity, a version of the PMBM filter which uses a grid-based intensity to represent undetected targets is derived.