Approximately Optimal Resource Management for Multi-Function Radar: Algorithmic Solutions Using a Generic Framework

Recent advances in Multi-Function Radar (MFR) systems led to an increase in their degrees of freedom. As a result, modern MFR systems are capable of adjusting many parameters during runtime. An automatic adaptation of the radar system to changing situations, like weather conditions, interference, or target maneuvers, is often mentioned in the context of MFR and is usually called Radar Resource Management (RRM). This thesis aims at developing a generic framework and approximately optimal algorithmic solutions for solving RRM problems. This is achieved by formulating the sensor tasks as Partially Observable Markov Decision Processes (POMDPs). Although the focus is on MFR, the approach is not limited to such sensor systems and has broader applicability.

In Chapter 2, a first step is taken by investigating Lagrangian Relaxation (LR) and the subgradient method for optimally distributing the sensor resources to the different tasks in a multi-target tracking scenario. A constrained optimization problem is formulated. Using LR, the constraints can be included in the cost function. In a time-invariant scenario, it is shown that the proposed Optimal Steady-State Budget Balancing (OSB) algorithm will lead to balanced budgets based on track parameters like maneuverability and measurement uncertainty. The time-invariant scenario is a special case of general tracking scenarios, and the presented solution can be seen as the optimal POMDP solution in that case. Since real-world applications quickly lead to time-varying scenarios, it is demonstrated how the approach can be extended to such cases. Finally, the proposed method is compared with other budget assignment strategies.

Subsequently, the tracking tasks are explicitly formulated as POMDPs, and the novel Approximately Optimal Dynamic Budget Balancing (AODB) algorithm is proposed in Chapter 3. The algorithm applies a combination of LR and Policy Rollout (PR). PR is a Monte Carlo sampling method for POMDPs to find the expected future cost. Due to its generic architecture, the framework can be applied to different radar or sensor systems and cost functions. In a time-invariant scenario, the algorithm calculates a solution close to the optimal steady-state solution, as presented in Chapter 2. This is shown through simulations of a two-dimensional tracking scenario. Moreover, it is demonstrated how the algorithm dynamically allocates the sensor time budgets to the tasks in a changing environment using a non-myopic fashion. Finally, the algorithm's performance is compared with different resource allocation techniques.

Based on the previous results, Chapter 4 conducts a detailed investigation of the computational load of the AODB algorithm. It is shown how the choice of several input parameters influences computational performance. Additionally, Model Predictive Control (MPC) is applied in the same framework as an alternative POMDP solution method. Compared to stochastic optimization methods such as PR, the computational load is dramatically reduced while the resource allocation results are similar. This is shown through simulations of dynamic multi-target tracking scenarios in which the cost and computational load of different approaches are compared.

So far, this thesis has used tracking scenarios to demonstrate the validity of the proposed algorithms. Chapter 5 shows how to apply the proposed framework and algorithmic solution to a multi-target joint tracking and classification scenario. It is shown that tracking and classification can be considered in a single task type. Furthermore, it is shown how the task resource allocations can be jointly optimized using a single carefully formulated cost function based on the task threat variance. Multiple two-dimensional radar scenarios demonstrate how sensor resources are allocated depending on the current knowledge of the target position and class.

Chapter 6 extends the single-sensor approach shown in the previous chapters to multiple sensors and demonstrates the usefulness of the proposed algorithm in two different multi-sensor multi-target tracking scenarios. The first scenario considers a generic surveillance situation. An approximately optimal approach based on the previously proposed algorithm is formulated assuming a central processor. Subsequently, a distributed implementation is introduced that converges to the same results as the centralized implementation and requires less computational resources. The performance of the proposed approach for both centralized and distributed implementation is demonstrated through dynamic tracking scenarios. The second scenario focuses explicitly on an automotive application. The proposed generic framework and algorithmic solution are used to allocate scarce resources across multiple mobile sensor nodes. A central system manages the nodes' transmission and shares sensing data with other sensor nodes if this improves the overall track accuracy. The proposed method allocates time and frequency resources. Through simulation of a typical traffic situation, the validity of the approach is demonstrated.

This thesis shows that the application of the proposed novel generic framework and algorithmic solution increases the performance w.r.t. heuristic solutions. Furthermore, it is demonstrated that the proposed framework allows the user to exchange elements such as cost function or POMDP solution method to adjust it to specific needs. The proposed method can be applied in many different areas involving different types of sensors. Possible applications include automotive scenarios, such as autonomous driving or traffic monitoring, (maritime) surveillance, and air traffic control.