Parameterizable FPGA-Based Kalman Filter Coprocessor Using Piecewise Affine Modeling

The Kalman Filter is a robust tool often employed as a plant observer in control systems. However, in the general case the high computational cost, especially for large system models or fast sample rates, makes it an impractical choice for typical low-power microcontrollers. Industry trends towards tighter integration and subsystem consolidation point to the use of powerful high-end SoCs, but this complicates the ability for a controls engineer to verify correct behavior of the system under all conditions, which is important in safety-critical systems. Dedicated FPGA hardware can provide computational speedup, in addition to firmer design partitioning in mixed-criticality systems and fully deterministic timing, which helps ensure a control system behaves as close as possible to offline simulations. We introduce and compare two variants of a software-configurable FPGA-based implementation of a Kalman Filter. The first is an implementation of an Extended Kalman Filter, while the second is a novel approach -- the Piecewise-Affine Kalman Filter - which may offer significant advantages for certain types of applications. The state estimate update time and resource requirements are analyzed for plant models up to 28 states. For large models, the designs provide a speedup of 7-12x compared to reference ARM9020T software implementations. An application-agnostic performance analysis demonstrates how the Piecewise-Affine Kalman Filter reduces the software workload and the communication overhead compared to the standard mixed hardware-software Extended Kalman Filter approach.