Architecture for Real-Time Nonparametric Probability Density Function Estimation

Adaptive systems are increasing in importance across a range of application domains. They rely on the ability to respond to environmental conditions, and hence real-time monitoring of statistics is a key enabler for such systems. Probability density function (PDF) estimation has been applied in numerous domains; computational limitations, however, have meant that proxies are often used. Parametric estimators attempt to approximate PDFs based on fitting data to an expected underlying distribution, but this is not always ideal. The density function can be estimated by rescaling a histogram of sampled data, but this requires many samples for a smooth curve. Kernel-based density estimation can provide a smoother curve from fewer data samples. We present a general architecture for nonparametric PDF estimation, using both histogram-based and kernel-based methods, which is designed for integration into streaming applications on field-programmable gate array (FPGAs). The architecture employs heterogeneous resources available on modern FPGAs within a highly parallelized and pipelined design, and is able to perform real-time computation on sampled data at speeds of over 250 million samples per second, while extracting a variety of statistical properties.