An Up-Sampled Particle Filter Fusion Technique and Its Application in Synthetic Aperture Radar Imaging

Global positioning system (GPS) and inertial measurement units (IMUs) are often combined to produce navigation systems for airborne imaging platforms. The current state-of-the-art radar technology allows for radars to pulse at very high rates. GPS and IMU update rates are not fast enough to accurately report the platform position for each radar pulse. Independent GPS and IMUs cannot provide positional accuracy for long term stability. Traditional techniques, such as the Kalman and particle filter, are used to fuse GPS and IMU measurements. The Kalman filter excels for linear and Gaussian systems whereas the particle filter excels at non-linear and non-Gaussian systems. Sensor fusion techniques are used to help correct for IMU errors and provide the positional accuracy required for synthetic aperture radar (SAR) imaging applications. However, SAR requires the fusion algorithms to provide faster update rates. This paper explores the use of an up-sampled particle filter (UPF) for SAR to provide highly accurate position estimates at sampling frequencies comparable to radar pulse rates and overcome the limitations of standard interpolation techniques. This up-sampled particle filter is proven through simulations and instrumentation with a NovAtel GPS and IMU. The UPF technique allows for the GPS/IMU sampling rate to be different from the radar pulse repetition frequency (PRF) while providing accurate position solutions for each radar pulse capable of compensating for the phase history required for focusing a SAR image. The algorithms are instrumented in a SAR system and the position estimates are further validated and demonstrated through captured SAR images.