Feedback median filter for robust preprocessing of glint noise

The Kalman filter is widely applied in target tracking problems. It is known to be the linear optimal filter in the white Gaussian noise environment. In some radar applications [1–9], the measurement noise may deviate from the Gaussian assumption. For instance, complex targets can cause irregular electromagnetic wave reflection. This phenomenon varies the target center in a radar and gives rise to outliers in angle tracking, known as “target glint.” The glint noise has a long-tailed distribution [1, 2] and can severely degrade the Kalman filter performance. Kalman filtering with non-Gaussian noise has been a difficult problem. In 1975, Masreliez [10, 11] introduced a score function based scheme. While this approach looks promising, he encountered some implementation problems. Wu [4, 5] developed an efficient method to approximate the score function and applied it to target tracking problems. He also incorporated the Masreliez filter into the interacting multiple model (IMM) algorithm and obtained a nonlinear IMM algorithm [6]. Daeipour and Bar-shalom [9] characterized glint noise as a mixture of two Gaussian components and used two different models to represent the noise arising from these two Gaussian components. By doing so, they were able to apply the original IMM tracking algorithm. When the radar pulse repetition rate is higher than the requisite tracking rate, a tracking system can provide more measurement data than that it can process. In this case, there is a simple approach to deal with glint noise: we can preprocess a batch of measurements and then forward the results to the Kalman filter. One intuitive thought to perform preprocessing may be the use of sample averaging. It can be easily shown that this simple operation is optimal when the target is still and the measurement noise is Gaussian. Wang and Varshney [12, 13] used the maximum likelihood (ML) estimation as the preprocessing algorithm to enhance tracking performance. They considered the case where the target has a constant velocity and the measurement noise is Gaussian. They found that the optimal estimate is also the averaging operation. When the measurement noise is non-Gaussian, averaging is not optimal anymore. Hewer, Martin, and Zeh [1] proposed to use the robust M-estimator as the preprocessing scheme. They showed that the Kalman filter performance can be greatly enhanced. Although the robust algorithm is effective, it requires intensive computations. In addition, this approach assumed that the target position is constant in the preprocessing batch, which may not hold in all situations. An alternative technique using the median filter is studied here. Due to its simplicity and good properties, the median filter is widely used in image processing [14—17]. There are three distinct