Arbitrary-step randomly delayed robust filter with application to boost phase tracking

The conventional filters such as extended Kalman filter, unscented Kalman filter and cubature Kalman filter assume that the measurement is available in real-time and the measurement noise is Gaussian white noise. But in practice, both two assumptions are invalid. To solve this problem, a novel algorithm is proposed by taking the following four steps. At first, the measurement model is modified by the Bernoulli random variables to describe the random delay. Then, the expression of predicted measurement and covariance are reformulated, which could get rid of the restriction that the maximum number of delay must be one or two and the assumption that probabilities of Bernoulli random variables taking the value one are equal. Next, the arbitrary-step randomly delayed high-degree cubature Kalman filter is derived based on the 5th-degree spherical-radial rule and the reformulated expressions. Finally, the arbitrary-step randomly delayed high-degree cubature Kalman filter is modified to the arbitrary-step randomly delayed high-degree cubature Huber-based filter based on the Huber technique, which is essentially an M-estimator. Therefore, the proposed filter is not only robust to the randomly delayed measurements, but robust to the glint noise. The application to the boost phase tracking example demonstrate the superiority of the proposed algorithms.