For a moving target indicating (MTI) radar system to eliminate ``blind speeds'' or synthetic aperture radar (SAR) to eliminate ``blind ranges,'' two or more pulse repetition intervals (PRIs) are often used sequentially. This article proposes a new correlation-matching algorithm to estimate the PRIs, despite the radar receiver possibly missing some time samples. This proposed algorithm operates in the orthonormal Ramanujan subspace, leading to fewer nonzero elements therein, thus reducing the computational load. This proposed algorithm employs the lp-norm (instead of the l₂-norm) in computing the correlation coefficients, for better robustness against outliers. Simultaneously, a new divisor rule, instead of the least common multiple (LCM) rule, and an algorithm for computing the threshold are proposed to identify the frame period of the staggered pulse train in the presence of spurious peaks. This new algorithm improves estimation accuracy and is robustness to missing pulse and PRI jitter.

In this study, the problem of spatio‐temporal‐polarisation filtering based on hypercomplex processes is considered for an electromagnetic (EM) vector‐sensor array. The quaternion domain facilitates modelling and processing of four‐dimensional real signals (or two‐dimensional complex signals). Based on the quaternion model of linear symmetric array with two‐components EM vector‐sensors, an interference and noise canceller (INC) is presented for polarised signals. Then, the output signal to interference‐plus‐noise ratio (SINR) expression of INC is derived and its performance is analysed. The performance analysis reveal explicitly the fact that even though no separation between the direction of arrival (DOAs) of the desired signal and interference, the maximum value of output SINR can be obtained employing the orthogonality between the polarisations of the desired signal and interference. Simulation results show that if sample size N is large enough, the INC has larger output SINR and better robustness against the DOA mismatch.

Motivated by the benefits of array signal processing in quaternion domain, we investigate the problem of adaptive beamforming based on complex quaternion processes in this paper. First, a complex quaternion least‐mean squares (CQLMS) algorithm is proposed and its performance is analyzed. The CQLMS algorithm is suitable for adaptive beamforming of vector‐sensor array. The weight vector update of CQLMS algorithm is derived based on the complex gradient, leading to lower computational complexity. Because the complex quaternion can exhibit the orthogonal structure of an electromagnetic vector‐sensor in a natural way, a complex quaternion model in time domain is provided for a 3‐component vector‐sensor array. And the normalized adaptive beamformer using CQLMS is presented. Finally, simulation results are given to validate the performance of the proposed adaptive beamformer.