In this study, an improved square root adaptive cubature Kalman filter (ISRACKF) is proposed to improve the filter performance in terms of accuracy, computation efficiency, and robustness. Through the evaluated measure of non-linearity value, the cubature rule under different accuracy levels can be adaptively selected in the dynamic process or measurement model. In this way, high accuracy can be maintained without sacrificing computation efficiency. Furthermore, the maximum correntropy criterion cost function can help improve the robustness of ISRACKF. The measure of non-Gaussianity value is utilised to control the computation complexity of the robust iterative process as well. The stability proof of estimated state error and covariance is given. The comparison results of the target tracking problem and integrated navigation system demonstrate the superior performance of the proposed ISRACKF in this study.

Compressive sensing deals with non-uniform sampling of a signal, at an average rate much less than the Nyquist rate, and recovery of the signal uniquely from these reduced set of measurements. Construction of an efficient measurement (sensing) matrix to enable unique recovery is a topic of interest since compressive sensing came to existence. The sensing operator should be efficient to capture the vital information content of the signal into a reduced set of discrete measurements. This study proposes a learning method to construct an efficient sensing matrix, having orthogonal rows, for compressed sensing of a class of signals. The learning scheme identifies the sensing matrix by maximising the entropy of measurement vectors. The bounds on the entropy of the measurement vector necessary for the unique recovery of a signal are proposed. A comparison of the performance of the designed sensing matrix and the sensing matrices constructed using other existing methods is also presented. The simulation results on the recovery of synthetic, speech, and image signals, compressively sensed using the sensing matrix identified, show an improvement in the accuracy of recovery. The reconstruction quality is better, using less number of measurements than those measured using sensing matrices identified by other methods.

This study presents a simple technique, which is used to estimate both channel state and carrier frequency offset (CFO) in decode-and-forward relay systems, where coded orthogonal frequency division multiplexing is employed without cyclic prefix. On the basis of the least-square criterion, we derive the estimate of CFO and channel with the aids of consecutive blocks of pilot symbols. The initially proposed estimation technique achieves a distinguished performance by using a two-dimensional complete search approach; however, the computation becomes more and more intensive when the search granularity becomes finer and finer. For this reason, we further present an iterative approach as an alternative solution, which provides a performance comparable with that of the complete search method, while greatly reducing the implementation complexity. Besides, we also derive a closed-form expression of the CFO estimate for the considered system, which allows us to avoid the exhaustive search during the estimation processing. Computer simulations have been conducted to verify the efficiency of the proposed schemes.