Kalman Filtered Compressive Sensing Using Pseudo-Measurements

In this paper, we combine the Kalman filter and compressive sensing using pseudo-measurements in order to reduce the number of measurements usually required by the Kalman filter. To overcome the non-sparsity of the measurement vectors, we make use of the change of their coefficients when represented in a certain basis, reduce the dimensionality of the coefficients, and learn a sparse basis for the measurement vectors. We further improve our proposed method by introducing dynamic weighting of the pseudo-measurements, by aiding compressive measurement reconstruction with Kalman filter estimates and by employing iterative versions of this process. Simulations show that our approach achieves a 37% improvement with respect to the mean-square error compared to the traditional Kalman filter with the same number of measurements. Our approach yields better results when the measurement noise is relatively large compared to the system noise, and it significantly improves the accuracy of state estimation in sensor networks with low sensor precision.