The work is on Dynamic Compressed Sensing (DCS) system for efficient acquisition and recovery of sparse and compressible time-varying signals. DCS has three key components to be addressed: Estimation of the Sparsity level, indices of those sparse basis functions and their amplitudes. Sparsity Order Estimation (SOE) algorithms based on both Bernoulli/Gaussian sensing matrices and optimal tracking algorithms such as the Kalman filter and Viterbi Algorithm were developed. The developed algorithms resulted in reducing the complexity of CS methods by 25-30 % taking them closer to practical realization.