Standard open loop linear adaptive signal processing algorithms derived from the least squares minimization criterion require estimates of the N-dimensional input interference and noise statistics. Often, estimated statistics are biased by contaminant data (such as outliers and non-stationary data) that do not fit the dominant distribution, which is often modeled as Gaussian. In particular, convergence of sample covariance matrices used in block processed adaptive algorithms, such as the Sample Matrix Inversion (SMI) algorithm, are known to be affected significantly by outliers, causing undue bias in subsequent adaptive weight vectors. The convergence measure of effectiveness (MOE) of the benchmark SMI algorithm is known to be relatively fast (order K = 2N training samples) and independent of the (effective) rank of the external interference covariance matrix, making it a useful method in practice for non-contaminated data environments. Novel robust adaptive algorithms are introduced here that perform superior to SMI algorithms in contaminated data environments while some retain its valuable convergence independence feature. Convergence performance is shown to be commensurate with SMI in non-contaminated environments as well. The robust algorithms are based on the Gram Schmidt Cascaded Canceller (GSCC) structure where novel building block algorithms are derived for it and analyzed using the theory of Robust Statistics. Coined M – cancellers after M – estimates of Huber, these novel cascaded cancellers combine robustness and statistical estimation efficiency in order to provide good adaptive performance in both contaminated and non-contaminated data environments. Additionally, a hybrid processor is derived by combining the Multistage Wiener Filter (MWF) and Median Cascaded Canceller (MCC) algorithms. Both simulated data and measured Space-Time Adaptive Processing (STAP) airborne radar data are used to show performance enhancements. The STAP application area is described in detail in order to further motivate research into robust adaptive processing. / Ph. D.