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This report presents a novel Kalman filtering approach to the suppression of narrowband interference from direct sequence spread spectrum communications systems. The algo-rithm is based on the digital phase-locked loop Kalman filter. Because the interference is assumed to be much stronger than either the signal or noise, the Kalman filter locks onto a function related to the interference. The net result is an estimate of the phase of the interference and its amplitude. The algorithm is characterized through computer simu-lation for the case of narrowband Gaussian noise interference. Examples of the phase-and envelope-tracking capabilties of the algorithm are presented, followed by bit error rate curves for interference bandwidths ranging from 0.5 % to 5.0 % of the chip rate of the spread spectrum signal. The report concludes with three adaptive architectures. The first is suitable for constant envelope interference; the second is a more general structure; and the third incorporates a decision-feedback structure accompanied with a training sequence. RtSUM]