This paper presents a simple, linear and robust filter for estimating the magnitudes of sinusoids of known frequencies embedded in an unknown measurement noise, which can be a mixture of both stochastic and deterministic signals. The algorithm is simple in comparison to Kalman filtering and is superior to the one-cycle Fourier transform algorithm, and can be easily implemented for real time measurements, when there is abnormal changes in the signal. Some typical case studies like the power network containing rectifier loads, thyristor controller reactors, harmonic rich non-linear loads, transformer circuits have been conducted. The results show the effectiveness of the filter in extracting the necessary signal components when noise is present along with the signal.