The small error approximation is used to derive a linear relationship between the source parameters (i.e. power levels and directions of arrival) and a measurement of the covariance error matrix, defined as the difference between a nonparametric consistent estimate of the spectral density matrix and a covariance model from the scenario parameters. The resulting framework allows the design of a Kalman-like algorithm which provides a simultaneous and adaptive estimation of the source parameter, no matter what the source waveform or modulation. Good performance is expected, mainly in the presence of sensors malfunctioning, low signal-to-noise ratio, etc.