Iterative and sequential algorithms for multisensor signal enhancement

In problems of enhancing a desired signal in the presence of noise, multiple sensor measurements will typically have components from both the signal and the noise sources. When the systems that couple the signal and the noise to the sensors are unknown, the problem becomes one of joint signal estimation and system identification. In this paper, we specifically consider the two-sensor signal enhancement problem in which the desired signal is modeled as a Gaussian autoregressive (AR) process, the noise is modeled as a white Gaussian process, and the coupling systems are modeled as linear time-invariant finite impulse response (FIR) filters. Our primary approach consists of modeling the observed signals as outputs of a stochastic dynamic linear system, and we apply the Estimate-Maximize (EM) algorithm for jointly estimating the desired signal, the coupling systems, and the unknown signal and noise spectral parameters. The resulting algorithm can be viewed as the time-domain version of our previously suggested frequency-domain approach [4], where instead of the noncausal frequency-domain Wiener filter, we use the Kalman smoother. This time-domain approach leads naturally to a SequentWadaptive algorithm by replacing the Kalman smoother with the Kalman filter, and in place of successive iterations on each data block, the algorithm proceeds sequentially through the data with exponential weighting applied to allow adaption to nonstationary changes in the structure of the data. A computationally efficient implementation of the algorithm is developed by exploiting the structure of the Kalman filtering equations. An expression for the log-likelihood gradient based on the Kalman smootherhlter output is also developed and used to incorporate efficient gradient-based algorithms in the estimation process.