ITERATIVE AND SEQUENTIAL ALGORITHMS FOR MULTISENSOR SIGNAL ENHANCEMENT

In problems of enhancing a desired signal in the presence of noise, mu ltiple sensor measurements will typically have components from both th e signal and the noise sources. When the systems that couple the signa l 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 whi ch the desired signal is modeled as a Gaussian autoregressive (AR) pro cess, the noise is modeled as a white Gaussian process, and the coupli ng systems are modeled as linear time-invariant finite impulse respons e (FIR) filters. Our primary approach consists of modeling the observe d signals as outputs of a stochastic dynamic linear system, and we app ly the Estimate-Maximize (EM) algorithm for jointly estimating the des ired signal, the coupling systems, and the unknown signal and noise sp ectral parameters. The resulting algorithm can be viewed as the time-d omain version of our previously suggested frequency-domain approach [4 ], where instead of the noncausal frequency-domain Wiener filter, we u se the Kalman smoother. This time-domain approach leads naturally to a sequential/adaptive algorithm by replacing the Kalman smoother with t he Kalman filter, and in place of successive iterations on each data b lock, the algorithm proceeds sequentially through the data with expone ntial 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 Kalma n filtering equations. An expression for the log-likelihood gradient b ased on the Kalman smoother/filter output is also developed and used t o incorporate efficient gradient-based algorithms in the estimation pr ocess.