Abstract-The paper addresses the problem of joint signal separation and estimation in a single-channel discrete-time signal composed of a wandering baseline and overlapping repetitions of unknown (or known) signal shapes. All signals are represented by a linear state space model (LSSM). The baseline model is driven by white Gaussian noise, but the other signal models are triggered by sparse inputs. Sparsity is achieved by normal priors with unknown variance (NUV) from sparse Bayesian learning. All signals and system parameters are jointly estimated with an efficient expectation maximization (EM) algorithm based on Gaussian message passing, which works both for known and unknown signal shapes. The proposed method outputs a sparse multi-channel representation of the given signal, which can be interpreted as a signal labeling.

Priors with a NUV representation (normal with unknown variance) have mostly been used for sparsity. In this paper, a novel NUV prior is proposed that effectively binarizes. While such a prior may have many uses, in this paper, we explore its use for discrete-level control (with M ≥ 2 levels) including, in particular, a practical scheme for digital-to-analog conversion. The resulting computations, for each planning period, amount to iterating forward-backward Gaussian message passing recursions (similar to Kalman smoothing), with a complexity (per iteration) that is linear in the planning horizon. In consequence, the proposed method is not limited to a short planning horizon and can therefore outperform "optimal" methods. A preference for sparse level switches can easily be incorporated.Index Terms-Discrete-level priors, normals with unknown variance (NUV), finite-control-set model predictive control (MPC), digital-to-analog conversion (DAC).

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The paper proposes a new method to determine a binary control signal for an analog linear system such that the state, or some output, of the system follows a given target trajectory. The method can also be used for digital-to-analog conversion.The heart of the proposed method is a new binaryenforcing NUV prior (normal with unknown variance). The resulting computations, for each planning period, amount to iterating forward-backward Gaussian message passing recursions (similar to Kalman smoothing), with a complexity (per iteration) that is linear in the planning horizon. In consequence, the proposed method is not limited to a short planning horizon.Index Terms-Discrete-level priors, normals with unknown variance (NUV), finite-control-set model predictive control (MPC), digital-to-analog conversion (DAC).

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