2022, Wildhaber, Reto, Baeriswil, Christof, Bertrand, Alexander

2017, Zalmai, Nour, Wildhaber, Reto, Loeliger, Hans-Andrea

The paper addresses the problem of fitting, at any given time, a parameterized signal generated by an autonomous linear state space model (LSSM) to discrete-time observations. When the cost function is the squared error, the fitting can be accomplished based on efficient recursions. In this paper, the squared error cost is generalized to more advanced cost functions while preserving recursive computations: first, the standard sample-wise squared error is augmented with a sampledependent polynomial error; second, the sample-wise errors are localized by a window function that is itself described by an autonomous LSSM. It is further demonstrated how such a signal estimation can be extended to handle unknown additive and/or multiplicative interference. All these results rely on two facts: first, the correlation function between a given discrete-time signal and a LSSM signal can be computed by efficient recursions; second, the set of LSSM signals is a ring.

2020, Wildhaber, Reto, Ren, Elizabeth, Waldmann, Frederic, Loeliger, Hans-Andrea

Local polynomial approximations represent a versatile feature space for time-domain signal analysis. The parameters of such polynomial approximations can be computed by efficient recursions using autonomous linear state space models and often allow analytical solutions for quantities of interest. The approach is illustrated by practical examples including the estimation of the delay difference between two acoustic signals and template matching in electrocardiogram signals with local variations in amplitude and time scale.

2016, Zalmai, Nour, Wildhaber, Reto, Clausen, Desiree, Loeliger, Hans-Andrea

Cell depolarization runs essentially in a uniform motion along the muscular tissue, which creates transient electrical potential differences measurable by nearby electrodes. Inferring the depolarization speed and direction from measurements is of great interest for physicians. In cardiology, this is part of the inverse ECG problem which often requires a large number of electrodes and intense computational power even if the simple common model of the single equivalent moving dipole (SEMD) is applied. In this paper, we model a depolarization process as a straight-line movement of a SEMD. We provide an efficient algorithm based on linear state space models that infers the SEMD movement using only 3 measurement channels from a tetrahedral electrode and with the presence of interferences. Our algorithm is tested both on simulated and experimental data.

2017, Wildhaber, Reto, Zalmai, Nour, Jacomet, Marcel, Loeliger, Hans-Andrea

We introduce a model-based approach for computationally efficient signal detection and discrimination, which is relevant for biological signals. Due to its low computational complexity and low memory need, this approach is well-suited for low power designs, as required for medical devices and implants. We use linear state space models to gain recursive, efficient computation rules and obtain the model parameters by minimizing the squared error on discrete-time observations. Furthermore we combine multiple models of different time-scales to match superpositions of signals of variable length. To give immediate access to our method, we highlight the use in several practical examples on standard and on esophageal ECG signals. This method was adapted and improved as part of a research and development project for medical devices.