Robust filtering for uncertain discrete-time systems with uncertain noise covariance and uncertain observations

The use of Kalman filtering is very common in state estimation problems. The problem with Kalman filters is that they require full prior knowledge about the system modeling. It is also assumed that all the observations are fully received. In real applications, the previous assumptions are not true all the time. It is hard to obtain the exact system model and the observations may be lost due to communication problems. In this paper, we consider the design of a robust Kalman filter for systems subject to uncertainties in the state and white noise covariances. The systems under consideration suffer from random interruptions in the measurements process. An upper bound for the estimation error covariance is proposed. The proposed upper bound is further minimized by selection of optimal filter parameters. Simulation example shows the effectiveness of the proposed filter.<br /

Spike sorting using hidden markov models

In this paper, hidden Markov models (HMM) is studied for&nbsp;spike sorting. We notice that HMM state sequences have capability to&nbsp;represent spikes precisely and concisely. We build a HMM for spikes, where HMM states respect spike significant shape variations. Four shape&nbsp;variations are introduced: silence, going up, going down and peak. They&nbsp;constitute every spike with an underlying probabilistic dependence that is modelled by HMM. Based on this representation, spikes sorting becomes&nbsp;a classification problem of compact HMM state sequences. In addition,&nbsp;we enhance the method by defining HMM on extracted Cepstrum features, which improves the accuracy of spike sorting. Simulation results&nbsp;demonstrate the effectiveness of the proposed method as well as the efficiency