In this paper, we discuss optimal synchronization of local clocks using Global Positioning System (GPS) one-pulse-per-second (1PPS) timing signals. To eliminate sawtooth errors that are peculiar to the 1PPS signals and optimally steer the clock errors each M seconds, we propose the use of a ramp-predictive finite-impulse-response (FIR) filter that is known to be optimal for clock models on large averaging horizons. A low-pass filter is used to smooth the hold filter output between the optimally predicted points. A GPS-locked crystal clock has been investigated in detail in terms of the time interval error, Allan deviation, and precision time protocol (PTP) variance. A high-efficiency implementation of the proposed synchronization algorithm is experimentally demonstrated.

Methods of the electrocardiography (ECG) signal features extraction are required to detect heart abnormalities and different kinds of diseases. However, different artefacts and measurement noise often hinder providing accurate features extraction. One of the standard techniques developed for ECG signals employs linear prediction. Referring to the fact that prediction is not required for ECG signal processing, smoothing can be more efficient. In this paper, we employ the p-shift unbiased finite impulse response (UFIR) filter, which becomes smooth by p<0. We develop this filter to have an adaptive averaging horizon: optimal for slow ECG behaviours and minimal for fast excursions. It is shown that the adaptive UFIR algorithm developed in such a way provides better denoising and suboptimal features extraction in terms of the output signal-noise ratio (SNR). The algorithm is developed to detect durations and amplitudes of the P-wave, QRS-complex, and T-wave in the standard ECG signal map. Better performance of the algorithm designed is demonstrated in a comparison with the standard linear predictor, UFIR filter, and UFIR predictive filter based on real ECG data associated with normal heartbeats.

Industrial wireless sensor networks (WSNs) often operate under harsh conditions that require robustness from an estimator of a measured quantity. We propose a novel distributed unbiased finite-impulse response (UFIR) filter called micro-UFIR filter that, unlike the micro-Kalman filter (micro-KF), is robust against modeling errors in uncertain noise environments. The micro-UFIR filter is derived based on average consensus on measurements and, unlike the micro-KF, requires only one consensus filter. Better robustness of the micro-UFIR filter is shown analytically and confirmed by simulations of a WSN and a vehicle travelling along a circular trajectory under unpredictable impacts, impulsive noise, and errors in the noise statistics.

The general unbiased finite-impulse response (UFIR) filter proposed in this brief has important structural advantages against its basic predecessor. It can be applied to systems with or without the control input. We derive this filter in a batch form and then design its fast iterative Kalman-like algorithm using recursions. The iterative UFIR algorithm proposed is applied to the three-state polynomial model which is basic in clock synchronization. We test it by the global positioning system-based frequency steering of an oven-controlled crystal oscillator. Better robustness and higher accuracy of the UFIR filter against the Kalman filter are shown experimentally.