Luis Arceo-Miquel

Optimal Synchronization of Local Clocks by GPS 1PPS Signals Using Predictive FIR Filters

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.

Efficient predictive estimator for holdover in GPS-based clock synchronization

This paper addresses an unbiased p-step predictive finite impulse response (FIR) filter of the local clock K-degree time interval error (TIE) polynomial model with applications to the global positioning system (GPS)-based clock synchronization. Generic coefficients are derived for a 2-parameter family of the polynomial filter gains. A generalization is provided for the p-step linear (ramp) gain allowing for close to optimal predictive filtering of the TIE. Basic holdover algorithms are discussed along with their most critical properties. Efficiency of the proposed filter in holdover is demonstrated by simulation and in real applications to GPS-based (sawtooth and sawtoothless) measurements of the TIE of a crystal clock.

Moving Average Hybrid FIR Filter in Ultrasound Image Processing

In this work, we present a novel technique for ultrasound image processing (2D signals). The moving average hybrid FIR filter (MAH-FIR) which it work with two different FIR filter, the moving average (MA) and median hybrid (FMH) filters. We experimented with continuous linear regression function and Lagrange multiplier to obtain the approximation of the MA-FIR and FMH-FIR filters, respectively. Furthermore, we showed both filters composed into a block diagram. Finally, we present evaluations qualitative and quantitative of ultrasound image processing.

Investigation of an Optimum Sampling Interval for a Local Clock TIE Model with an Unbiased FIR Filtering Algorithm

An investigation of the optimal time step (sampling interval) is provided for the time interval error (TIE) model of a local crystal clock in GPS-based timekeeping. For the sawtooth noise of a receiver, the local clock states are estimated employing an unbiased finite impulse response (FIR) filtering algorithm. We exploit the local crystal clock imbedded to the Stanford Frequency Counter SR620. The measurements are provided using the SynPaQ III GPS Sensor as a timing receiver and rubidium clock (SR625) as a reference source of time for the crystal clock

Experimental Comparison of the Unbiased FIR Estimates vs. the Sawtooth Correction in GPS-based Timekeeping

The trade-off is investigated experimentally between the real-time unbiased FIR estimates of the time interval error (TIE) model of a local clock and the sawtooth correction implemented to the measurement set. We exploit the crystal oscillator embedded to the Stanford Frequency Counter SR620 as a local clock and rubidium oscillator attached to SR625 as a reference clock. The SynPaQ III GPS Sensor is used as the GPS timing receiver. We show that the unbiased FIR estimates produce a lower error than the sawtooth correction. The error becomes much lower when the TIE changes very slowly. The unbiased FIR estimates of the fractional frequency offset are consistent to the rubidium measurements and produce much lower noise than in the measurements with the sawtooth correction

Efficient predictive steering of local clocks in GPS-based timekeeping

We discuss optimal synchronization of local clocks by the Global Positioning System (GPS) one pulse per second (1PPS) timing signals. To eliminate sawtooth errors peculiar to the 1PPS signals and optimally steer the clock errors each M seconds, we propose using 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 demonstrated experimentally.

A numerical comparison of the unbiased FIR and Kalman filters in applications to GPS-based timekeeping

The 3-state unbiased finite impulse response (FIR) filter and the 3-state Kalman filters are investigated for the time interval error (TIE) K-degree polynomial model of a local crystal clock in GPS-based timekeeping in presence of the sawtooth noise induced by the receiver. We show that both algorithms produce consistent estimates for the reference (rubidium) measurements. We also demonstrate that the unbiased FIR algorithm produces a lower error than the standard Kalman filter in presence of the sawtooth noise

Real-time Frequency Estimation of Local Oscillators Using GPS Timing Receivers

In this paper, we show that recently designed the finite impulse response (FIR) filtering algorithm provides realtime estimation of the fractional frequency offset of a local clock with high accuracy via GPS-based measurements of the time interval error (TIE). Such a splendid property of the algorithm is due to small produced noise in the estimates of the TIE. It is also shown that the algorithm applied to sawtooth measurements serves as a nice estimator of the Allan deviation. The latter cannot be estimated via sawtooth-less measurements.

Optimum Time Step and Memory for GPS-based Unbiased FIR Estimates of the Local Clock TIE Model

In this paper, we address a theoretical analysis of errors of the l-degree unbiased finite impulse response (FIR) filter applied to the if-degree time interval error (TIE) model of a local clock. Emphasizing the fact that the TIE model originates from the slowly changing Brownian phase and thus cannot obligatorily be distinct on a horizon of N points, we investigate estimates for l ne K and derive optimal horizons Nopt(Topt) as functions of the optimal time step Topt. Practical justification is provided based upon GPS-based sawtooth measurements of the TIE of a crystal clock imbedded to the Stanford Frequency Counter SR620 and using the SynPaQ III GPS Sensor and Symmetricom cesium standard of frequency as a reference source.

Experimental evaluation of the tie of the crystal clock vs. gps timing receiver without/with the negative sawtooth correction

The time interval error (TIE) is a measure of inaccuracy that is widely used now in timekeeping and evaluating the clock performance. In this paper, we investigate and develop a system (hardware and software) for TIE measurements. The system contains two TIE counters, a divider of frequency, reference rubidium clock, local crystal clock, and GPS timing receiver. Applied software provides reading and processing the TIE and decodes the negative sawtooth from the GPS timing receiver. The objective is to estimate the TIE of a local clock with and without the sawtooth correction.