Kalman Clock Synchronization With DAC Gain State Estimation
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Solution Overview
Problem
Existing time synchronization systems using Kalman filters face inaccuracies due to variability in the unit step gain (kv) of digital-to-analog converters (DACs) affecting the precision of phase and frequency error estimation in voltage-controlled crystal oscillators, leading to unsatisfactory state estimate accuracy.
Innovation Solution
A system and method that utilize a Kalman filter with a state transition matrix including a coefficient associated with the DAC to determine state variables, specifically a unit step variable, to synchronize a local clock with a master clock, accounting for the variability in the unit step gain, thereby improving synchronization precision.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If a traditional Kalman filter with constant kv is used, then the system is simple to implement, but the state estimate accuracy deteriorates due to variability in unit step gain
Solution Approach 1:
The patent transforms the static, constant kv model into a dynamic model where kv becomes a time-varying state variable estimated by the Kalman filter. The state transition matrix incorporates kv variability through terms like (1 + αT) and the control gain matrix adapts using estimated kv values, allowing the system to track and compensate for gain variations over time and operating conditions.
Solution Approach 2:
The patent changes the parameter representation by treating kv not as a fixed constant but as an estimated state variable that evolves over time. The state vector includes kv,n and the state transition matrix uses parameters like α (gain variation coefficient) to model how kv changes, enabling the filter to adapt to parameter variations while maintaining estimation accuracy.
2Ease of manufacture
If a constant model for kv according to manufacturer specification sheets is used, then the formulation is simple, but synchronization precision deteriorates for applications requiring precise synchronization
Solution Approach 1:
The patent implements feedback by using the Kalman filter to continuously estimate kv based on observed synchronization errors and DAC inputs. The estimated kv,n values are fed back into the control gain matrix Bn and state transition matrix Fn, creating a closed-loop system that automatically compensates for gain variations without requiring manual calibration or complex manufacturing specifications.
Solution Approach 2:
The system performs self-calibration by estimating kv from its own operation data. The Kalman filter uses the relationship between DAC inputs dn and observed frequency/phase errors to automatically determine the actual kv values for that specific device and operating condition, eliminating dependence on manufacturer specification sheets and part-to-part variability.
3Device complexity
If the traditional linear relationship between fe,n and dn is assumed, then the model is simple, but accuracy deteriorates because the relationship is not generally linear in practice
Solution Approach 1:
The patent addresses non-linearity by making the control gain matrix Bn time-varying and state-dependent. Instead of a constant linear relationship, Bn uses the estimated kv,n values to adapt the gain at each time step, and the state transition matrix Fn includes terms like (1 + αT) that model non-linear behavior. This allows the model to capture non-linear relationships while maintaining a computationally tractable form.
Data Source
AI summary
In one embodiment, a local clock is synchronized to a master clock using a Kalman filter to determine state variables using a state transition matrix that includes at least one coefficient that is associated with a digital-to-analog converter (DAC), where the state variables include a unit step variable indicative of a unit step for the system. The local clock is controlled based on the state variables determined using the Kalman filter. The unit step is indicative of an amount by which the frequency of the local clock signal changes in response to a change in the digital input of the DAC.