Discrete State-Space Filtering for Asynchronous Sample Timing
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Solution Overview
Problem
Existing digital signal processing algorithms face challenges in handling asynchronously sampled data, as they are designed for uniform sampling, leading to increased costs, reduced performance, and complexity when dealing with asynchronous sampling due to factors like jitter, dropouts, and varying sampling periods.
Innovation Solution
A method and system that use a discrete state-space representation to directly apply a linear transfer function to asynchronously sampled data, allowing for the propagation of filter states independent of sample time, thereby adapting IIR filtering and control modeling to asynchronous conditions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If synchronous sampling is enforced to maintain filter performance, then measurement precision is improved, but device complexity and cost increase due to global clock requirements and synchronization infrastructure
Solution Approach 1:
The patent replaces the mechanical clock-synchronization system with a software-based time-stamping mechanism. Each asynchronous sample is tagged with its precise acquisition time, and the filter uses these time stamps to compute state transitions without requiring a global clock or synchronous sampling infrastructure.
Solution Approach 2:
The patent changes the sampling parameter from fixed time intervals (synchronous) to variable time intervals with explicit time recording (asynchronous). The filter adapts by using the actual time differences between samples as input parameters for its state transition calculations, rather than assuming uniform sampling periods.
2Device complexity
If asynchronous sampling is allowed to reduce system cost and complexity, then device complexity is reduced, but measurement precision deteriorates due to timing errors and data dropouts
Solution Approach 1:
The patent incorporates feedback by using the actual time difference between consecutive samples (Δt) as a key parameter in the state transition calculation. The filter continuously adapts to the actual sampling rhythm, whether uniform or irregular, by feeding the time stamp information back into the computation of the state transition matrix.
Solution Approach 2:
The patent makes the filter dynamic by allowing the state transition parameters to vary with each sample based on the actual time elapsed since the previous sample. Rather than using fixed transition matrices designed for uniform sampling, the filter recomputes or selects transition parameters based on the measured time difference, adapting to asynchronous conditions in real-time.
3Measurement precision
If oversampling is used to handle asynchronous data, then measurement precision is improved, but productivity decreases due to increased computational burden
Solution Approach 1:
The patent extracts and processes only the essential information from asynchronous samples: the data value and its time stamp. By working directly with the asynchronous sample stream and using the time difference as a computational parameter, the filter avoids the need to extract, interpolate, or resample data to create an oversampled synchronous sequence, thereby reducing computational overhead.
4Ease of operation
If synchronous sampling is enforced to simplify filtering algorithms, then ease of operation is improved, but adaptability worsens due to inability to handle variable sampling rates and dropouts
Solution Approach 1:
The patent creates a universal filter that can handle both synchronous and asynchronous sampling modes through the same algorithmic framework. By using time stamps and computing state transitions based on actual time differences rather than assuming uniform sampling, the filter becomes multi-functional, adapting to various sampling scenarios without requiring separate processing paths or complexity increases.
Data Source
Figure 1a~1b
Figure 2
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AI summary
A discrete state-space filter directly applies a linear transfer function that describes the frequency -domain representation of an IIR filter or control plant to asynchronously sampled data. The discrete state-space technique maps a continuous lime transfer function into the discrete state-space filter and stores the states of the filter in a sample-time independent fashion in a discrete state-space vector (step 18). The filter states are propagated with the asynchronous time measurements provided with the input data to generate the filtered output (steps 20 and 22)