Online Mean And Variance Computation With A Forgetting Factor
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Solution Overview
Problem
Computing sample mean and variance of large data sets is computationally expensive and requires significant memory, making it challenging for online applications such as tracking/filtering of road users with radars.
Innovation Solution
A computer-implemented method using a forgetting factor to iteratively update intermediate data for determining mean and variance, reducing the need for storing all measurements and allowing online applications with time-varying signals.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If computing sample mean and variance of large data sets is performed using traditional methods, then measurement precision is improved, but computational cost and memory requirements increase significantly
Solution Approach 1:
The patent extracts only the necessary statistical information (mean and variance) from the large dataset by using recursive computation formulas, rather than storing and processing all raw data points. This allows accurate computation of statistical parameters while avoiding the need to retain the entire dataset in memory.
Solution Approach 2:
The patent transforms the computation from a batch processing approach to an online recursive approach by changing the parameters of computation. Instead of computing mean and variance from all data at once, it uses updated values from previous time steps combined with current measurements, reducing memory and computational requirements at each step.
2Measurement precision
If all measurement data is stored for offline analysis, then measurement precision is improved, but adaptability for online applications deteriorates
Solution Approach 1:
The patent implements a dynamic computation system that adapts to online data streams by continuously updating statistical parameters as new measurements arrive. The recursive formulas allow the system to maintain accurate mean and variance estimates in real-time without requiring offline batch processing, enabling deployment in dynamic online applications.
3Adaptability or versatility
If intermediate data is updated iteratively using forgetting factor, then adaptability for time-varying signals is improved, but computational complexity increases
Solution Approach 1:
The patent maintains continuous computation of statistical parameters using recursive formulas that update mean and variance at each time step. The forgetting factor enables continuous adaptation to time-varying signals by weighting recent measurements higher than older ones, while the iterative nature of the computation keeps the system lightweight and suitable for real-time applications.
Data Source
AI summary
A computer implemented method for determining a mean and a variance of measurement data comprises the following steps carried out by computer hardware components: acquiring measurement data for a present time step using a sensor; updating a plurality of intermediate data for a previous time step based on the measurement data for the present time and based on a forgetting factor to obtain a plurality of intermediate data for the present time step; and determining the mean and the variance for the present time step based on the plurality of intermediate data for the present time step.