Running Mean and Variance Updates for Real-Time Radar Tracking
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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 and filtering of road users with radars.
Innovation Solution
An iterative and adaptive method using a forgetting factor to update intermediate data, allowing for efficient determination of mean and variance in real-time without storing all measurements, utilizing a computer system with a processor, memory, and non-transitory data storage to implement the method.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If all measurement data is stored and processed to compute mean and variance, then measurement precision is improved, but device complexity and memory requirements increase
Solution Approach 1:
The patent extracts only the essential statistical information (mean and variance) from the measurement data stream without storing all raw data points. By maintaining running sums and sums of squares, the system computes accurate statistical parameters while discarding the need to retain individual measurement values, thereby reducing memory requirements and computational complexity.
Solution Approach 2:
The patent transforms the problem from storing and processing N individual data points to maintaining three running parameters (sum of measurements, sum of squared measurements, and count). This parameter transformation enables constant-time updates and O(1) memory usage while preserving the ability to compute accurate mean and variance values.
2Measurement precision
If all measurement data is stored for offline processing, then measurement precision is improved, but loss of time increases
Solution Approach 1:
The patent performs preliminary computation by continuously updating running sums and sums of squares as measurements arrive. This preliminary action enables immediate computation of mean and variance without waiting for data collection to complete, eliminating processing delays while maintaining statistical accuracy.
Solution Approach 2:
The patent implements continuous computation where the running sums and sums of squares are updated continuously as new measurements arrive. This continuous action allows the system to provide up-to-date statistical information in real-time rather than requiring batch processing, thereby eliminating time loss while preserving measurement precision.
Data Source
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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.