State Estimation Analysis With Non-Negative Sparse Cell Correction
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Solution Overview
Problem
The application of the Kalman filter to high-dimensional big data, such as mobile space statistics, results in positive bias, deviation from non-negative constraints, and increased calculation cost due to an increase in the number of non-zero cells, leading to decreased accuracy in state estimation.
Innovation Solution
An analysis device that performs state estimation using a Kalman filter on first sequence data generated by applying a first conversion to observation data, followed by an elaboration process to ensure non-negative values and suppress non-zero cells, using a state space model and inverse conversion to output estimated observation data.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the Kalman filter is applied to high-dimensional big data, then state estimation can be performed, but calculation cost increases and accuracy decreases due to positive bias and increase in non-zero cells
Solution Approach 1:
The invention extracts only the necessary state variables for state estimation rather than processing all state variables in high-dimensional big data. By identifying and extracting key state variables that contribute most to estimation accuracy, the system reduces calculation cost while maintaining estimation precision, directly addressing the contradiction between accuracy and computational burden
Solution Approach 2:
The invention segments the high-dimensional state space into multiple groups or clusters, processing each segment separately rather than as a whole. This segmentation reduces the complexity of the Kalman filter calculations by breaking down the large-scale problem into smaller, more manageable sub-problems, thereby reducing calculation cost while preserving state estimation accuracy
2Measurement precision
If the Kalman filter is applied to high-dimensional big data, then state estimation can be performed, but positive bias occurs causing state variables to become non-zero when they should be zero
Solution Approach 1:
The invention applies preliminary anti-action by introducing correction mechanisms that counteract the positive bias before it significantly degrades estimation accuracy. The system proactively adjusts state variables to prevent them from becoming non-zero when they should remain zero, thereby maintaining both accuracy and constraint satisfaction simultaneously
Solution Approach 2:
The invention changes key parameters of the Kalman filter, such as the process noise covariance matrix or measurement noise covariance matrix, to reduce the occurrence of positive bias. By optimizing these parameters specifically for high-dimensional data, the system maintains state estimation accuracy while preventing state variables from incorrectly becoming non-zero
3Measurement precision
If the Kalman filter is applied to high-dimensional big data, then state estimation can be performed, but deviation from non-negative constraint occurs causing cell values to become negative
Solution Approach 1:
The invention applies inversion by transforming the state estimation problem to work in a transformed space where non-negative constraints are naturally satisfied, then inverting the transformation to obtain the final estimates. Alternatively, it inverts the conventional approach by first ensuring non-negativity through transformation and then performing estimation, thereby maintaining both accuracy and constraint compliance
4Measurement precision
If the Kalman filter is applied to high-dimensional big data, then state estimation can be performed, but the number of non-zero cells increases leading to increased calculation cost
Solution Approach 1:
The invention extracts only the essential non-zero state variables that contribute meaningfully to state estimation, discarding or suppressing less significant variables. This extraction approach reduces the number of non-zero cells that need to be processed, thereby reducing system complexity and calculation cost while preserving estimation accuracy
Solution Approach 2:
The invention applies local quality by allowing non-zero values only in specific regions or dimensions of the state space where they are most informative for estimation, while maintaining zero values in other regions. This selective approach reduces the overall number of non-zero cells and associated computational complexity while preserving accuracy in critical areas
Data Source
AI summary
An analysis device includes: an estimation unit that obtains a current state variable by state estimation based on a state variable for first sequence data generated by applying a first conversion to observation data, a state space model, and each element included in the first sequence data; an observation unit that generates second sequence data by applying an observation process to the current state variable; an elaboration unit that generates third sequence data by performing an elaboration process of correcting each element included in the second sequence data so that a value of each cell of the estimated observation data does not become a negative value and the number of cells having a value other than 0 included in the estimated observation data is suppressed; and a second conversion unit that generates the estimated observation data by applying a second conversion to the third sequence data.