Precision Evaluation in Discrete Kalman Filtering: A Posteriori Perspective
Bibliographic record
Abstract
This manuscript is focused on standardizing the process of the a posteriori precision evaluation in discrete Kalman filtering. Although the a posteriori precision evaluation of the solution was considered as indispensable within the method of least squares, the solution of a Kalman filter shows a lack of a posteriori precision evaluation for too long. Even worse, there often exists appalling confusion about what is considered as the a posteriori precision of the solution in Kalman filtering. The authors hereto propose to put the a posteriori precision evaluation of the solution into practice at four different levels in Discrete Kalman filtering through estimating: (i) the a posteriori variance of unit weight (or reference variance), (ii) the separate a posteriori variance factors for the process and measurement noise vectors, respectively, (iii) the individual a posteriori variance factors for the independent noise groups, and (iv) the individual a posteriori variance factors (or components) for the independent process noise factors and measurement types. A working example is presented to illustrate the proposed a posteriori precision evaluation in Kalman filtering using a road test based on the double-differenced GPS L1 C/A, L1 and L2 carrier phases and the specific force and angular rate measurements from an MEMS IMU. With the rapidly increasing utilization of the Kalman filter in modern applications, the inclusion of the proposed a posteriori solution precision evaluation, as part of the standard solution, in discrete Kalman filtering is not only necessary, but also can be expected to happen soon within our grasp.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.007 | 0.023 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".