Linear- and Linear-Matrix-Inequality-Constrained State Estimation for Nonlinear Systems
Bibliographic record
Abstract
This paper considers nonlinear state estimation subject to inequality constraints in the form of linear and linear-matrix inequalities. Rewriting the standard maximum likelihood objective function used to derive the Kalman filter allows the Kalman gain to be found by solving a constrained optimization problem with a linear objective function subject to a linear-matrix-inequality constraint. Additional constraints, such as weighted-norm- or linear-inequality constraints, that the state estimate must satisfy are easily augmented to the constrained optimization problem. The proposed constrained estimation methodology is applied in the extended Kalman filter (EKF) and sigma point Kalman filter (SPKF) frameworks. Motivated by estimation problems involving a vehicle that can rotate and translate in space, multiplicative versions of the constrained EKF and SPKF formulations are discussed. Simulation results for a ground-based mobile robot operating in a constrained three-dimensional terrain are presented and are compared to results that use the traditional multiplicative EKF and SPKF, as well as filters that enforce inequality constraints by simply projecting the state estimate into the constrained domain along the shortest Euclidean distance.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".