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feat(estimators): add recursive instrumental variables - #352

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feat/recursive-instrumental-variables
Oct 20, 2026
Merged

feat(estimators): add recursive instrumental variables#352
gabrielfrasantos merged 1 commit into
mainfrom
feat/recursive-instrumental-variables

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@gabrielfrasantos gabrielfrasantos commented Oct 20, 2026

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Summary

Adds estimators::RecursiveInstrumentalVariables<T, Features> next to RecursiveLeastSquares. It is recursive least squares with the gain taken along an instrument z instead of the regressor x:

  • K = P z / (λ + xᵀ P z)
  • θ ← θ + K (y − xᵀ θ)
  • P ← (P − K xᵀ P) / λ

When a regressor is itself measured, least squares converges to an attenuated coefficient (regression dilution). An instrument that moves with the true regressor but not with its noise removes that bias. A typical instrument is an injected excitation. With z = x the recursion is RLS, at the same O(p²) cost.

Motivation

In e-foc the online winding estimator takes dI/dt from two single noisy current samples. On the bench motor the RLS estimate read the inductance 55 % low. With the injected d-axis reference as the instrument it reads within +4 to +8 % of the offline calibration, measured in 3 hardware runs. e-foc carries a local copy of this class today, on an open branch; that copy will be replaced by this one once this PR merges.

Changes

  • numerical/estimators/online/RecursiveInstrumentalVariables.hpp: generic T with a static_assert for floating point, OPTIMIZE_FOR_SPEED on Update, and an extern template for the coverage build.
    • Update(regressor, instrument, y) returns the same EstimationMetrics as RLS.
    • It reuses RLS's forgetting-factor check.
  • RecursiveInstrumentalVariables.cpp: coverage instantiation <float, 2>.
  • test/TestRecursiveInstrumentalVariables.cpp, two TEST_Fs on float:
    • with z = x it matches RLS in coefficients and all three metrics;
    • with a noisy regressor and a clean instrument it recovers the true slope and intercept.
  • doc/estimators/RecursiveInstrumentalVariables.md follows doc/TEMPLATE.md, with an exact four-step walkthrough. Rows were added to doc/estimators/README.md and to the README.md documentation table.

Validation

  • numerical.estimators.online_test: all tests pass (host, Debug).
  • clang-format --dry-run --Werror is clean on the new sources.

Generated by Claude Code

@gabrielfrasantos @claude
feat(estimators): add recursive instrumental variables
eb8346d 
Recursive least squares with its gain taken along an instrument instead of the regressor. When a
regressor is itself measured, least squares reads its noise as a weaker dependence on that column
and converges to an attenuated coefficient. An instrument that moves with the true regressor but
not with its noise, such as an injected excitation, removes that bias. With the regressor as its
own instrument the recursion is the recursive least-squares one, at the same cost.

e-foc uses it to identify a winding's inductance online from a derivative of measured current, with
the injected d-axis current reference as the instrument: on a bench motor the least-squares estimate
read the inductance 55 % low and this one reads it within 8 %.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_011XTZKRSD8pDL7QvwFrVnoK
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✅⚠️MegaLinter analysis: Success with warnings

Descriptor Linter Files Fixed Errors Max errors Warnings Elapsed time
✅ ACTION actionlint 7 0 0 0.58s
✅ CPP clang-format 433 11 0 0 4.62s
✅ CPP cppcheck 433 0 0 9.0s
✅ DOCKERFILE hadolint 1 0 0 0.64s
✅ JSON jsonlint 8 0 0 0.1s
✅ JSON prettier 8 8 0 0 0.43s
⚠️ MARKDOWN markdownlint 133 3 178 0 3.22s
✅ MARKDOWN markdown-table-formatter 133 24 0 0 0.38s
⚠️ SPELL lychee 242 26 0 28.49s
✅ YAML prettier 12 3 0 0 0.61s
✅ YAML yamllint 12 0 0 0.63s

Detailed Issues

⚠️ SPELL / lychee - 26 errors 
📝 Summary
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🔍 Total..........568
🔗 Unique.........437
✅ Successful.....530
⏳ Timeouts.........0
🔀 Redirected.....149
👻 Excluded........11
❓ Unknown..........0
🚫 Errors..........26
⛔ Unsupported.....26

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Errors in doc/filters/active/AhrsMadgwickMahony.md
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[ERROR] file://doc/filters/solvers/DiscreteAlgebraicRiccatiEquation.md (at 134:3) | File not found. Check if file exists and path is correct

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[403] https://developer.arm.com/documentation/100166/latest/ (at 472:3) | Rejected status code: 403 Forbidden
[403] https://developer.arm.com/documentation/dui0473/latest (at 474:3) | Rejected status code: 403 Forbidden

Errors in README.md
[ERROR] file:///releases/latest (at 38:14) | File not found. Check if file exists and path is correct
[404] https://embedded-pro.github.io/embedded-dsp-control/ (at 37:1) | Rejected status code: 404 Not Found

Errors in roadmap/README.md
[ERROR] file://roadmap/filters/passive/ExponentialMovingAverage/implementation.md (at 24:1) | File not found. Check if file exists and path is correct

Hint: Followed 149 redirects. You might want to consider replacing redirecting URLs with the resolved URLs. Use verbose mode (`-v`/`-vv`) to see redirection details.
Hint: You can configure accepted/rejected response codes with `-a` or `--accept`
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README.md:25:140 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
README.md:26:174 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
README.md:27:363 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
README.md:28:158 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
README.md:29:205 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
roadmap/math/SE3Transform/implementation.md:7 error MD040/fenced-code-language Fenced code blocks should have a language specified [Context: "```"]
roadmap/math/SE3Transform/implementation.md:21 error MD040/fenced-code-language Fenced code blocks should have a language specified [Context: "```"]
roadmap/math/SE3Transform/implementation.md:35 error MD040/fenced-code-language Fenced code blocks should have a language specified [Context: "```"]
roadmap/math/SE3Transform/tests.md:7 error MD040/fenced-code-language Fenced code blocks should have a language specified [Context: "```"]
roadmap/math/SE3Transform/tests.md:16 error MD040/fenced-code-language Fenced code blocks should have a language specified [Context: "```"]
roadmap/README.md:11 error MD040/fenced-code-language Fenced code blocks should have a language specified [Context: "```"]

(Truncated to last 20000 characters out of 24106)

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github-actions[bot]
github-actions Bot reviewed Oct 20, 2026
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Comment thread README.md Resolved
github-actions[bot]
github-actions Bot reviewed Oct 20, 2026
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Comment thread README.md Resolved
@sonarqubecloud

sonarqubecloud Bot commented Oct 20, 2026

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Quality Gate Passed Quality Gate passed

Issues
0 New issues
0 Accepted issues

Measures
0 Security Hotspots
100.0% Coverage on New Code
0.0% Duplication on New Code

See analysis details on SonarQube Cloud

@gabrielfrasantos
gabrielfrasantos merged commit 9b37e08 into main Oct 20, 2026
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@gabrielfrasantos
gabrielfrasantos deleted the feat/recursive-instrumental-variables branch October 20, 2026 18:49
@embedded-releaser-app embedded-releaser-app Bot mentioned this pull request Oct 20, 2026
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@gabrielfrasantos gabrielfrasantos mentioned this pull request Oct 20, 2026
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