Pointing Error Budget

Pointing Error Budget (space-systems/adcs/pointing-error-budget)

Use when the task is the ADCS pointing error chain: summing the independent 1-sigma error contributors of the attitude determination and control system into one RSS pointing error, converting it to 3-sigma, checking it against the pointing requirement, allocating the remaining budget to the contributor that is not yet sized (typically the control deadband), and ranking the contributors by variance share. This leaf is the assembly layer between the sensor noise metrology of the ADCS and the payload or antenna that consumes the delivered pointing error. Pure Python, stdlib only, unit-agnostic with the ADCS example in arcsec.

Domain quick reference

• RSS combination: rss_1sigma = sqrt(sum(c_i^2)) over the independent 1-sigma contributors. Independence is assumed; correlated errors are summed linearly, not by RSS.
• 3-sigma conversion: rss_3sigma = 3 * rss_1sigma (normal distribution convention).
• Requirement verdict: requirement_met = rss_3sigma <= requirement_3sigma.
• Budget allocation to one remaining contributor: remaining_1sigma = sqrt((requirement_3sigma / 3)^2 - sum(c_fixed^2)). The fixed RSS must stay below requirement / 3 or the radicand is negative and the allocation fails.
• Variance share: share_i = c_i^2 / sum(c_j^2); the dominant error source is the contributor with the largest share.
• Units: the functions are unit-agnostic; the reference ADCS chain uses arcsec (1-sigma) and the requirement uses arcsec (3-sigma).

Workflow

1. List the independent 1-sigma contributors in arcsec: star tracker determination noise, gyro propagation, control deadband, jitter, thermal distortion (add other known terms as needed).
2. Combine them with rss_pointing_error to get the 1-sigma RSS.
3. Convert with three_sigma_error and judge the requirement with three_sigma_verdict against the 3-sigma pointing requirement.
4. When one contributor is not yet sized (the control deadband in the reference chain), allocate its budget with allocate_error_budget using the requirement and the fixed contributors.
5. Rank the contributors by variance share with dominant_error_source; pass a dict of {name: value} to get the dominant contributor name back.
6. Assemble the full picture with pointing_error_budget, which returns the RSS values, the verdict, the dominant index and share, and the per-contributor variance shares in one dict.
7. Confirm the deterministic checks with the contract test scripts/test_pointing_error_budget.py.

Worked example

Reference ADCS chain (arcsec, 1-sigma): star tracker determination noise 3, gyro propagation 2, control deadband 25, jitter 8, thermal distortion 5; pointing requirement 90 arcsec 3-sigma.

• rss_pointing_error([3, 2, 25, 8, 5]) = sqrt(9 + 4 + 625 + 64 + 25) = sqrt(727) = 26.962938 arcsec.
• three_sigma_error([3, 2, 25, 8, 5]) = 3 * 26.962938 = 80.888813 arcsec.
• three_sigma_verdict([3, 2, 25, 8, 5], 90) = True: 80.888813 <= 90, the requirement is met with margin.
• allocate_error_budget(90, [3, 2, 8, 5]) = sqrt(30^2 - (9 + 4 + 64 + 25)) = sqrt(798) = 28.248894 arcsec, the budget left for the control deadband. It exceeds the 25 arcsec actual deadband, consistent with the requirement verdict True.
• dominant_error_source([3, 2, 25, 8, 5]) = (index 2, control deadband, share 625/727 = 0.8597), so the control deadband carries 86.0% of the error variance.

Pitfalls

• Mixing 1-sigma and 3-sigma: the contributors are 1-sigma and the requirement is 3-sigma; compare three_sigma_error against the requirement, not the raw RSS.
• Adding correlated contributors by RSS: the root-sum-square assumes independence; correlated errors sum linearly, so RSS understates the chain when the terms share a common source.
• Allocating against an already-over budget: allocate_error_budget raises ValueError when the fixed contributors push the radicand negative (fixed RSS above requirement / 3); size the fixed chain first.
• Trusting a verdict at the exact boundary: a requirement exactly equal to the 3-sigma value returns True with zero margin - treat boundary equality as met but not robust.
• Ranking by magnitude instead of variance share: the dominant source is the largest share of the variance (the 25 arcsec deadband carries 625/727 = 86.0% in the worked example), and an all-zero contributor list raises ValueError.
• Forgetting that a zero contributor is inert: adding a zero leaves the RSS unchanged and reversing the input order leaves it unchanged, so the input list order must not leak into the reported dominant index.

Verification

• Confirm rss_pointing_error([3, 2, 25, 8, 5]) returns 26.962938 arcsec and three_sigma_error returns 80.888813 arcsec.
• Confirm adding a zero contributor leaves the RSS unchanged, reversing the input order leaves it unchanged, and a contributor equal to the RSS of the others raises the total by sqrt(2).
• Confirm the verdict boundary: a requirement exactly equal to the 3-sigma value returns True.
• Confirm allocate_error_budget(90, [3, 2, 8, 5]) returns 28.248894 arcsec, and that shrinking the requirement shrinks the allocation.
• Confirm ValueError is raised for an empty contributor list, any negative contributor, a non-positive requirement, a negative radicand in the allocation (fixed contributors already over the 1-sigma budget), and an all-zero contributor list in the dominant-source ranking.
• Run the contract test offline: python3 scripts/test_pointing_error_budget.py (34 tests, deterministic).

Related leaves

• space-systems/adcs/attitude-control-sizing: actuator sizing sibling; boundary is actuator sizing and margins versus this leaf's error chain sum.
• space-systems/adcs/attitude-determination-quest: determination sibling whose residual feeds this leaf's determination-noise entry.
• space-systems/subsystems/antenna-aperture-sizing: downstream consumer of the delivered pointing error as a signal loss term.
• space-systems/adcs/gyro-allan-variance: sensor noise metrology that characterizes the gyro propagation entry.

Behavior contract (gate 3)

Run the deterministic contract test (stdlib unittest, offline):

python3 scripts/test_pointing_error_budget.py

The test covers the reference-chain contract (RSS 26.962938 arcsec, 3-sigma 80.888813 arcsec, verdict True at 90 arcsec, allocation 28.248894 arcsec, control deadband dominant at 86.0% variance share), the RSS identities (zero padding, order invariance, single component, sqrt(2) growth), the verdict boundary, allocation monotonicity and negative-radicand rejection, dominant-source ranking on the [1, 100] case at 99.99%, dict-name support, the convenience-dict keys, run-to- run determinism, and ValueError rejection of non-physical inputs.

Compliance

• Standards referenced, not reproduced: the ECSS ADCS error-budget convention (reference-only per standards-map.yaml). The relations above are standard engineering methodology, summary-only.
• compliance: STANDARDS-REF, gated: false.