{"uid":"cap_mc4q8j0yfD3ltaIfPbxJg","slug":"linear-covariance-pushforward-affine-uncertainty-propagation-4d4cc7e6","name":"Linear Covariance Pushforward (Affine Uncertainty Propagation)","description":"Applies the standard affine propagation of uncertainty: the mean goes through the transform and offset, the covariance through the transform on both sides, and the independent noise covariance is added. This is the prediction step of a Kalman filter and the workhorse of any linear error budget.","url":"https://stat.halowerk.com/v1/oss-openblas-linear-covariance-pushforward?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","$schema":"https://json-schema.org/draft/2020-12/schema","required":["input"],"properties":{"input":{"type":"object","required":["type","method","bodyType"],"properties":{"type":{"const":"http"},"method":{"const":"POST"},"bodyType":{"const":"json"},"schemaUrl":{"type":"string","format":"uri"},"exampleUrl":{"type":"string","format":"uri"}},"additionalProperties":true},"output":{"type":"object","required":["type"],"properties":{"type":{"const":"json"},"schemaUrl":{"type":"string","format":"uri"},"exampleUrl":{"type":"string","format":"uri"}},"additionalProperties":true}},"additionalProperties":true},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.0015","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.0015/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.0015","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.0015","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_TP2-Gv9amvMgJNZYIrTb0","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.0015","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Propagates a Gaussian distribution through an affine transformation by updating the mean and covariance, adding process noise — implementing the prediction step of a Kalman filter.","exampleAgentPrompt":"I have a state mean vector [1.0, 2.0, 0.5], covariance matrix [[0.1,0,0],[0,0.2,0],[0,0,0.05]], a linear transform F, an offset b, and a process noise covariance Q — can you propagate the distribution through the affine map F*x + b and give me the new mean and covariance?","exampleUseCases":[{"title":"Kalman filter prediction step","prompt":"I'm running a Kalman filter for a 3D position tracker. My current state mean is [10.0, 5.0, 2.0] with covariance [[0.4,0,0],[0,0.4,0],[0,0,0.1]], my state transition matrix is the identity plus a velocity term, offset is zero, and my process noise covariance Q is [[0.01,0,0],[0,0,0.01],[0,0,0.005]]. Can you compute the predicted mean and covariance for the next time step?"},{"title":"Sensor model uncertainty propagation","prompt":"I need to push my IMU measurement uncertainty through a rotation matrix to get the covariance in the world frame. The input mean is [0.0, 9.81, 0.0], input covariance is [[0.02,0,0],[0,0.02,0],[0,0,0.02]], the rotation matrix R is my 3x3 transform, the offset is zero, and there's no additional noise. What's the output mean and covariance after applying R?"},{"title":"Linear error budget for an optical system","prompt":"For my linear error budget I have a state mean of [0.5, -0.3] with covariance [[0.001,0],[0,0.002]], a 2x2 sensitivity matrix A, no offset, and a residual noise covariance of [[0.0005,0],[0,0.0005]]. Can you compute the total output covariance after propagating through A and adding the residual noise?"}],"resultDescription":"Returns the pushed-forward Gaussian parameters: the transformed mean vector (F*x + offset) and the full propagated covariance matrix (F * Sigma * F^T + Q), ready to use as the prior in the next estimation or measurement update step.","failureModes":["Dimension mismatch between mean, transform, covariance, or noise_covariance matrices returns a 400 error","Non-positive-semidefinite covariance or noise_covariance inputs may cause numerical issues or a validation error","Values outside the [-1e6, 1e6] range or array lengths exceeding 128 will be rejected","Missing required fields (mean, covariance, transform) return a 422 validation error","Singular or near-singular transform matrices may produce numerically unstable covariance outputs"],"whenToPreferThis":"Choose this endpoint when you need a reliable, numerically consistent affine covariance propagation as a hosted API call — ideal for Kalman filter prediction steps, sensor fusion pipelines, or linear error budget computations where you want to avoid implementing the matrix algebra yourself. Prefer this over general-purpose matrix libraries when your pipeline is agent-driven or you need pay-per-call access without managing compute infrastructure. Not suitable for nonlinear propagation (use sigma-point or EKF Jacobian methods instead) or for dimensions exceeding 128.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-29T00:31:48.193Z","isFirstParty":false,"canonicalSlug":"linear-covariance-pushforward-affine-uncertainty-propagation-4d4cc7e6"}