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Linear Covariance Pushforward (Affine Uncertainty Propagation)
x402
Linear Covariance Pushforward (Affine Uncertainty Propagation) is a paid API for AI agents from stat.halowerk.com, paid per call via x402, $0.0015/call, status unknown (last checked 2026-10-29).
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.
Price / call$0.0015
Success—
StatusUnknown
How this service works
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.
Output
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.
Example use cases
Kalman filter prediction step
“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?”
Sensor model uncertainty propagation
“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?”
Linear error budget for an optical system
“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?”
Technical details
Endpoint
POSThttps://stat.halowerk.com/v1/oss-openblas-linear-covariance-pushforward?utm_source=zero.xyzWhen to prefer
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.
Side effects
- 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
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| inputrequired | object | |
| output | object |
Tags
x402
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