Mission 01 · System authority test
Trace one angular rate
from acquisition to physical response.
Fifteen transformations sit between a gyro reading and a control surface moving. Every one is arithmetic you can check by hand, and every one can be got wrong in a way that is invisible from either end.
Nothing here is graded and nothing is timed. Saying you do not know what a stage does is a real answer and it is more useful than a guess that happens to be right.
Not whether you were right. What you decided, in the order you decided it, assembled from what you actually recorded.
Show the derivation Every stage worked through, with the plots and the argument
Below is the path the measurement takes. Six stages, and one thin path that leaves the last stage and returns to the first, because the aircraft moving is what the gyro measures next. One stage has no name on it. That is deliberate, and you will name it yourself later in this mission once you have the evidence to argue for what it should do.
The same structure, in words
The drawing and this list say the same thing, with the same blanks. Use whichever you prefer, or both.
Name the stages
In your own words. Short is fine. Stage 03 is the one nobody names correctly on the first pass, and it is the one this mission is really about.
Knowing what you are unsure of is a different skill from knowing the answer, and it is the one that cannot be recovered from a correct answer.
The gyro does not report degrees per second. It reports a count: an integer produced by an analogue to digital converter, meaningful only against the scale factor and offset measured for that specific part on a rate table. Here is the marked sample.
A number without a unit is not a measurement. Every readout on this page carries its unit beside it, and the count carries "counts" for exactly the same reason: the count is a real quantity, it is just not a quantity of degrees per second.
The converter has a finite number of steps. Anything finer than one step never existed as far as every stage downstream is concerned. This is the first place information can be lost, and it happens before a single line of flight software runs.
At 8 bit the step is larger than the vibration amplitude, so the vibration simply is not in the record. No amount of filtering downstream recovers it, because there is nothing to recover. Choosing a converter is choosing what the rest of the system is allowed to know.
The converter is read at a fixed rate. Between reads, the aircraft carries on doing whatever it was doing, unobserved. The record you get is not the motion; it is a list of instants pulled out of the motion.
Look at what the samples now describe. The 22 Hz vibration is faster than this rate can follow, so it has folded down and appears in the record as a slow oscillation. That oscillation is not happening to the aircraft. Software downstream has no way to tell the difference, because to software the samples are all there is.
How old is the number when it is finally used?
Sampling is not the only delay. Each stage of the chain takes time, and the control law acts on a measurement describing an aircraft that has already moved on.
The command is computed from a picture of the aircraft that is · old. Nothing is wrong: this is what every flight control system does. It matters because a control gain that is stable against a fresh measurement can be unstable against a stale one, which is section I.
The system does not meet each measurement with no expectations. An inertial model is propagating its own estimate of pitch rate forward in time, independently of this gyro. The difference between what arrived and what was expected is the residual, and it is the single most useful number in the chain.
The same residual, under two different uncertainties
A residual on its own says nothing. It has to be compared against how much disagreement this pair of sources produces when nothing at all is wrong.
A residual is evidence. It is not an explanation. A normalised residual of nine says the gyro and the model disagree by nine times what they normally disagree by. It does not say the gyro is broken. The model could be wrong. The aircraft could be doing something the model does not represent. Something upstream of both could have changed. Deciding which, on this evidence, is the next section.
This is the stage the drawing left unnamed. Something has to decide what this measurement is allowed to do next, and it has to decide now, with this evidence and no more.
What should stage 03 do with this measurement?
There is no correct answer waiting behind this and what you write is not marked. It is here because a reason you gave before reading somebody else's is worth something, and one you gave afterwards is worth very little.
There are two gyros on this axis. De-weighting one is not a switch; it is a change to how much each is allowed to move the answer.
x̂ = (w₁z₁ + w₂z₂) / (w₁ + w₂)
Introductory weighting model. This is a teaching arrangement, not a production aerospace fusion algorithm. A real system weights by estimated variance, propagates that variance forward, and keeps a record of how each source has behaved over time. What survives from this simplification is the part worth carrying: whichever source you trust most is the one whose failure moves the answer furthest.
A single sample is not a state. The estimate carries information forward from every sample before it, and how much it carries is the one number you get to choose.
There is no setting of alpha that is smooth and fast at the same time. That is not a limitation of this simplified filter; it is the trade every estimator makes, and a more sophisticated one buys a better position on the same curve rather than escaping it. This is not a Kalman filter and calling it one would hide exactly the thing worth seeing.
The estimate finally becomes an action. The control law compares the estimate against what was asked for, computes a command, and the actuator does what it physically can with it.
Illustrative A first order response standing in for the aircraft. It is not a validated flight dynamics model and no number taken from it describes a real aeroplane.
The surface, and the aeroplane
The command is a number until an actuator moves. Here is the same number, as a deflection and then as motion.
Illustrative The airframe is drawn to scale against its own geometry, not against a specific aircraft. The deflection angle shown is the computed command, exaggerated by a stated factor so that a one degree change is visible.
Nothing about the chain changes here. One thing changes about the sensor: gyro A acquires a fixed bias part way through the record. Watch where that bias becomes visible, and where it becomes consequential.
Every answer here costs something. A stage that isolates a sensor on weak evidence throws away a good measurement; a stage that never isolates one passes a bias straight to the surface. Say which cost you would accept.
This is the record of what you did: the values you followed, the settings you chose, the decision you committed and the reason you gave for it. It is hashed so that it can be cited later without either of us having to trust a memory of it.
Recording writes an artifact to this browser and nowhere else. It carries the dataset identifier and hash, so a claim you make from it in a later mission can be checked against the same numbers rather than against a screenshot.