Figures you can move
Plots with sliders and draggable points, predictions you place before the answer shows, simulations you play and step.
Recall after a review. Drag to change stability, the day recall falls to 90%.
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How the tutor teaches.
Ask for a subject, the depth you want and the minutes a day you have. Your tutor finds out what you already know, plans a course with sources it picked, and teaches it in short lessons you work through, not read through. Reviews bring each idea back just before you’d forget it. Study time is tracked on a task, and starting a course can add a study goal and study blocks to your plan.
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A course shaped around you.
- 1
You ask
A subject, how deep, minutes a day. Attach a paper or your notes if you have them.
- 2
It finds out what you know
A few questions that have you try something, so the course skips what you already know.
- 3
It proposes a plan
The goal you’ll reach, units that each end in something you can do, and the sources it picked, each with why. Start it, or ask for changes.
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It keeps adjusting
Ask for a change, or let a review show a gap. It proposes a new plan without losing what you learned.
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📡 Kalman filter
4 units · 7 concepts
10 questions
The Learn tab
Proposed plan
Goal: tune an EKF for your robot, and explain why it works.
1
Why filter at all
Task: smooth a noisy GPS track
2
Predict and update
Task: run one step by hand
3
The gain K
Task: tune R on your own data
4
The extended filter
Task: an EKF for your robot
Sources
Kalman 1960
Why: the original paper
Probabilistic Robotics, ch. 3
Why: the clearest derivation
Your thesis notes
Why: your own setup and words
Ask for changesStart the course
A course plan, proposed
Lessons built on how people learn.
Each concept goes through the same short loop, and each step is there because learning research supports it. No points or badges: the interest comes from the idea.
Proposed plan
Goal: tune an EKF for your robot, and explain why it works.
1
Why filter at all
Task: smooth a noisy GPS track
2
Predict and update
Task: run one step by hand
3
The gain K
Task: tune R on your own data
4
The extended filter
Task: an EKF for your robot
Sources
Kalman 1960
Why: the original paper
Probabilistic Robotics, ch. 3
Why: the clearest derivation
Your thesis notes
Why: your own setup and words
Ask for changesStart the course
Kalman filter · The update step
Warm-up
Last time: what does the predict step do to the uncertainty P?
AIt grows: the process noise Q is added
BIt shrinks
CIt stays the same
Right. Predicting moves the estimate forward and adds Q, so P grows until a measurement comes in.
ContinueKalman filter · The update step
The guess
Which matters more for the gain K: the measurement noise R or the prediction’s uncertainty P?
AThe measurement noise R
BHow the two compare
CThe prediction’s uncertainty P
Both, as a ratio. K weighs P against R. The rest of this lesson shows why.
See whyKalman filter · The update step
The idea
The update blends two guesses.
Each guess is a Gaussian. Multiply them and the result is narrower than both, pulled toward the more certain one.
Explain it differentlyToo easyToo hard
ContinueKalman filter · The update step
Your turn
Finish the predict step.
x̂⁻ = F x̂ + B u
P⁻ = F P Fᵀ + Q
The rule: predicting adds the uncertainty of the motion itself.
Kalman filter · The update step
A deeper question
Why does a larger R make the filter trust its prediction more?
Because K gets smaller, so the measurement moves the estimate less.
Key points
K shrinks as R grows
The measurement is weighted less
Missing: P itself does not depend on R
Kalman filter · The update step
Recall
From memory: the update of the estimate.
x̂ = x̂⁻ + K (z − H x̂⁻)
Saved for review. Two cards from this lesson come back in your reviews, spaced by FSRS.
Finish lesson- 01Warm-upSpaced retrieval
- 02The guessPretesting
- 03The idea, then an exampleWorked examples
- 04Your turnFading
- 05A deeper questionSelf-explanation
- 06RecallRetrieval practice
01 Warm-up Spaced retrievalA quick check on what came before, starting with what you missed or forgot.
02 The guess PretestingA question on the key idea before it’s taught, answered with a tap. The answer and its why come right after.
03 The idea, then an example Worked examplesIntuition before the math, and an example from your own field. Ask for it explained differently, or say it was too easy or too hard.
04 Your turn FadingThe same example with a step left to you, the rule behind that step, then one problem on your own. Checked at once, with a second try.
05 A deeper question Self-explanationExplain it back or use it somewhere new. The tutor grades it against its key points, with up to three hints and the confidence you give.
06 Recall Retrieval practiceThe key idea from memory. What’s worth keeping becomes review cards, spaced by FSRS, the open scheduler Anki also offers.
01
Warm-up
Spaced retrievalA quick check on what came before, starting with what you missed or forgot.
02
The guess
PretestingA question on the key idea before it’s taught, answered with a tap. The answer and its why come right after.
03
The idea, then an example
Worked examplesIntuition before the math, and an example from your own field. Ask for it explained differently, or say it was too easy or too hard.
04
Your turn
FadingThe same example with a step left to you, the rule behind that step, then one problem on your own. Checked at once, with a second try.
05
A deeper question
Self-explanationExplain it back or use it somewhere new. The tutor grades it against its key points, with up to three hints and the confidence you give.
06
Recall
Retrieval practiceThe key idea from memory. What’s worth keeping becomes review cards, spaced by FSRS, the open scheduler Anki also offers.
Pick an option · type a number · put steps in order · match pairs · fill blanks from tiles · type an expression on a math keyboard, where any equal form counts
Stuck? Ask about any step, or select a passage, formulas included, and ask about just that. On a question you haven’t answered, the tutor gives hints, not the answer.
Work on paper
For a derivation, a proof or a drawing, photograph your pages. The tutor reads them back and points to the first wrong step.
1K = P Hᵀ (H P Hᵀ + R)⁻¹2x̂ = x̂⁻ + K (z − H x̂⁻)3P = (I − K H) P⁻ Hᵀ4P = (I − K H) P⁻
“Line 3: the H should be transposed.”
No paper with you? It asks another way.
Reviews that stick
Spaced by FSRS, the open scheduler Anki also offers. Short answers are checked as you type, even offline. A light day keeps only what’s about to slip, and nothing resets when you skip.
RightAlmostNot yet
Taught from the best sources
The tutor picks a few of the best references and says why. Give it a paper and lessons show the paper’s own figures. Give it a book and each lesson reads the pages it teaches from.
How I learn
A page you write for your tutor: analogies from your field, short lessons on low-energy days, a tablet for handwritten work. It reads it for every course and never edits it; it can suggest a line for you to add.
Spaced so it stays.
FSRS brings each card back when your chance of recalling it falls to 90%, so every review lets the next gap grow. Type your answer and the tutor grades it with its reasons, or rate it yourself.
The same day
What you struggled with in a lesson comes back a few hours later.
Mixed
Reviews mix your courses and never test the same concept twice in a row.
Light days
A light day keeps only what is about to slip. Nothing resets when you skip.
Why each step is there.
The tutor follows a teaching guide built from published learning research. Changes to it are scored on ten fixed courses, judged blind against a rubric drawn from that research, before they ship.
StepWhat the research showsSource
The guessA question on the key idea before it’s taught helps learn that idea (g ≈ 0.66), and nothing else.Pan & Carpenter 2023
Attempt first on contrasting casesTrying a problem before instruction helps conceptual understanding and transfer (g = .36, up to .58 with good design).Sinha & Kapur 2021
Worked examples that fadeAsking for the principle behind a faded step improves near and far transfer at no extra time.Atkinson, Renkl & Merrill 2003
Explaining it backPrompts to self-explain help (g = .55).Bisra et al. 2018
Feedback that explainsExplanations after an answer beat right/wrong alone (ES 0.49 against 0.05).Van der Kleij et al. 2015
Hints, not answersAnswer-giving AI help lowered exam scores by 17%, where hints drawn from the teacher’s solution did not.Bastani et al. 2025
Mixed practiceInterleaving problem types helps (d = 0.83), though not for word lists.Rohrer et al. 2019; Brunmair & Richter 2019
Spacing and retrievalRetrieval spaced across sessions is where practice pays; nine same-session problems did no better than three a month later.Dunlosky et al. 2013; Rohrer & Taylor 2006
Pictures with a jobWords with a relevant picture beat words alone (g ≈ 0.37).Mayer 2017; Cromley & Chen 2025
No decorationStories and trivia inside an explanation cost learning (seductive details).Sundararajan & Adesope 2020
Confident errorsErrors made with confidence are corrected best when the reasoning is shown.Metcalfe 2017
ReviewsFSRS schedules each card for when recall falls to 90%.FSRS-6, as Improved implements it