FixTheRobot Explore Robotics / Guidance, Navigation and Control / M7 / M7-L1

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Guidance, Navigation and Control · Aided Navigation and Attitude Determination · M7-L1 · Intermediate

Solve the Fix

Bench log · Hopper on the test range

10:05. Hopper's range beacons all stand on the ground, and Hopper flies at 60 m. The fix is crisp in east and north and wanders by tens of metres in height. The beacon contractor has one more transmitter in the van and asks where to put it.

You will decide where it goes, write the least-squares fix that includes the receiver clock, and compute the dilution of precision that explains why.

Your task

    Simulation
    solution.pyLoading Python…
    Ctrl+Enter runs
    What Python can I use?

    Plain Python 3 with the standard library and the course library gnckit (import gnckit as g: transfer functions and margins, state space and LQR, the Hopper model, quaternions, a convex solver). NumPy is not available in the browser. Your code runs in a background worker: an endless loop is stopped after a few seconds and the page stays usable. It runs in your browser and is never sent anywhere.

    Hints

    What this lab teaches

    Stage 1: dilution of precision follows from geometry: beacons all near the same height leave the vertical position confused with the clock bias, and one beacon high above the range fixes it. Stage 2: the iterated least-squares fix with the clock bias as a fourth unknown. Stage 3: the covariance matrix (H′H)⁻¹ and the horizontal, vertical and time dilution of precision.

    Grading checks the vertical DOP of your chosen beacon, your fix to a micrometre on hidden positions and clock biases, and your DOP against the reference.

    Theory for this lab

    Aided Navigation and Attitude Determination labs

    1. M7-L1: Solve the Fix: this lab.
    2. M7-L2: Two Vectors, One Attitude
    3. M7-L3: Ride Through the Outage

    Educational simplification: a local flat frame, white pseudorange noise of 1 m and no multipath or beacon faults; module 7 adds the integrity and the fault of the third lab.

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