Okay, let’s start breaking down the task. I need to create 20 multiple-choice questions with 4 options each, all based on the provided content about Kalman filtering in DP systems and related concepts. The difficulty is supposed to be hard, so I have to ensure the questions are detailed and possibly test for nuanced understanding.
First, I’ll go through each section of the content and identify key points that can be turned into questions. The content covers several main topics: Kalman filtering basics, PRS voting, common-mode failures, PRS handling procedures, different tests (Prediction, Variance, Bias, Median), thresholds, and specific details about Kongsberg Simrad systems.
Starting with the Kalman filter part. The key aspects here are combining model and measurements, weighting based on variance, PRS noise affecting weighting, etc. For example, a question could ask about what happens when a PRS is noisy, and the answer would involve higher weighting on the model. Another question might test knowledge about what two factors the Kalman filter combines.
Moving to PRS voting. The main points are using the median instead of average to avoid pollution from erroneous data, median test limits (5-6 meters), and the maximum positional jump being half that limit. Questions here could ask why median is used instead of average, what the median test limit is set to, or consequences of rejection based on the median test.
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Common-Mode Failure is another topic. Key points include scenarios where two PRS fail in the same way, examples like two DGPS failing and causing the third to be rejected, and the problem with having two of the same PRS type. Possible questions here might ask about common-mode failure definitions, situations that lead to them, or related examples from the text.
PRS Handling procedures involve steps for first and subsequent PRS selection, calibration criteria (3 vs. 10 returns), Manual vs. Auto mode during calibration, monitoring mode, re-selecting PRS to improve calibration, and symbols like the asterisk and circle. Questions here can test the number of required returns for initial vs. subsequent PRS, modes required during selection, or interface elements in Kongsberg systems.
Then there are the different tests: Prediction, Variance, Bias, Median. Each has specific purposes, limits, and outcomes. For instance, the Variance Test checks standard deviation against expected accuracy. The Bias Test detects offset from the model but doesn’t auto-reject. The Median Test is for slow drift and uses a limit based on the Prediction error. Questions need to differentiate between these tests, their purposes, limits, and actions taken.
Also, technical details like the Standard Deviation Limit calculation (three times expected accuracy), the formula for the second stage filtering (9 times old + new)/10, Weighting being inversely proportional to Variance, total of weightings always 1.0. Numeric questions here could be tricky but necessary for a hard level.
I have to make sure each question has plausible distractors. For example, if the correct answer is “median”, the options might include “average”, “mean”, “mode”. Or for numbers like the median test limit being 5-6 meters; distractors could be 2-3, 7-8, etc.
I should also check the content thoroughly to avoid mistakes. For instance, the median test limit’s maximum positional jump is half of the median test limit (so 2.5-3 meters). Another point is that the first PRS requires 3 successive returns within 10m in Manual, while subsequent PRS need 10. Recalibrating by deselecting and reselecting the first PRS improves calibration because the initial was 3 returns but reselecting uses 10.
In the Kongsberg system details, symbols like the asterisk and circle (separate after recalibration), RefSys view info, filtering stages—each of these can form a question. For example, what does the asterisk vs. circle represent after recalibration?
Common-Mode Failure example: using two DGPS leading to both failing and the system rejecting the third good one. So a question might present that scenario and ask what problem is occurring.
Ensuring that for each of the 20 questions I cover different sections and don’t repeat topics unnecessarily. Sometimes similar concepts come up, but phrasing the questions differently would help. Like one question on why median is used over average, another on the consequence of using average instead.
Also, tests have different parameters. For example, the Bias Test vs. Median Test. Make sure questions differentiate their purposes—Bias Test gives a warning, Median can be set to warn or reject. The Bias Test is one of the slow drift tests, as is the Median Test.
The third stage of filtering mixes PRS measurements to compute vessel position. If a PRS is close to Variance Test limit, maybe it’s given less weight. Questions here might ask about stage three’s purpose or how noisy PRS affects the mix.
The Variance Test’s standard deviation check is against three times the expected accuracy (default 2.24m → threshold is ~6.72m). Any PRS with SD exceeding that is rejected. So a question here could ask for the calculation based on given accuracy.
For the second stage filtering (9 old + new)/10, the question could present the formula and ask what stage it belongs to, or what’s the effect of this filtering.
Weighting being inversely proportional to variance: higher variance (less accurate) PRS have lower weight. A question might ask how a PRS with high variance is weighted, with the correct answer being lower weight.
Total weighting sum to 1.0 regardless of number of PRS. So if three PRS are enabled, summing their weights equals 1.
Prediction Test vs. Median Test limits. The median test’s limit is 80% of the minimum Prediction error limit. And since the Prediction error limit is never less than 5m, the Median Test limit would be at least 4m (80% of 5m). A question could ask about this relationship.
Another detail: the Median Test is independent of the vessel model. A PRS could be rejected even if aligned with the model. So a question might present that scenario and ask which test is responsible.
In PRS handling, when in Monitoring mode, the PRS is not used for position but monitored—so a question could ask what Monitoring mode allows the DPO to do.
Making sure to vary question types: some about definitions, some about specific numbers, some about procedural steps, some about understanding consequences or reasons behind methods.
Let me start drafting possible questions, keeping track to cover different sections and ensure 20 distinct questions without overlap. Each question must have a correct answer and three plausible distractors based on the content. Examples:
- What is the primary reason for using the median instead of the average in PRS voting?
- A. To minimize computational complexity.
- B. To avoid pollution of data from erroneous systems.
- C. To ensure the highest possible accuracy.
- D. To reduce the number of required PRS. Correct: B.
- What is the maximum positional jump after a PRS is rejected in the Median Test?
- A. 5-6 meters
- B. 2.5-3 meters
- C. 1-2 meters
- D. Equal to the test limit Correct: B.
- During initial calibration of the first PRS, how many successive returns within 10m are needed?
- A. 3
- B. 5
- C. 10
- D. 15 Correct: A.
Etc. For each key point, extract a question. Now, need to ensure that all 20 are covered and vary the topics. I need to check each section to ensure coverage.
Here are 20 challenging multiple-choice questions based on the provided content about Kalman filtering and dynamic positioning (DP) systems:
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