Right, let's pick this up — Page 282, Lesson 279

Right, let's pick this up. We've just dealt with that apparent longitude divergence between IRS positions, and now we're moving into the heart of how the navigation computer actually resolves these errors. This is the Kalman filter. I want you to think of the Kalman filter as the brain of the navigation computer. Its entire job is to combine two different sources of information to get the best possible position. Specifically, it combines the short term accuracy of the IRS with the long term accuracy of the external reference. That's the core definition. The IRS is brilliant for a short while, but it drifts. The external reference, like a DME or VOR, is steady over the long haul. The Kalman filter is the process that marries these two. Now, how does it actually work? The model inside the computer assesses the velocity and position errors from the IRS. It does this by comparing the IRS position with the external reference. From that comparison, it produces its own prediction of position and velocity. So it's not just picking one or the other; it's constantly comparing them and building a blended prediction. Here's the key part about the weighting. At the start of the flight, the IRS information is the most accurate. So the weighting system within the model initially favours the IRS information. But as the flight progresses, the IRS errors build up—that's the ramp effect we talked about. As that happens, the external reference becomes the most accurate, and the model becomes more biased towards it. So the weighting shifts gradually from the IRS to the external reference. What's the consequence of this? The position will be most accurate right after the position update on the runway threshold. That's when the IRS is fresh and the external reference has just confirmed the position. But then, as the flight progresses, the position accuracy will gradually decay down to the accuracy of the external reference. It won't get worse than that, because the external reference is holding it steady. Then, when the aircraft is on final approach using a precision system—that's ILS or MLS—the position information will improve again. Those systems give a very precise update. One more thing on the Kalman filter: the more complex the model, the better the quality. The more factors it includes, the better the system position and velocity will be. So a sophisticated model with lots of inputs gives a better output. Now, let's look at the accuracy of the IRS when it's combined with DME. This is a specific case. The position accuracy of the IRS continually degrades throughout the flight. But here's the important distinction: the heading and ground speed maintain a high degree of accuracy. So even though the position drifts, the heading and ground speed stay good. The measurement of position is subject to random errors which depend on two things: the range to the DME and the cut of the position lines. The "cut" is the angle at which the position lines from two DMEs intersect. If they cross at a shallow angle, the fix is poor. If they cross at a good angle, the fix is good. The computer solves that problem by selecting DMEs that are positioned so a good cut will be obtained. It picks the pair that gives the best geometry. Now, the slant range error is compensated for in the calculation. That's the error caused by measuring the straight-line distance to the DME rather than the horizontal distance. But the DME error itself is constant. It's plus or minus 0.25 nautical miles, plus or minus 1.25% of the range. So let's do that calculation. At 100 nautical miles, the error will be a maximum of 1.5 nautical miles. Let me show you that: 0.25 plus 1.25% of 100, which is 1.25, gives you 1.5 nautical miles total. Here's the crucial comparison. At the start of a flight, this DME error is large compared with the IRS error. The IRS is fresh and accurate, so the DME looks bad. But as the flight progresses, the IRS is degrading at around 1 nautical mile per hour. After several hours, since the DME error is constant, the DME fixing will be significantly more accurate than the IRS. So the roles reverse over time, exactly as the Kalman filter weighting predicted. Now, I see there's a multiple-choice question here that tests this exact concept. It asks what the FMC combines. Let me read you the options. Option A says the FMC combines the short term accuracy of the IRS with the long term accuracy of the external reference. Option B says it combines the long term accuracy of the IRS with the long term accuracy of the external reference. Option C says it combines the short term accuracy of the IRS with the short term accuracy of the external reference. And option D says it combines the short term accuracy of the IRS with the long term accuracy of the external reference. Now, I'm not going to tell you the answer, because you should work through it. But think about what we just covered. The Kalman filter combines the short term accuracy of the IRS with the long term accuracy of the external reference. That's the definition we started with. So which option matches that exactly? Look at the wording carefully. Option A and option D look very similar, but there's a subtle difference. Read them again. One says "the FMC combines" and the other says "the FMC combines"—wait, let me look again. Option A says "the FMC combines the short term accuracy of the IRS with the long term accuracy of the external reference." Option D says "the FMC combines the short term accuracy of the IRS with the long term accuracy of the external reference." They look identical to me. Let me read them again very carefully. Option A: "the FMC combines the short term accuracy of the IRS with the long term accuracy of the external reference." Option D: "the FMC combines the short term accuracy of the IRS with the long term accuracy of the external reference." Hmm, they appear to be the same statement. That's a quirk of the source material. But the point stands: the correct concept is the one that matches our definition. The IRS gives short term accuracy, the external reference gives long term accuracy, and the FMC combines them. So whichever option states that combination is the one you want. I'll leave you to identify it on the page. So to summarise what we've covered: the Kalman filter blends the IRS and the external reference, weighting shifts from IRS to external as the flight progresses, position is best at the runway threshold and on final approach with ILS or MLS, and DME error is constant at plus or minus 0.25 NM plus 1.25% of range, while the IRS degrades at about 1 NM per hour. That's the full picture.