1 00:00:04,120 --> 00:00:08,830 So now that we have finished implementing the prediction step for the Senate to come filter, we can 2 00:00:08,830 --> 00:00:11,800 have a look at a few things that we should have notice while we were doing this. 3 00:00:13,590 --> 00:00:18,720 The first thing we should have noticed is that the inclusion of the gyroscope allows the filter to respond 4 00:00:18,720 --> 00:00:24,150 quicker to a directional changes, such as the car turning as the filter now has a concept of direction 5 00:00:24,150 --> 00:00:27,520 and heading and heading right or you're right from the gyroscope. 6 00:00:28,020 --> 00:00:34,400 This cannot be done in the linear field due to the non-linear process model required for this to happen. 7 00:00:35,190 --> 00:00:41,700 So when we run the external filler and the linear comma filter for the same profile, we can see that 8 00:00:41,700 --> 00:00:47,670 the estimated state can more quickly change its direction as it now has a concept of the direction and 9 00:00:47,670 --> 00:00:52,950 it has the inherent knowledge that the car always has to be travelling in the direction it's facing. 10 00:00:53,850 --> 00:00:55,590 When we're using the linear common filter. 11 00:00:55,770 --> 00:00:58,790 The linear common filter has no concept of heading or anything. 12 00:00:58,800 --> 00:01:04,810 It only has X and Y velocity and position it that you can't link the two together using the direction. 13 00:01:05,250 --> 00:01:08,580 So this is one of the advantages of using the extended computer. 14 00:01:08,820 --> 00:01:12,060 We can include this extra information inside the process model. 15 00:01:15,470 --> 00:01:18,290 So we can see where they run, both in the simulation side by side. 16 00:01:18,320 --> 00:01:21,490 There is a dramatic difference, especially when the vehicle starts turning. 17 00:01:21,860 --> 00:01:24,560 We get a lot more information about how the vehicle turns. 18 00:01:24,640 --> 00:01:30,290 I can see that the uncertainty slips in the extended Kamikura rotates with the vehicle while in the 19 00:01:30,290 --> 00:01:32,830 2D linear coming through like this cannot be established. 20 00:01:33,080 --> 00:01:39,260 And so the estimated state sort of drifts off to the side as it turns and takes a while for it to converge 21 00:01:39,260 --> 00:01:41,030 back down to the vehicle location. 22 00:01:48,970 --> 00:01:53,740 However, with the extended calm theater, we have come across this other problem, the extended coming 23 00:01:53,740 --> 00:01:59,170 theater is very sensitive or can be sensitive to the initial conditions for the state and the covariance. 24 00:01:59,590 --> 00:02:03,790 The extended coming theater is not guaranteed to converge to the true state. 25 00:02:04,120 --> 00:02:10,900 Unlike the linnear coming theater, the extended theater can diverge if the estimated state is too far 26 00:02:10,900 --> 00:02:11,990 away from the true state. 27 00:02:12,610 --> 00:02:16,460 This is because we're using the linear approximation of the nonlinear system. 28 00:02:17,320 --> 00:02:22,800 We can also see that we have to try to initialize the a theater as best as possible. 29 00:02:22,810 --> 00:02:27,210 We want to initialize it with the full state and covariance from measurement data. 30 00:02:27,520 --> 00:02:33,190 We can't just assume zero state with a of uncertainty and expect it to converge. 31 00:02:33,520 --> 00:02:38,140 So we can see that when we run the linear common filter and the extended common filter for the same 32 00:02:38,140 --> 00:02:44,770 profile where we have non-zero initial conditions, we can see that the extended field looks on and 33 00:02:44,770 --> 00:02:47,350 converges to a wrong heading value. 34 00:02:47,350 --> 00:02:50,680 The heading that is actually one hundred and eighty degrees out of phase. 35 00:02:51,100 --> 00:02:52,480 Now this is going to become a problem. 36 00:02:52,480 --> 00:02:56,380 If the vehicle starts turning because of JavaScript information, it's going to be back to front. 37 00:02:56,860 --> 00:03:02,620 And you can see that inside this situation where the extended current filter has converged to the wrong 38 00:03:02,620 --> 00:03:07,510 value is going to produce very bad estimates, is not going to work at all. 39 00:03:07,720 --> 00:03:12,640 And in fact, if the vehicle starts turning, is a good chance that the external computer is just going 40 00:03:12,640 --> 00:03:13,730 to diverge and blow up. 41 00:03:14,080 --> 00:03:18,880 But even in the current state, the information that the extended computer is giving us is going to 42 00:03:18,880 --> 00:03:25,540 be useless for if we wanted to control the car or do any other processes that require this information 43 00:03:25,540 --> 00:03:30,110 because its information is incorrect, if we try to use it is just going to be very bad. 44 00:03:31,480 --> 00:03:33,870 So this is one of the problems with the extended common filter. 45 00:03:33,880 --> 00:03:40,410 We always want to initialize it, the full state and covariance as closely as possible to the truth. 46 00:03:40,870 --> 00:03:46,570 We can't just let my filter converge because there's no guarantee that it will converge to the truth. 47 00:03:48,350 --> 00:03:53,780 In real life, to handle the situation, if we can't assume that we know the perimeter correctly, when 48 00:03:53,780 --> 00:03:58,710 we first turn on the field, we're going to have to wait until we get enough knowledge to initialize 49 00:03:58,710 --> 00:03:59,190 the filter. 50 00:03:59,540 --> 00:04:04,310 So this might mean we might need to take multiple measurements and do a bit of processing on top of 51 00:04:04,310 --> 00:04:04,520 them. 52 00:04:04,520 --> 00:04:09,620 So we might need to take multiple measurements while it's moving then to try to estimate the heading 53 00:04:09,620 --> 00:04:10,230 of the vehicle. 54 00:04:10,580 --> 00:04:16,460 However, this means that we can't use any we can't use any control or anything on top of this which 55 00:04:16,460 --> 00:04:19,480 uses the filter information into the filter is converged. 56 00:04:19,760 --> 00:04:25,250 So there's a bit of a tradeoff between how how quickly we start the filter and then how quickly we can 57 00:04:25,250 --> 00:04:26,780 start using data from the filter. 58 00:04:27,140 --> 00:04:30,140 So this is going to be an engineering process, engineering problem. 59 00:04:30,800 --> 00:04:33,740 We always want to make sure we get the best situation possible. 60 00:04:34,820 --> 00:04:38,350 So we have to come up with ways to try to mitigate this problem or work around it.