1 00:00:03,680 --> 00:00:08,180 Now that we've gone over how the common thread update updates, works and the equations behind it, 2 00:00:08,690 --> 00:00:14,570 we're going to look at implementing it in the third, try to come and filter example, the update measurement 3 00:00:14,570 --> 00:00:18,980 model that we're going to use in our tutee track a filter is going to be a very simple model. 4 00:00:19,430 --> 00:00:24,740 All it's going to be is just a measurement of the position in the X and Y axes with a bit of noise added 5 00:00:24,740 --> 00:00:25,100 to it. 6 00:00:25,800 --> 00:00:29,570 So we can represent this using the common field of measurement model equation. 7 00:00:30,230 --> 00:00:35,790 So the measurement is just going to be a linear combination of the state with some additive noise. 8 00:00:35,990 --> 00:00:41,180 So this matrix, the measurement model is just going to be a simple identity matrix with a one and one 9 00:00:41,180 --> 00:00:43,890 in the X and Y columns. 10 00:00:44,660 --> 00:00:49,730 So this model here just gives us the measurement model, which is just the X and Y position measurements, 11 00:00:50,240 --> 00:00:52,600 and then we're going to have a bit of additive noise to it. 12 00:00:53,030 --> 00:00:59,060 And this additive noise this week is just going to be of a normal distribution with a zero mean and 13 00:00:59,060 --> 00:00:59,720 covariance. 14 00:00:59,720 --> 00:01:06,830 Uh, where are is just a diagonal matrix so that the X and Y noises aren't correlated and the X and 15 00:01:06,830 --> 00:01:11,930 Y noise is just going to have a standard deviation of the Sigma X squared and Sigma Y squared. 16 00:01:12,410 --> 00:01:17,290 And we're actually just going to assume that these two components here are just going to be the same. 17 00:01:17,300 --> 00:01:18,740 So it's just going to be a sigma measurement. 18 00:01:19,190 --> 00:01:24,020 So we're going to have equal noise on the X and Y axes, so we're not going to be biased towards one 19 00:01:24,020 --> 00:01:24,710 or the other. 20 00:01:26,770 --> 00:01:32,740 Now, the actual exercise step for the update process is to implement the common or update equations 21 00:01:32,740 --> 00:01:35,510 and the 2D tracking measurement model, which we discovered. 22 00:01:36,070 --> 00:01:39,950 So the first step is to open the Python file assignment, one update. 23 00:01:40,840 --> 00:01:44,470 Now, when we run it, as is, we see the object starts moving from the origin. 24 00:01:44,470 --> 00:01:49,950 So X and Y equals zero zero, but it moves in a random direction and speed. 25 00:01:50,200 --> 00:01:53,770 So every time you run it, the direction and speed are going to be slightly different. 26 00:01:54,190 --> 00:01:56,740 So the V, X and the Y are unknown. 27 00:01:56,950 --> 00:02:01,810 So we want to implement the update step to help estimate these parameters. 28 00:02:04,140 --> 00:02:09,770 So we want to go down to the initialization part and implement the Haganah matrixes as shown here, 29 00:02:11,040 --> 00:02:16,010 and all we want to do is fill in the and Matrix's as written on the right here. 30 00:02:16,530 --> 00:02:20,530 And we also want to assume that the precision measurements have a standard deviation of 10. 31 00:02:20,970 --> 00:02:24,240 So basically here we have 10 squared, 10 squared for the R matrix. 32 00:02:24,240 --> 00:02:28,310 So it's probably best just to use a variable so we can quickly change it later. 33 00:02:29,600 --> 00:02:34,430 So once we have set up the original matrix, the next step in the process is to implement the common 34 00:02:34,430 --> 00:02:36,040 filter updates to the equations. 35 00:02:36,620 --> 00:02:41,660 So inside the code, we have a function called Update Step and we want to go through and implement a 36 00:02:41,660 --> 00:02:44,390 different common for update equations that are required. 37 00:02:44,870 --> 00:02:49,850 So you can see here these equations on the right are the commentor update equations, which we're going 38 00:02:49,850 --> 00:02:50,150 through. 39 00:02:50,510 --> 00:02:55,760 So we want to mathematically write them in code under the update and you'll find the different positions 40 00:02:55,760 --> 00:02:56,510 inside the code. 41 00:02:56,510 --> 00:02:58,100 So you can see here we have Z ahat. 42 00:02:58,400 --> 00:03:03,170 So in this line of code here would work at al-Said Hat, which is our predictive measurements, which 43 00:03:03,170 --> 00:03:05,870 is Hech times X, which is also written here. 44 00:03:06,710 --> 00:03:10,010 So we'll go through and implement the common filter equations in this part of the code. 45 00:03:10,490 --> 00:03:13,020 And then the last step is to run the simulation. 46 00:03:13,700 --> 00:03:19,180 So if we run the simulation, as is, we'll say that the Kamasutra estimate does not change or is updated. 47 00:03:19,580 --> 00:03:22,680 This is because the initial uncertainty is set to zero. 48 00:03:22,700 --> 00:03:26,760 So we're basically taking the field that we know exactly where it is at the initial time. 49 00:03:27,080 --> 00:03:31,790 Therefore, any other information that we try to use to tell it otherwise is just going to be ignored. 50 00:03:32,670 --> 00:03:38,030 So what we do is then change initial velocity sanitisation to 10 and rerun the simulation. 51 00:03:38,630 --> 00:03:43,700 And then when we do that, we should be seeing that the common filter updates, the state estimates. 52 00:03:43,700 --> 00:03:50,270 As time goes on and we start tracking the object and the covariance around the object starts to decrease 53 00:03:50,270 --> 00:03:52,710 and shrink down and converge to the true position. 54 00:03:53,360 --> 00:03:58,880 And when we do this, we should also see that the main position and main velocity square there should 55 00:03:58,880 --> 00:03:59,980 be fairly small as well. 56 00:03:59,990 --> 00:04:02,030 So it should be tracking the object fairly well. 57 00:04:04,850 --> 00:04:10,630 So I'll let you go away and implement those equations inside the Python files and run the exercise. 58 00:04:11,090 --> 00:04:15,560 So after you've done that in the next video, we'll go through an explanation of what's happening behind 59 00:04:15,560 --> 00:04:18,470 the scenes and what we are actually seeing in the responses.