1 00:00:03,820 --> 00:00:08,470 In this video, we're going to look at the process model that we're going to use inside our extended 2 00:00:08,470 --> 00:00:09,920 home in Philadelphia, this example. 3 00:00:10,120 --> 00:00:14,020 So this is going to cover a 2D non-linear vehicle process model. 4 00:00:15,640 --> 00:00:22,090 So looking back at the work we did for the linear filter example, we used a linear 2D, constant velocity 5 00:00:22,090 --> 00:00:26,910 motion model and in this model we represented the vehicle as a point mass. 6 00:00:26,920 --> 00:00:34,870 It had a position PXP y to denote the position of the vehicle and it had a velocity in the X and Y directions. 7 00:00:35,350 --> 00:00:41,110 So the state vector for this process model was the position in the X position in the Y velocity, any 8 00:00:41,110 --> 00:00:49,090 X and velocity in the Y, the discrete linear model can be described by these equations here. 9 00:00:49,450 --> 00:00:52,210 So this first matrix here is a process model matrix. 10 00:00:52,390 --> 00:00:56,440 It takes the current state and predicts a forward one time step over here. 11 00:00:56,440 --> 00:00:58,170 We have the control input matrix. 12 00:00:58,180 --> 00:01:04,180 So this takes the control input, in this case, acceleration in the X and Y and calculates the effect 13 00:01:04,180 --> 00:01:07,300 on the state to calculate the next predicted state. 14 00:01:09,640 --> 00:01:14,740 And of course, this model has a few assumptions, it treats the motion as a point, so a point has 15 00:01:14,740 --> 00:01:18,190 no orientation and it can accelerate in any direction. 16 00:01:19,300 --> 00:01:24,790 Now, these assumptions might not be very applicable to vehicles as vehicles do not typically operate 17 00:01:24,790 --> 00:01:25,340 this way. 18 00:01:26,020 --> 00:01:29,320 For example, a car can usually only travel in the direction is facings. 19 00:01:29,320 --> 00:01:32,490 I can either go forward or reverse in a direction it travels. 20 00:01:32,770 --> 00:01:34,360 It rarely goes sideways. 21 00:01:36,290 --> 00:01:39,750 So to compensate for this, we are going to use a non-linear motion model. 22 00:01:39,760 --> 00:01:41,980 And this is why we need the to come and filter. 23 00:01:42,640 --> 00:01:47,770 So extend extended Campbellfield up process model that we're going to use is going to be a 2D constant 24 00:01:47,770 --> 00:01:48,900 Vosta immersion model. 25 00:01:49,330 --> 00:01:55,090 We're going to have the vehicle represented here is going to have a position PXP y, but is also going 26 00:01:55,090 --> 00:01:59,400 to have a heading and inside the setting is going to have a Vosta along the heading direction. 27 00:01:59,890 --> 00:02:04,450 So if we're going forward here, it's going to be moving this way with a positive Rosty, if we go in 28 00:02:04,750 --> 00:02:07,960 reverse, is going to be moving this way with a negative velocity. 29 00:02:08,920 --> 00:02:15,100 So we can describe the state vector of the system as the velocity, the heading position and the X and 30 00:02:15,100 --> 00:02:21,430 the position in Y and then the discrete, nonlinear process model which describes this can be represented 31 00:02:21,430 --> 00:02:22,650 in this form here. 32 00:02:22,660 --> 00:02:28,810 So we have a precise model, nonlinear function called F that takes in the previous state the current 33 00:02:28,810 --> 00:02:34,030 control and calculates the current state and it can be written in this form here. 34 00:02:34,900 --> 00:02:40,270 So first off, we can see that the velocity at the time set K is just going to be the previous velocity 35 00:02:40,270 --> 00:02:43,520 at the previous timestep plus our Delta times. 36 00:02:43,520 --> 00:02:46,720 The acceleration and the same thing can be said about the heading angle. 37 00:02:46,720 --> 00:02:53,440 The heading angle is just going to be a constant integration over details of the heading right now where 38 00:02:53,440 --> 00:02:54,780 the system becomes non-linear. 39 00:02:54,790 --> 00:02:56,100 Are these terms down here? 40 00:02:56,110 --> 00:02:57,680 So we have a sign and a cause. 41 00:02:58,030 --> 00:03:01,750 So this is what makes the function cannot be written as a linear system. 42 00:03:02,260 --> 00:03:05,410 We can see that the cause is going to be a cause of the heading angle. 43 00:03:05,650 --> 00:03:09,450 The heading angle is one of the states and also has a sign of heading angle. 44 00:03:10,060 --> 00:03:13,270 So this is where the nonlinear realities come into the system. 45 00:03:14,110 --> 00:03:18,730 Now we also have these two terms up here, the acceleration and the heading right now. 46 00:03:18,730 --> 00:03:20,440 These are going to be the model inputs. 47 00:03:20,710 --> 00:03:24,160 So this is what's going to come in in the control vector here. 48 00:03:25,570 --> 00:03:31,600 So now when we look at this nonlinear process model, we can see that it contains our orientation information. 49 00:03:31,950 --> 00:03:37,720 So this means that vehicle can travel forward and reverse at velocity, but it cannot travel sideways. 50 00:03:38,320 --> 00:03:41,400 Now, the vehicle can only move along the direction it is facing. 51 00:03:42,190 --> 00:03:46,010 Now, these assumptions are a lot more appropriate for modeling a vehicle. 52 00:03:46,330 --> 00:03:51,490 So now when we use the extend the common filter, we can use this nonlinear process model to better 53 00:03:51,490 --> 00:03:57,220 represent the dynamics of the system that we want to estimate, which hopefully will move to improve 54 00:03:57,220 --> 00:03:58,600 the performance of the filter.