1
00:00:03,970 --> 00:00:08,110
So in this video, we're going to look at the common food prediction step, but we're actually going

2
00:00:08,110 --> 00:00:12,050
to go through an example using the process model that we have developed before.

3
00:00:12,760 --> 00:00:16,690
So in this example, we're going to use our vehicle process model shown here.

4
00:00:16,720 --> 00:00:23,380
So this is the nonlinear process model it takes in the current state, which is going to vasti our heading.

5
00:00:23,380 --> 00:00:27,210
Our position in the X and Y takes in the input of an acceleration.

6
00:00:27,220 --> 00:00:28,150
And you're right.

7
00:00:28,690 --> 00:00:31,870
And it calculates the next they start using these equations here.

8
00:00:32,650 --> 00:00:35,140
For this example, we're going to start off with our current state.

9
00:00:35,140 --> 00:00:38,150
X is going to be five zero zero zero.

10
00:00:38,170 --> 00:00:40,590
So this is saying we're traveling at five meters a second.

11
00:00:40,600 --> 00:00:45,260
We have zero heading and we're starting at zero position in the X and zero position.

12
00:00:45,270 --> 00:00:46,750
And why now?

13
00:00:46,750 --> 00:00:49,170
At this time, we're also going to have the current input.

14
00:00:49,390 --> 00:00:55,800
So we're going to say at this time, step one, we're going to be rotating at a loss this point to radians.

15
00:00:55,800 --> 00:01:00,760
The second we're going to be accelerating at two meters per second squared and we're going to have a

16
00:01:00,760 --> 00:01:02,910
timestep of point one seconds.

17
00:01:03,490 --> 00:01:09,190
So using this information here and this process model up here, we can put these values into the process

18
00:01:09,190 --> 00:01:12,490
model and calculate our new predicted state for Tompsett one.

19
00:01:14,720 --> 00:01:19,760
So when we do that, we end up with these equations here so you can see this vector here is our current

20
00:01:19,760 --> 00:01:26,120
state of K minus one, so we can substitute this in here and we get a five we can put in outdate over

21
00:01:26,120 --> 00:01:27,750
here our input.

22
00:01:27,780 --> 00:01:30,350
So you're right, an acceleration right into here.

23
00:01:30,770 --> 00:01:36,950
And we pull in our current velocity, which is five, five and a heading which is zero zero into these

24
00:01:36,950 --> 00:01:37,600
terms here.

25
00:01:37,610 --> 00:01:42,390
So we end up with this equation here and we end up with this vector here.

26
00:01:42,410 --> 00:01:45,340
So this is going to be our predicted state four times that one.

27
00:01:45,710 --> 00:01:48,740
So this is how we can take our best estimate at time.

28
00:01:48,740 --> 00:01:54,550
Zero predicted forward using our current input and the process model to get our new predicted state

29
00:01:54,680 --> 00:01:55,670
four times that one.

30
00:01:58,190 --> 00:02:03,650
Now we can do the same thing, looking at the covariance prediction step, so we already have seen that

31
00:02:03,650 --> 00:02:09,470
we can calculate the Jacobean matrix for this process model using this equation off the top here so

32
00:02:09,470 --> 00:02:14,590
we can take a current state estimate, which is this Victor, right here, which is five zero zero zero.

33
00:02:14,840 --> 00:02:20,170
And we can substitute it into our Jaconi matrix here to end up with this Jakobsson matrix.

34
00:02:20,180 --> 00:02:26,150
So basically where we have data, we substitute in a point, one where we have Sci., our current Saligari

35
00:02:26,150 --> 00:02:26,570
Zero.

36
00:02:26,570 --> 00:02:27,740
So we substitute in zero.

37
00:02:28,040 --> 00:02:33,910
And where we have V, we take in our current five recurrent velocity, which is five and something like

38
00:02:33,920 --> 00:02:34,640
that in there.

39
00:02:35,120 --> 00:02:39,000
So when we evaluate all this all out, we end up with this matrix here.

40
00:02:39,020 --> 00:02:45,560
So this is the Jacobean matrix for the state model with respect to the state vector.

41
00:02:46,250 --> 00:02:49,790
And it's going to be evaluated around this state estimate here.

42
00:02:52,200 --> 00:02:57,270
There's also assume that we have a current covariance, so we have a P value here and this is going

43
00:02:57,270 --> 00:03:00,120
to be this matrix here.

44
00:03:00,120 --> 00:03:05,700
So we're going to have a value of ten and certainly for our velocity, a value one, uncertainty for

45
00:03:05,700 --> 00:03:06,240
our heading.

46
00:03:06,480 --> 00:03:12,750
And we assume we have a good position estimate for the X and Y so we can use our common field.

47
00:03:12,750 --> 00:03:18,000
Our prediction step for the covariance, this equation here, and we're going to assume that we have

48
00:03:18,000 --> 00:03:19,620
zero process, more noise.

49
00:03:19,810 --> 00:03:22,610
So we assume that we know the input into the system.

50
00:03:22,660 --> 00:03:23,790
Al, you're right.

51
00:03:23,790 --> 00:03:24,550
An acceleration.

52
00:03:24,570 --> 00:03:25,080
Exactly.

53
00:03:25,560 --> 00:03:28,900
So this is the key term here is just going to end up being zero.

54
00:03:29,490 --> 00:03:36,180
So we take this equation here and expand it out so we can take an objective in this matrix here, multiply

55
00:03:36,180 --> 00:03:43,840
it by Cabarrus Matrix, multiply by transpose of Jacobean and this equation t we can go through, do

56
00:03:43,860 --> 00:03:47,910
all the calculations, expand out and we end up with this matrix here.

57
00:03:48,330 --> 00:03:52,740
So this is going to be our predicted covariance matrix for TimeStep one.

58
00:03:54,200 --> 00:03:59,600
So this is basically the whole extended minefield, our predictions, that process, we probably get

59
00:03:59,600 --> 00:04:05,420
the last best estimates set forward using the process model, and then we also take into account the

60
00:04:05,420 --> 00:04:10,880
uncertainty in the system by propagating forward the covariance matrix from the previous TOMPSETT to

61
00:04:10,880 --> 00:04:11,810
the current time set.

62
00:04:13,470 --> 00:04:17,010
So this pretty much outlines the whole extended method of prediction step.