1 00:00:03,350 --> 00:00:08,240 Data fusion is a wide subject area, so we'll concentrate on one of the most powerful methods for data 2 00:00:08,240 --> 00:00:11,450 fusion, which is Bayesian or probabilistic data fusion. 3 00:00:11,840 --> 00:00:16,440 This is where the state of the dynamic system is encapsulated as a probability distribution. 4 00:00:16,790 --> 00:00:22,430 This distribution is an updated with the distributions of sensor measurements or other sources of information 5 00:00:22,640 --> 00:00:25,760 to form the most optimal estimate of the state of the system. 6 00:00:25,760 --> 00:00:31,730 At this particular time, probability is a very powerful framework to build data fusion algorithms upon. 7 00:00:32,150 --> 00:00:37,580 It inherently allows us to capture the uncertainty with the process model and measurement model, and 8 00:00:37,580 --> 00:00:41,220 it helps us to understand how good the estimates of the state are. 9 00:00:41,570 --> 00:00:42,980 Let's take an example. 10 00:00:43,370 --> 00:00:49,200 We have a car that can travel in one direction as seen here, so its position can shift left and right. 11 00:00:49,670 --> 00:00:54,950 Our goal is to estimate or track the position of the car as it moves and evolves of time. 12 00:00:55,850 --> 00:01:00,700 So the state to be estimate it is the position and the dynamic system is the vehicle kinematics. 13 00:01:01,640 --> 00:01:07,070 If we knew the exact position of the car or had some way to measure it without any error, then we wouldn't 14 00:01:07,070 --> 00:01:08,570 need any state estimation. 15 00:01:08,780 --> 00:01:13,990 But since we don't, we have to use noisy sensor measurements of a decision to estimate where it is. 16 00:01:14,570 --> 00:01:16,210 This is where data fusion comes in. 17 00:01:17,360 --> 00:01:20,740 Initially, we might not have a great idea of where the car is located. 18 00:01:21,110 --> 00:01:25,340 So if we do a probability function of where the car might be, it might look like this. 19 00:01:26,120 --> 00:01:29,170 We have a rough idea of where it is at this initial point in time. 20 00:01:29,480 --> 00:01:32,070 This is where the distribution has a large amount of area. 21 00:01:32,300 --> 00:01:36,200 So this is where it's most likely to be here, but we don't know for sure. 22 00:01:37,410 --> 00:01:43,050 Now, as time evolves, the car can move, so the probability evolves and grows with time, the amount 23 00:01:43,050 --> 00:01:45,090 of uncertainty in the system is growing. 24 00:01:45,540 --> 00:01:50,760 The initial probability distribution grows with time in conjunction with the system dynamics, or in 25 00:01:50,760 --> 00:01:56,490 this case, the we kinematics to form a predicted probability distribution for the current time in the 26 00:01:56,490 --> 00:01:56,940 future. 27 00:01:59,000 --> 00:02:05,090 Now we get a bit of information from a censor such as from GPS, it tells us an estimate of the cost 28 00:02:05,090 --> 00:02:11,720 position that the car is located somewhere here with this measurement probability distribution, this 29 00:02:11,720 --> 00:02:14,480 measurement distribution comes from the properties of the sensor. 30 00:02:14,720 --> 00:02:19,490 A sensor will only be accurate to a certain position and such in real life. 31 00:02:19,490 --> 00:02:24,840 Normal standard GPS such as what's in your mobile phone is only accurate to tens of meters. 32 00:02:25,580 --> 00:02:30,390 This gives us information about the shape of the measurement distribution and how much uncertainty or 33 00:02:30,390 --> 00:02:32,090 error each measurement may have. 34 00:02:33,590 --> 00:02:38,930 We can combine the measurement distribution with the current best estimate distribution to come up with 35 00:02:38,930 --> 00:02:41,240 an even better estimate of the composition. 36 00:02:42,330 --> 00:02:46,980 And we can keep repeating this process, evolving the distribution of time and then constraining it 37 00:02:46,980 --> 00:02:52,260 with measurements after each update, the distribution is always smaller than before. 38 00:02:53,720 --> 00:03:00,110 So you can see from this simple example that sensor data fusion is usually split into two phases, most 39 00:03:00,110 --> 00:03:05,300 estimation processes follow the simple processes of breaking the problem up into two recursive steps. 40 00:03:05,510 --> 00:03:07,610 The first step is the prediction step. 41 00:03:08,420 --> 00:03:13,790 The prediction step is used to calculate the best estimate of the state for the current time using all 42 00:03:13,790 --> 00:03:16,640 the available information we have at that specific time. 43 00:03:17,300 --> 00:03:19,600 This is where the uncertainty in the estimates grow. 44 00:03:20,930 --> 00:03:26,390 The update step is where the current best state estimate is update of measurements or information when 45 00:03:26,390 --> 00:03:27,360 they become available. 46 00:03:27,740 --> 00:03:30,080 This is to produce an even better estimate. 47 00:03:30,350 --> 00:03:32,930 This is where the uncertainty in the estimate shrinks. 48 00:03:34,260 --> 00:03:39,150 Now, these two steps don't have to be rerun in sequence, you might have different senses or different 49 00:03:39,150 --> 00:03:41,160 measurements being made at different rates. 50 00:03:41,700 --> 00:03:47,490 So you might make multiple prediction steps before the next sense of measurement is fused in now to 51 00:03:47,490 --> 00:03:51,720 carry out the mathematical operations required to do all the above calculations. 52 00:03:51,750 --> 00:03:57,450 It can become very numerically difficult and computationally slow, especially if we start to estimate 53 00:03:57,450 --> 00:03:59,230 more than one state at the time. 54 00:04:00,030 --> 00:04:05,850 This is where the power of the common filter comes into play by making a few assumptions about the probability 55 00:04:05,850 --> 00:04:06,580 distributions. 56 00:04:06,900 --> 00:04:13,050 We can dramatically simplify the calculations, which is open up a huge wide range of applications, 57 00:04:13,050 --> 00:04:18,660 with some of the first being navigating a spacecraft to the moon and back with less computational power 58 00:04:19,230 --> 00:04:20,820 than a mobile phone in your pocket. 59 00:04:21,930 --> 00:04:28,290 So to recap, the key ideas are that we can represent the estimated state as a probability distribution, 60 00:04:29,310 --> 00:04:34,320 represent the measurements or observations of the current state, or a function of the states as a probability 61 00:04:34,320 --> 00:04:34,950 distribution. 62 00:04:35,670 --> 00:04:40,150 And we can optimally fuse the two distributions together to get a better estimate. 63 00:04:40,980 --> 00:04:45,680 Now, when we do the prediction step, the uncertainty of the system increases with time. 64 00:04:46,380 --> 00:04:49,620 When we do the update and measurement step, it decreases. 65 00:04:49,620 --> 00:04:56,100 The uncertainty at that time become a filter allows us to do this numerically and mathematically simple 66 00:04:56,100 --> 00:05:01,350 by making a few assumptions about the probability distributions and a few other properties of the dynamic 67 00:05:01,350 --> 00:05:03,420 system in question that we would like to estimate.