1 00:00:03,670 --> 00:00:08,580 It is video we're going to look at how to deal with stochastic biases inside the system. 2 00:00:08,980 --> 00:00:10,750 So we've already covered that. 3 00:00:10,750 --> 00:00:15,350 If it's a deterministic bias, we can use a calibration procedure to calibrate it out. 4 00:00:15,760 --> 00:00:17,710 But first, DiCicco biases. 5 00:00:17,710 --> 00:00:21,360 They have to be estimated on the fly as we run the system. 6 00:00:21,400 --> 00:00:25,420 The no prior information can be used to compensate for them. 7 00:00:25,960 --> 00:00:32,710 So random or stochastic biases or biases that are deterministic so they can't be correctly calibrated 8 00:00:32,710 --> 00:00:33,880 out of the system. 9 00:00:33,880 --> 00:00:36,010 They can't be corrected by calibration. 10 00:00:36,670 --> 00:00:42,880 They must be corrected on the fly during the sensor operation, which means that we have to estimate 11 00:00:42,880 --> 00:00:46,720 the bias parameters using filtering as we run the system. 12 00:00:47,380 --> 00:00:51,190 And to do this we use something called bias parameter estimation. 13 00:00:52,180 --> 00:00:58,000 We can use a joint estimation process to estimate the bias parameter along with the other states that 14 00:00:58,000 --> 00:01:00,610 we want to estimate as we are operating the field on. 15 00:01:01,960 --> 00:01:07,810 And to do this, we include the bias parameter inside the measurement model and also as estimated, 16 00:01:07,810 --> 00:01:11,880 the state inside the state vector to form an Augmentin vector. 17 00:01:13,270 --> 00:01:18,580 So basically inside the measurement model, we can add the bias into the measurement models. 18 00:01:18,580 --> 00:01:19,750 We are this Batan here. 19 00:01:20,350 --> 00:01:22,690 We can also add it inside the state model. 20 00:01:22,930 --> 00:01:25,720 So it is going to be something else to estimate. 21 00:01:25,720 --> 00:01:31,630 So the common field of estimates and state that X but want to estimate the statement X plus the bias 22 00:01:31,630 --> 00:01:35,110 Tambe, so they form this argument model. 23 00:01:35,800 --> 00:01:42,250 So we form this augmented state system that we want to estimate instead of just estimating the X Factor, 24 00:01:42,250 --> 00:01:44,680 we want to estimate this X augmented vector. 25 00:01:46,150 --> 00:01:49,270 So to do this, we also need to augment the state process model. 26 00:01:49,270 --> 00:01:54,520 So we have the typical process model here, but then we also have the dynamics of the bias. 27 00:01:54,730 --> 00:02:00,670 And what we're going to say is the bias is pretty much just going to be a constant bias subject to some 28 00:02:00,670 --> 00:02:02,900 random noise WB here. 29 00:02:03,670 --> 00:02:10,880 So the process model noise is actually just again augmented with the original one, plus the noise value, 30 00:02:10,880 --> 00:02:13,690 the standard deviation of this noise term here. 31 00:02:15,690 --> 00:02:21,240 So we can model the dynamics of this bias, Premier, as a stationary concept, which is basically saying 32 00:02:21,240 --> 00:02:25,900 that the derivative is going to be equal to zero so that B is equal to zero. 33 00:02:26,460 --> 00:02:28,990 So this is saying that we want to estimate a constant. 34 00:02:29,970 --> 00:02:36,720 We can then use a person's model noise, this Sigma B squared here, which is the amount of noise the 35 00:02:37,080 --> 00:02:43,110 for the bias, we can use this parameter to set how quickly we want this president estimate to change 36 00:02:43,110 --> 00:02:44,610 or converge or drift. 37 00:02:45,240 --> 00:02:49,590 So if we set this to zero, it's saying that we know the bias exactly. 38 00:02:49,590 --> 00:02:50,700 Is not going to estimate it. 39 00:02:50,880 --> 00:02:55,260 If we set this value to a large number, it means that we have no idea what the bias is. 40 00:02:55,260 --> 00:02:58,290 So a lot of the error is going to get put into the bias. 41 00:02:59,280 --> 00:03:05,070 So it's going to come down to a waiting factor, a cheating factor between how large this value is compared 42 00:03:05,070 --> 00:03:07,170 to how much noise we get in the system. 43 00:03:08,610 --> 00:03:11,190 So there are some limitations of doing this. 44 00:03:11,580 --> 00:03:15,930 The first one is that the bias parameter must be observable by the system. 45 00:03:16,830 --> 00:03:21,700 So additional measurements or system dynamics need to be such that the bias can be estimated. 46 00:03:22,260 --> 00:03:28,460 However, it does not need to be directly observable so the estimation can happen over a long time horizon. 47 00:03:29,070 --> 00:03:34,230 So even though we might have a bias in the sensor, we might be able to estimate what the bias is if 48 00:03:34,230 --> 00:03:35,760 we run the filter for long enough. 49 00:03:36,900 --> 00:03:43,050 A typical example is if there's a bias on the right sensor, such as a gyroscope, we could estimate 50 00:03:43,050 --> 00:03:48,810 this bias if we also fused in heading information, which is basically the integral of the right. 51 00:03:49,380 --> 00:03:54,690 The motion model, i.e. the integration process of the right along with the heading measurements, would 52 00:03:54,690 --> 00:04:00,900 allow the right bias to be estimated over time, as the bias would call that Anglet era, which can 53 00:04:00,900 --> 00:04:03,140 be identified from the Angella measurements. 54 00:04:03,900 --> 00:04:09,690 So basically, if we know the heading information, we can work out what the ideal heading right would 55 00:04:09,690 --> 00:04:10,050 be. 56 00:04:10,230 --> 00:04:13,700 And this heading right will be different to the measured heading right. 57 00:04:13,890 --> 00:04:14,970 Based on the bias. 58 00:04:15,280 --> 00:04:20,700 So we can estimate what the bias would be slightly over time to take out the bias from the measurement.