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Just to show you mathematically that they're right consider that if you have two sensors that are both measuring the same thing. One is Norm(mean=0, std=0.00001

Just to show you mathematically that they're right consider that if you have two sensors that are both measuring the same thing. One is Norm(mean=0, std=0.00001) and the other is Norm(mean=0, std=10). The true quantity is always zero in the real world. Given this scenario and these two senors you get the result of 0.11 and 11 as your return from the two sensors. Lets say we average the result of these two sensors. The average is farther from the true value than the first sensor was. The less reliable sensor is adding noise to our measurement. It isn't high utility.

JoshCole 5y ago
A crafty person here will draw on ideas like kalman filters and sensor fusion to notice that as the number of measurements increase you can gain precision even in the presence of an unreliable sensor. This is very true and it might be where the bad intuition that having multiple unreliable sensors is good is coming from. Multiple noisy readings can be averaged to get a more reliable reading if the distribution of reading errors is normally distributed. You can take ten Norm(0, 10) and average them and the result of that will be a normal distribution with a standard deviation which is lower than the standard deviation of the distribution that we sampled from. See basic statistics for the e There are a few reasons why this doesn't apply in this case: 1. The measurements aren't going to be of the same thing. At time step t, the state of the world is potentially different from t+1. Since we have one radar sensor averaging the results of the two sensor readings doesn't give us the true position. Kalman filters solve this with a dynamics function so this problem isn't something that is impossible to solve. 2. So lets say we solve it. Even if we did measure the same thing we have another problem. We don't have time to take advantage of the central limit theorem. Yes, multiple noisy readings of the same thing average to the true reading, but since we have only a split second to decide whether to slam on the break to avoid an accident we don't have the capacity to await convergence of the noisy sensor and noisy dynamic function to the true measurement. But lets say we did even though we don't. 3. The radar sensor isn't actually a normal distribution in terms of its noise. It's actually more accurate in certain low visibility conditions because it goes through occlusion, but less accurate given certain environments like going under an underpass. Since the noise isn't normally distributed you don't have the guarantees from statistics which you were hoping to rely on.

JoshCole 5y ago

A crafty person here will draw on ideas like kalman filters and sensor fusion to notice that as the number of measurements increase you can gain precision even in the presence of an unreliable sensor. This is very true and it might be where the bad intuition that having multiple unreliable sensors is good is coming from. Multiple noisy readings can be averaged to get a more reliable reading if the distribution of reading errors is normally distributed. You can take ten Norm(0, 10) and average them and the result of that will be a normal distribution with a standard deviation which is lower than the standard deviation of the distribution that we sampled from. See basic statistics for the e There are a few reasons why this doesn't apply in this case: 1. The measurements aren't going to be of the same thing. At time step t, the state of the world is potentially different from t+1. Since we have one radar sensor averaging the results of the two sensor readings doesn't give us the true position. Kalman filters solve this with a dynamics function so this problem isn't something that is impossible to solve. 2. So lets say we solve it. Even if we did measure the same thing we have another problem. We don't have time to take advantage of the central limit theorem. Yes, multiple noisy readings of the same thing average to the true reading, but since we have only a split second to decide whether to slam on the break to avoid an accident we don't have the capacity to await convergence of the noisy sensor and noisy dynamic function to the true measurement. But lets say we did even though we don't. 3. The radar sensor isn't actually a normal distribution in terms of its noise. It's actually more accurate in certain low visibility conditions because it goes through occlusion, but less accurate given certain environments like going under an underpass. Since the noise isn't normally distributed you don't have the guarantees from statistics which you were hoping to rely on.