It is video we're going to look at how to deal with stochastic biases inside the system.
So we've already covered that.
If it's a deterministic bias, we can use a calibration procedure to calibrate it out.
But first, DiCicco biases.
They have to be estimated on the fly as we run the system.
The no prior information can be used to compensate for them.
So random or stochastic biases or biases that are deterministic so they can't be correctly calibrated
out of the system.
They can't be corrected by calibration.
They must be corrected on the fly during the sensor operation, which means that we have to estimate
the bias parameters using filtering as we run the system.
And to do this we use something called bias parameter estimation.
We can use a joint estimation process to estimate the bias parameter along with the other states that
we want to estimate as we are operating the field on.
And to do this, we include the bias parameter inside the measurement model and also as estimated,
the state inside the state vector to form an Augmentin vector.
So basically inside the measurement model, we can add the bias into the measurement models.
We are this Batan here.
We can also add it inside the state model.
So it is going to be something else to estimate.
So the common field of estimates and state that X but want to estimate the statement X plus the bias
Tambe, so they form this argument model.
So we form this augmented state system that we want to estimate instead of just estimating the X Factor,
we want to estimate this X augmented vector.
So to do this, we also need to augment the state process model.
So we have the typical process model here, but then we also have the dynamics of the bias.
And what we're going to say is the bias is pretty much just going to be a constant bias subject to some
random noise WB here.
So the process model noise is actually just again augmented with the original one, plus the noise value,
the standard deviation of this noise term here.
So we can model the dynamics of this bias, Premier, as a stationary concept, which is basically saying
that the derivative is going to be equal to zero so that B is equal to zero.
So this is saying that we want to estimate a constant.
We can then use a person's model noise, this Sigma B squared here, which is the amount of noise the
for the bias, we can use this parameter to set how quickly we want this president estimate to change
or converge or drift.
So if we set this to zero, it's saying that we know the bias exactly.
Is not going to estimate it.
If we set this value to a large number, it means that we have no idea what the bias is.
So a lot of the error is going to get put into the bias.
So it's going to come down to a waiting factor, a cheating factor between how large this value is compared
to how much noise we get in the system.
So there are some limitations of doing this.
The first one is that the bias parameter must be observable by the system.
So additional measurements or system dynamics need to be such that the bias can be estimated.
However, it does not need to be directly observable so the estimation can happen over a long time horizon.
So even though we might have a bias in the sensor, we might be able to estimate what the bias is if
we run the filter for long enough.
A typical example is if there's a bias on the right sensor, such as a gyroscope, we could estimate
this bias if we also fused in heading information, which is basically the integral of the right.
The motion model, i.e. the integration process of the right along with the heading measurements, would
allow the right bias to be estimated over time, as the bias would call that Anglet era, which can
be identified from the Angella measurements.
So basically, if we know the heading information, we can work out what the ideal heading right would
be.
And this heading right will be different to the measured heading right.
Based on the bias.
So we can estimate what the bias would be slightly over time to take out the bias from the measurement.