Kalman Filtering need

Question

I have a swarm robotic project. The localization system is done using ultrasonic and infrared transmitters/receivers. The accuracy is +-7 cm. I was able to do follow the leader algorithm. However, i was wondering why do i still have to use Kalman filter if the sensors raw data are good? what will it improve? isn't just will delay the coordinate being sent to the robots (the coordinates won't be updated instantly as it will take time to do the kalman filter math as each robot send its coordinates 4 times a second)

Answer 1

Sensor data is NEVER the truth, no matter how good they are. They will always be perturbed by some noise. Additionally, they do have finite precision. So sensor data is nothing but an observation that you make, and what you want to do is estimate the true state based on these observations. In mathematical terms, you want to estimate a likelihood or joint probability based on those measurements. You can do that using different tools depending on the context. One such tool is the Kalman filter, which in the simplest case is just a moving average, but is usually used in conjunction with dynamic models and some assumptions on error/state distributions in order to be useful. The dynamic models model the state propagation ( eg motion knowing previous states) and the observation (measurements), and in robotics/SLAM one often assumes the error is Gaussian. A very important and useful product of such filters is an estimation of the uncertainty in terms of covariances.

Now, what are the potential improvements? Basically, you make sure that your sensor measurements are coherent with a mathematical model and that they are "smooth". For example, if you want to estimate the position of a moving vehicle, the kinematic equations will tell you where you expect the vehicle to be, and you have an associated covariance. Your measurements also come with a covariance. So, if you get measurements that have low certainty, you will end up trusting the mathematical model instead of trusting the measurements, and vice-versa.

Finally, if you are worried about the delay... Note that the complexity of a standard extended Kalman filter is roughly O(N^3) where N is the number of landmarks. So if you really don't have enough computational power you can just reduce the state to pose, velocity and then the overhead will be negligible.

Answer 2

In general, Kalman filter helps to improve sensor accuracy by summing (with right coefficients) measurement (sensor output) and prediction for the sensor output. Prediction is the hardest part, because you need to create model that predicts in some way sensors' output. And I think in your case it is unnecessary to spend time creating this model.

Answer 3

Although you are getting accurate data from sensors but they cannot be consistent always. The Kalman filter will not only identify any outliers in the measurement data but also can predict it when some measurement is missing. However, if you are really looking for something with less computational requirements then you can go for a complimentary filter.