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)
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 (e.g 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.
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.
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.
Related
I have an electromagnetic sensor which reports how much electromagnetic field strength it reads in space.
And I also have a device that emits electromagnetic field. It covers 1 meter area.
So I want to kind of predict position of the sensor using its reading.
But the sensor is affected by metal so it makes the position prediction drifts.
It's like if the reading is 1, and you put it near a metal, you get 2.
Something like that. It's not just noise, it's a permanent drift. Unless you remove the metal it will give reading 2 always.
What are the techniques or topics I need to learn in general to recover reading 1 from 2?
Suppose that the metal is fixed somewhere in space and I can calibrate the sensor by putting it near metal first.
You can suggest anything about removing the drift in general. Also please consider that I can have another emitter putting somewhere so I should be able to recover the true reading easier.
Let me suggest that you view your sensor output as a combination of two factors:
sensor_output = emitter_effect + environment_effect
And you want to obtain emitter_effect without the addition of environment_effect. So, of course you need to subtract:
emitter_effect = sensor_output - environment_effect
Subtracting the environment's effect on your sensor is usually called compensation. In order to compensate, you need to be able to model or predict the effect your environment (extra metal floating around) is having on the sensor. The form of the model for your environment effect can be very simple or very complex.
Simple methods generally use a seperate sensor to estimate environment_effect. I'm not sure exactly what your scenario is, but you may be able to select a sensor which would independently measure the quantity of interference (metal) in your setup.
More complex methods can perform compensation without referring to an independent sensor for measuring inteference. For example, if you expect the distance to be at 10.0 on average with only occasional deviations, you could use that fact to estimate how much interference is present. In my experience, this type of method is less reliable; systems with independent sensors for measuring interference are more predictable and reliable.
You can start reading about Kalman filtering if you're interested in model-based estimation:
https://en.wikipedia.org/wiki/Kalman_filter
It's a complex topic, so you should expect a steep learning curve. Kalman filtering (and related Bayesian estimation methods) are the formal way to convert from "bad sensor reading" to "corrected sensor reading".
I am looking at data points that have lat, lng, and date/time of event. One of the algorithms I came across when looking at clustering algorithms was DBSCAN. While it works ok at clustering lat and lng, my concern is it will fall apart when incorporating temporal information, since it's not of the same scale or same type of distance.
What are my options for incorporating temporal data into the DBSCAN algorithm?
Look up Generalized DBSCAN by the same authors.
Sander, Jörg; Ester, Martin; Kriegel, Hans-Peter; Xu, Xiaowei (1998). Density-Based Clustering in Spatial Databases: The Algorithm GDBSCAN and Its Applications. Data Mining and Knowledge Discovery (Berlin: Springer-Verlag) 2(2): 169–194. doi:10.1023/A:1009745219419.
For (Generalized) DBSCAN, you need two functions:
findNeighbors - get all "related" objects from your database
corePoint - decide whether this set is enough to start a cluster
then you can repeatedly find neighbors to grow the clusters.
Function 1 is where you want to hook into, for example by using two thresholds: one that is geographic and one that is temporal (i.e. within 100 miles, and within 1 hour).
tl;dr you are going to have to modify your feature set, i.e. scaling your date/time to match the magnitude of your geo data.
DBSCAN's input is simply a vector, and the algorithm itself doesn't know that one dimension (time) is orders of magnitudes bigger or smaller than another (distance). Thus, when calculating the density of data points, the difference in scaling will screw it up.
Now I suppose you can modify the algorithm itself to treat different dimensions differently. This can be done by changing the definition of "distance" between two points, i.e. supplying your own distance function, instead of using the default Euclidean distance.
IMHO, though, the easier thing to do is to scale one of your dimension to match another. just multiply your time values by a fixed, linear factor so they are on the same order of magnitude as the geo values, and you should be good to go.
more generally, this is part of the features selection process, which is arguably the most important part of solving any machine learning algorithm. choose the right features, and transform them correctly, and you'd be more than halfway to a solution.
I am trying to get smooth rssi value from Bluetooth low energy beacons deployed at ceiling of my lab. I used Weighted-mean filter and moving average filter but couldn't get good result. Through various journal papers I got to know that Kalman filter can be used for this purpose. But I couldn't get a proper mathematical equation to code with objective-c. Can somebody provide any hint regarding mathematical equation or Kalman filter implementation?Thanks a lot.
A one-dimensional case like this means that all of the matrices are actually just scalar values. You need to know two things:
R, the measurement variance. You can directly measure this by recording a series of RSSI values (in a fixed location) exactly how you would normally and then measuring their variance. You can do this easily with Excel, or python, or even write your own code from scratch.
Q, the process variance. This is how much you expect RSSI to actually change in the same amount of time (between measurements). You can also measure this, or you can reason about it.
If you look at the Kalman Filter equations you'll notice that P is not dependent on your actual measurements, only the two values above. As a result, since they are constant, P will converge to a fixed value. And since K (the Kalman gain) only relies on those values, it will also converge. For an application like yours, it is usually sufficient to find the steady-state K and use it all the time.
This is now just a complicated (but optimal in a least-squares sense) way of creating a simple moving average filter.
If you are looking for a swift implementation of Kalman Filter, then it is worth looking at this framework. It is a generic implementation of conventional filter algorithm and it also provides a Matrix struct and all the necessary operations on Matrices that are used in Kalman filter
If I am right, Wavelet packet decomposition (WPT) breaks a signal into various filter banks.
The same thing can be done using many band pass filters.
My aim is to find the energy content of a signal with a large sapmling rate ((2000 hz) in various frequency bands like 1-200, 200-400, 400-600.
What are the advantages and disadvantages of using a WPT of band pass filters?
with wpt (or dwt indeed) you have quadrature mirror filters that will ensure that if you add up all the reconstructed signals in the last level (the leaves) of the wpt tree you get exactly the original signal except for the math processor finite word length aproximations. The algorithm is pretty fast.
Moreover if your signal is non-stationary you can gain the time-frequency localization although this will drastically decrease as you go down on the tree (inverted).
The other aspect is that if yoy are lucky to get a wavelet that correlates well with the non stationary components of your signal the transform will map this components more efficiently.
For you application firstly see how many levels you have to go down in the wpt tree to go from your sampling frequency to the desired freq intervals, you may not get excately 200-400, 400-600 etc,the downer you go in the tree the more accurate are the feq limits, and you may have to join nodes to get your bands.
I have been given 2 data sets and want to perform cluster analysis for the sets using KNIME.
Once I have completed the clustering, I wish to carry out a performance comparison of 2 different clustering algorithms.
With regard to performance analysis of clustering algorithms, would this be a measure of time (algorithm time complexity and the time taken to perform the clustering of the data etc) or the validity of the output of the clusters? (or both)
Is there any other angle one look at to identify the performance (or lack of) for a clustering algorithm?
Many thanks in advance,
T
It depends a lot on what data you have available.
A common way of measuring the performance is with respect to existing ("external") labels (albeit that would make more sense for classification than for clustering). There are around two dozen measures you can use for this.
When using an "internal" quality measure, make sure that it is independent of the algorithms. For example, k-means optimizes such a measure, and will always come out best when evaluating with respect to this measure.
There are two categories of clustering evaluation methods and the choice depends
on whether a ground truth is available. The first category is the extrinsic methods which require the existence of a ground truth and the other category is the intrinsic methods. In general, extrinsic methods try to assign a score to a clustering, given the ground truth, whereas intrinsic methods evaluate clustering by examining how well the clusters are separated and how compact they are.
For extrinsic methods (remember you need to have a ground available) one option is to use the BCubed precision and recall metrics. The BCubed precion and recall metrics differ from the traditional precision and recall in the sense that clustering is an unsupervised learning technique and therefore we do not know the labels of the clusters beforehand. For this reason BCubed metrics evaluate the precion and recall for evry object in a clustering on a given dataset according to the ground truth. The precision of an example is an indication of how many other examples in the same cluster belong to the same category as the example. The recall of an example reflects how many examples of the same category are assigned to the same cluster. Finally, we can combine these two metrics in one using the F2 metric.
Sources:
Data Mining Concepts and Techniques by Jiawei Han, Micheline, Kamber and Jian Pei
http://www.cs.utsa.edu/~qitian/seminar/Spring11/03_11_11/IR2009.pdf
My own experience in evaluating the performance of clustering
A simple approach for the extrinsic methods where there is a ground truth available is to use a distance metric between clusterings; the ground truth is simply considered to be a clustering. Two good measures to use are the Variation of Information by Meila and, in my humble opinion, the split join distance by myself also discussed by Meila. I do not recommend the Mirkin index or the Rand index - I've written more about it here on stackexchange.
These metrics can be split into two constituent parts, each representing the distance of one of the clusterings to the largest common subclustering. It is worthwhile to consider both parts; if the ground truth part (to common subclustering) is very small, it means that the tested clustering is close to a superclustering; if the other part is small it means that the tested clustering is close to the common subclustering and hence close to a subclustering of the ground truth. In both cases the clustering can be said to be compatible with the ground truth. For more information see the link above.
There are several benchmarks for the clustering algorithms evaluation with extrinsic quality measures (accuracy) and intrinsic measures (some internal statistics of the formed clusters):
Clubmark demonstrated in ICDM'18
WebOCD, see description in the paper
Circulo
ParallelComMetric
CluSim
CoDAR (the sources might be acquired from the paper authors)
Selection of the appropriate benchmark depends on the kind of the clustering algorithm (hard or soft clustering), kind (pairwise relations, attributed datasets or mixed) and size of the clustering data, required evaluation metrics and the admissible amount of the supervision. The Clubmark paper describes evaluation criteria in details.
The Clubmark is developed for the fully automatic parallel evaluation of many clustering algorithms (processing input data specified by the pairwise relations) on many large datasets (millions and billions of clustering elements) and evaluated mostly by accuracy metrics tracing resource consumption (processing and execution time, peak resident memory consumption, etc.).
But for a couple of algorithms on a couple of datasets even the manual evaluation is appropriate.