Hi,

I get two errors when trying the example, first is: Uncaught ReferenceError: R_k is not defined

That one was easy enough to fix by changing line 59 to: function KalmanObservation(z_k,H_k,R_k){

But then there is the following error: Uncaught TypeError: Cannot read property '1' of undefined

it traces to line 49: this.K_k = this.P_k_k_.x(o.H_k.transpose().x(this.S_k.inverse()));//Optimal Kalman gain

I tried to trace it back but no luck yet, thoughts?

In the KalmanModel.update() Predict part, the calculation for P (P = FPF(T) + Q) misses the Q part (which is not used anywhere else). I think this.P_k_k_ = this.F_k.x(this.P_k_.x(this.F_k.transpose())); should be this.P_k_k_ = this.F_k.x(this.P_k_.x(this.F_k.transpose())).add(this.Q_k);

In my tests this modification fixed the problem that new measurements did not really have much effect.

Fixing several references in the Kalman Model. (mostly adding a this. or an o. in front of the variables.) Also, fixed a vector addition to use the add method.

like below, for predicate <--> measurement loop: KalmanModel.prototype.predicate = function()
{ //init
this.x_k_ = this.x_k;
this.P_k_ = this.P_k;
//Predict
this.x_k_k_ = this.F_k.x(this.x_k_);
this.P_k_k_ = this.F_k.x(this.P_k_.x(this.F_k.transpose())).add(this.Q_k);
} KalmanModel.prototype.update = function(o)
{ this.I = Matrix.I(this.P_k.rows());
this.y_k = o.z_k.subtract(o.H_k.x(this.x_k_k_)); //observation residual
this.S_k = o.H_k.x(this.P_k_k_.x(o.H_k.transpose())).add(o.R_k); //residual covariance
this.K_k = this.P_k_k_.x(o.H_k.transpose().x(this.S_k.inverse())); //Optimal Kalman gain
this.x_k = this.x_k_k_.add(this.K_k.x(this.y_k));
this.P_k = this.I.subtract(this.K_k.x(o.H_k)).x(this.P_k_k_);
}

I've made your library into a bower component so that its easier for other people to install and would like to make a merge request. At the moment, though, your test isn't passing.

https://github.com/htmlfusion/kalman

Despite adding the same version of sylvester (0.1.3) as is used in your test, there appears to be a slight different between them. The difference lies in the determinant function.

The version installed in your test directory looks like so:

  // Returns the determinant for square matrices
  determinant: function() {
    if (this.elements.length === 0) { return 1; }
    if (!this.isSquare()) { return null; }
    var M = this.toRightTriangular();
    var det = M.elements[0][0], n = M.elements.length;
    for (var i = 1; i < n; i++) {
      det = det * M.elements[i][i];
    }
    return det;
  },

While the version installed by bower looks like:

  // Returns the determinant for square matrices
  determinant: function() {
    if (!this.isSquare()) { return null; }
    var M = this.toRightTriangular();
    var det = M.elements[0][0], n = M.elements.length - 1, k = n, i;
    do { i = k - n + 1;
      det = det * M.elements[i][i];
    } while (--n);
    return det;
  },

This is the only difference between the two files and results in the following error.

 Uncaught TypeError: Cannot read property '1' of undefined
sylvester.src.js:586
Matrix.determinantsylvester.src.js:595 
Matrix.isSingularsylvester.src.js:643
Matrix.inversekalman.js:49
KalmanModel.updatetest.html:23 (anonymous function)

I can see both the model and update functions require a Vector and a set of Matrices as parameters.

Would it be possible to get a brief explanation of how one would derive these values? I am using the .alpha, .beta and .gamma readings from the deviceOrientation API which come out as floating point numbers. Am I right in thinking these form the 3 parts of the first Vector argument? What is the purpose of the remaining Matrices.

I put a question up on StackOverflow hoping someone might be able to explain. Any help would be gratefully received

https://stackoverflow.com/questions/25744984/implement-a-kalman-filter-to-smooth-data-from-deviceorientation-api