// y: Measurments
// u: Actuator thrust
func (k *ExtKalmanFilter) Step(y, u matrix.Matrix) (x matrix.Matrix) {
var y_ = k.h(k.x)
var H = k.dhdx(k.x)
var Ht = matrix.Transpose(H)
// -----------------
// Estimation
// Kalman gain matrix
// K = P * H^t * (H*P*Ht + R)⁻¹
var inv = matrix.Inverse(matrix.Sum(matrix.Product(H, k.mP, Ht), k.mR))
var K = matrix.Product(k.mP, Ht, inv)
var Kt = matrix.Transpose(K)
// State estimation update
// x_ = x + K * (y - h(x))
var ydiff, _ = y.Minus(y_)
if k.normalize_ydiff != nil {
ydiff = k.normalize_ydiff(ydiff)
}
var x_ = matrix.Sum(k.x, matrix.Product(K, ydiff))
// Error covariance update
// P_ = (I - K*H) * P * (I - K*H)^t + K*R*K^t
var IKH, _ = matrix.Eye(H.Cols()).Minus(matrix.Product(K, H))
var IKHt = matrix.Transpose(IKH)
var P_ = matrix.Sum(matrix.Product(IKH, k.mP, IKHt), matrix.Product(K, k.mR, Kt))
// -----------------
// Propagation
var F = k.dfdx(x_, u)
var Ft = matrix.Transpose(F)
// State estimation propagation
// x(k+1) = A*x_(k) + B*u
k.x = k.f(x_, u)
// Error covariance propagation
// P(k+1) = A*P_*A^t + W*Q*W^t
k.mP = matrix.Sum(matrix.Product(F, P_, Ft), k.cWQWt)
return k.x
}
func ExtendedKalman(
W, R, Q, x0, P0 matrix.Matrix,
f, dfdx func(matrix.Matrix, matrix.Matrix) matrix.Matrix,
h, dhdx, normalize_ydiff func(matrix.Matrix) matrix.Matrix) (k *ExtKalmanFilter) {
k = new(ExtKalmanFilter)
k.mW = W
k.mR = R
k.mQ = Q
k.x = x0
k.mP = P0
k.f = f
k.dfdx = dfdx
k.h = h
k.dhdx = dhdx
k.normalize_ydiff = normalize_ydiff
// Pre calculated constant
k.cWQWt = matrix.Product(W, Q, matrix.Transpose(W))
return
}