kalman__vb.txt

卡尔曼滤波的vb源程序(现设线性时变系统的离散状态防城和观测方程)

现设线性时变系统的离散状态防城和观测方程为：
X(k) = F(k,k-1)·X(k-1)+T(k,k-1)·U(k-1)
Y(k) = H(k)·X(k)+N(k)

其中

X(k)和Y(k)分别是k时刻的状态矢量和观测矢量
F(k,k-1)为状态转移矩阵
U(k)为k时刻动态噪声
T(k,k-1)为系统控制矩阵
H(k)为k时刻观测矩阵
N(k)为k时刻观测噪声
则卡尔曼滤波的算法流程为：

预估计X(k)^= F(k,k-1)·X(k-1)

计算预估计协方差矩阵
C(k)^=F(k,k-1)×C(k)×F(k,k-1)'+T(k,k-1)×Q(k)×T(k,k-1)'
Q(k) = U(k)×U(k)'

计算卡尔曼增益矩阵
K(k) = C(k)^×H(k)'×[H(k)×C(k)^×H(k)'+R(k)]^(-1)
R(k) = N(k)×N(k)' 

更新估计
X(k)~=X(k)^+K(k)×[Y(k)-H(k)×X(k)^] 

计算更新后估计协防差矩阵
C(k)~ = [I-K(k)×H(k)]×C(k)^×[I-K(k)×H(k)]'+K(k)×R(k)×K(k)' 
X(k+1) = X(k)~
C(k+1) = C(k)~
重复以上步骤

（没有测试，输出部分要配合相应的过程）


Dim num1, num2, num3
Dim a(), a1(), e() As Single
Dim alf, xgm(), p(), k1(), k2, k(), p1(), p2(), c(), c1, k3(), k4(), cc() As Single
Private Sub Command1_Click()
CommonDialog1.ShowOpen
Open CommonDialog1.FileName For Input As #1
num3 = Val(Text1.Text) + 2
num2 = Val(Text2.Text)
ReDim a(num3, num2)

For j = 1 To num3
For i = 1 To num2
Input #1, a(j, i)
Next i
Next j
Close #1


Private Sub Command2_Click()
CommonDialog1.ShowSave
Open CommonDialog1.FileName For Append As #2

For i = 1 To num2
Print #2, cc(i, 1), cc(i, 2), cc(i, 3)
Next i

Shell "c:\windows\notepad " & CommonDialog1.FileName
End Sub

Private Sub Command3_Click()

num1 = Val(Text1.Text) + 1
num2 = Val(Text2.Text)
num3 = Val(Text1.Text) + 2
ReDim a1(num2), e(num1, num2) As Single
ReDim xgm(num1), p(num1, num1), k1(num1), k(num1), p1(num1, num1), p2(num1, num1), c(num1), k3(num1), k4(num1), cc(num2, num1) As Single

c(1) = c(2) = c(3) = 0
r = 0.000001
alf = 10

For j = 1 To num1
For i = 1 To num2
e(j, i) = a(j, i)
a1(i) = a(num3, i)
Next i
Next j

For x = 1 To num1
xgm(x) = alf * Sqr(r / e(x, 1))
p(x, x) = xgm(x)^2
Next x

For q = 1 To num2

For i = 1 To num1
k3(i) = k4(i) = 0
Next i
k2 = 0

For i = 1 To num1
For j = 1 To num1
X0 p1(i, j) = p2(i, j) = 0
Next j
Next i

c1 = 0

For m = 1 To num1
k3(m) = 0
For n = 1 To num1
k3(m) = k3(m) + e(n, q) * p(n, m)
Next n
Next m

For m = 1 To num1
k4(m) = 0
k4(m) = k4(m) + 1000 * k3(m) * e(m, q)
Next m

For i = 1 To num1
k2 = k2 + k4(i)
Next i

For v = 1 To num1
k(v) = 0
k(v) = k3(v) * (k2 / 1000 + r)^-1
Next v

For i = 1 To num1
For j = 1 To 3
p1(i, j) = k(i) * e(j, q)
Next j
Next i

For l = 1 To num1
For i = 1 To num1
p2(l, i) = 0
For j = 1 To num1
p2(l, i) = 1000 * p1(l, j) * p(j, i) + p2(l, i)
Next j
Next i
Next l

For i = 1 To num1
For j = 1 To num1
p(i, j) = p(i, j) - p2(i, j) / 1000
Next j
Next i

For i = 1 To num1
c1 = c1 + e(i, q) * c(i)
Next i

For i = 1 To num1
c(i) = c(i) + k(i) * (a1(q) - c1)
Next i

For i = 1 To num1
cc(q, i) = c(i)
Next i

Next q

End Sub

Private Sub Command4_Click()
End
End Sub