Step 2: Create a KalmanFilter object with these parameters.
Step 3: Simulate the movement of the object for a number of time steps, generating true states and measurements.
Step 3: For each measurement, predict the next state using kf.predict().
Step 4: Update the state estimate based on the measurement using kf.update().
Step 5: Store the estimated state in a list.
Step 6: Plot the true and estimated positions.
import numpy as np
import matplotlib.pyplot as plt
class KalmanFi1ter:
def __init__(self, F, H, Q, R, x0, P0):
self.F=F
self.H=H
self.Q=Q
self.R=R
self.x=x0
self.P=P0
def predict (self):
self.x=np.dot(self.F,self.x)
self.P=np.dot(np.dot(self. F,self. P),self.F.T)+self.Q
def update(self,z):
y=z-np.dot(self.H,self.x)
s=np.dot(np.dot(self.H,self.P),self.H.T)+self.R
K=np.dot(np.dot(self.P,self.H.T),np.linalg.inv(s))
self.x=self.x+np.dot(K,y)
self.P=np.dot(np.eye(self.F.shape[0])-np.dot(K,self.H),self.P)
dt=0.1
F=np.array([[1,dt],[0,1]])
H=np.array([[1,0]])
Q=np.diag([0.1,0.1])
R=np.array([[1]])
x0=np.array([0,0])
P0=np.diag([1,1])
kf=KalmanFi1ter(F,H,Q,R,x0,P0)
truestates=[]
measurements=[]
for i in range(100):
truestates.append([i*dt,1])
measurements.append(i*dt+np.random.normal(scale=1))
est_states=[]
for z in measurements:
kf.predict()
kf.update(np.array([z]))
est_states.append(kf.x)
plt.plot([s[0] for s in truestates],label="true")
plt.plot([s[0] for s in est_states],label="Estimate")
plt.legend()
plt.show()
Thus, Kalman filter is implemented to predict the next position and velocity in Python
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