-
Notifications
You must be signed in to change notification settings - Fork 1
/
basic_env.py
80 lines (64 loc) · 2.46 KB
/
basic_env.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
# Environment Setup
# Objective: Simulate Motion of the Hyperloop Pod
# Key Components: 1) Equation to Simulate true motion of the Hyperloop Pod
# 2) Equation to model measured Position
# 3) Physics Based Expected Position and Velocity Equation
# Assumptions: - Sample Measured position with 1m standard deviation
# - Sample Measured velocity with 0.1km/hr standard deviation
# - Constant Acceleration
import filterpy
import numpy as np
from filterpy.filterpy.kalman import KalmanFilter
from filterpy.filterpy.stats import plot_covariance_ellipse
# State Transition Function: choose state variables x and y for 2 dimensions
# x_bar = Fx
# transition function is implemented as: next state = matrix F * previous state
tracker = KalmanFilter(dim_x=4, dim_z=2)
dt = 1. # time step 1 second
tracker.F = np.array([1, dt, 0, 0],
[0, 1, 0 ,0],
[0, 0, 1, dt],
[0, 0, 0, 1])
# Control Function
# tracker.B
# Measurement Function H
tracker.H = np.array([[1/0.3048, 0, 0, 0],
[0, 0, 1/0.3048, 0]])
# Measurement Noise Matrix R
tracker.R = np.array([[5., 0],
[0, 5]])
# Initial Conditions
tracker.x = np.array([[0, 0, 0, 0]]).T
tracker.P = np.eye(4) * 500.
# Implement the Filter
R_std = 0.35
Q_std = 0.04
def tracker1():
tracker = KalmanFilter(dim_x=4, dim_z=2)
dt = 1.0 # time step
tracker.F = np.array([[1, dt, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, dt],
[0, 0, 0, 1]])
tracker.u = 0.
tracker.H = np.array([[1/0.3048, 0, 0, 0],
[0, 0, 1/0.3048, 0]])
tracker.R = np.eye(2) * R_std**2
q = Q_discrete_white_noise(dim=2, dt=dt, var=Q_std**2)
tracker.Q = block_diag(q, q)
tracker.x = np.array([[0, 0, 0, 0]]).T
tracker.P = np.eye(4) * 500.
return tracker
# simulate robot movement
N = 30
sensor = PosSensor((0, 0), (2, .2), noise_std=R_std)
zs = np.array([sensor.read() for _ in range(N)])
# run filter
robot_tracker = tracker1()
mu, cov, _, _ = robot_tracker.batch_filter(zs)
for x, P in zip(mu, cov):
# covariance of x and y
cov = np.array([[P[0, 0], P[2, 0]],
[P[0, 2], P[2, 2]]])
mean = (x[0, 0], x[2, 0])
plot_covariance_ellipse(mean, cov=cov, fc='g', std=3, alpha=0.5)