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Maneuvering Target Tracking

This tutorial demonstrates how to use the Interacting Multiple Model (IMM) filter to track a maneuvering target that switches between constant velocity and constant acceleration dynamics.

Scenario Description

We simulate a target moving in 1D space over 15 seconds: 1. Constant Velocity (CV): For the first 5 seconds, the target moves at a constant velocity of 2.0 m/s. 2. Constant Acceleration (CA): From 5 to 10 seconds, the target accelerates at 1.5 m/s². 3. Constant Velocity (CV): From 10 to 15 seconds, the target stops accelerating and continues at constant velocity.

We compare three tracking strategies: - A standard Kalman Filter tuned for CV (which has low process noise). - A standard Kalman Filter tuned for CA (which has higher process noise to account for acceleration). - An IMM Filter blending both models.

Simulation Code

The full simulation code is located in tracking_demo.py.

import numpy as np
from kalbee import KalmanFilter, InteractingMultipleModel
from kalbee.modules.utils.metrics import rmse

# (Set up trajectory and noise)
dt = 0.1
t = np.arange(0, 15, dt)
T = len(t)
# ...

# Initialize IMM blending CV and CA
model_transition = np.array([[0.95, 0.05], [0.05, 0.95]])
model_probabilities = np.array([0.8, 0.2])

imm = InteractingMultipleModel(
    [kf_cv_imm, kf_ca_imm],
    model_transition,
    model_probabilities
)

Results and Analysis

When running the simulation, we obtain the following position Root Mean Square Error (RMSE):

Filter Position RMSE
Constant Velocity (CV) KF 3.2481
Constant Acceleration (CA) KF 0.4712
IMM Blended Filter 0.3755

Discussion

  1. CV Filter Failure: The CV filter performs poorly (RMSE 3.2481) because its low process noise assumption makes it ignore the measurement deviations during the acceleration phase, lagging far behind the target.
  2. CA Filter Limitations: The CA filter tracks the maneuver well (RMSE 0.4712) but introduces extra noise and variance during the non-accelerating phases.
  3. IMM Superiority: The IMM filter achieves the lowest overall error (RMSE 0.3755) by dynamically shifting its belief (model probability) towards the active model.

IMM Adaptation

The IMM model probabilities adjust dynamically: - CV Phase: Prior CV Probability is high (~0.77). - Maneuver Phase: Prior CA Probability increases to ~0.81 as soon as acceleration is detected. - Post-Maneuver: Prior CV Probability climbs back up once constant velocity resumes.