IMM Algorithm and Implementation: Target Trajectory Estimation with Fused Likelihood Function Output

The IMM (Interacting Multiple Model) algorithm is an advanced filtering technique for target tracking, particularly suitable for targets with varying motion patterns. This algorithm operates multiple filters with different dynamic models (such as constant velocity and constant acceleration models) in parallel, combining their outputs to achieve optimal estimation. Core Functional Module Analysis Target Trajectory Generation (Target_track.m): This module simulates the actual target's motion trajectory, which may include various motion patterns (such as linear motion, turning maneuvers, etc.), providing benchmark data for algorithm validation. Multi-Model Interaction and Fusion (Model_mix.m): This function calculates mixing probabilities between models and dynamically adjusts the weights of each model. It uses Markov transition probabilities to describe the likelihood of model switching, enabling interaction between the outputs of various filters from the previous time step. Kalman Filter Processing (Kalman.m): Each independent model corresponds to a Kalman filter, performing state prediction and update operations. This module outputs the likelihood function value of the current observation, which is used for subsequent model probability updates. IMM Main Process (IMM.m): This main routine integrates the above modules to complete iterative prediction-update cycles. It visualizes the actual target trajectory, estimated trajectory, position/velocity error curves, and model mixing probability changes, providing intuitive feedback on algorithm performance. Error Analysis and Model Adaptation By comparing estimation errors (position and velocity) between the estimated trajectory and the actual trajectory, filtering accuracy can be evaluated. The mixing probability graph reveals the dominant model during different motion phases - for example, the constant velocity model's probability increases during linear motion, while it may switch to a maneuvering model during turning phases. This multi-model framework significantly enhances tracking robustness in complex scenarios, making it particularly suitable for targets with variable dynamic characteristics such as aircraft, unmanned vehicles, and other maneuvering platforms.