Interactive Kalman filtering:
In the previous sections, we have introduced the common Kalman filter, that is, the linear Kalman filter (KF) used in the linear link, the extended Kalman filter (EKF) and the unscented Kalman filter ( UKF), in this section, I will further enrich our constraints and further explore new variants of the Kalman filter.
Problem Description
The Kalman filter we introduced before deals with the motion model of the target as one, which is obviously unreasonable in reality. Most of the target motion in reality cannot be described by only one motion model, but in a switch between multiple target models, and the interactive multi-model Kalman filter we introduced in this section is used to deal with this of the situation.
Interactive multi-model Kalman filter (IMM) principle
The IMM algorithm uses multiple Kalman filters for parallel processing. Each filter corresponds to a different state space model, and different state space models describe different target maneuver models. Therefore, each filter estimates the target state differently. The basic idea of the IMM algorithm is that at each moment, assuming that a certain model is valid at the current moment, the initial condition of the filter that matches the specific model is obtained by mixing the state estimates of all filters at the previous moment, and then Each model performs filtering in parallel; finally, the model probability is updated based on the model matching likelihood function, and the state estimates corrected by all filters are combined (weighted sum) to obtain a state estimate. Therefore, the estimation result of the IMM algorithm is a combination of estimates obtained from different models, rather than just selecting the completely correct model estimation at each moment.
The general steps of the IMM algorithm are described below.
Therefore, according to step 4, the total state estimation expression, we can see that the total output of the filter is the weighted average of the estimation results of multiple filters. The weight is the probability that the model correctly models the target movement at this moment, referred to as the model probability.
Matlab simulation analysis
Simulation parameters:
Steps 1-20: the target maneuvers with the CV model; 21-30 the target maneuvers with the turning model, w=-pi/180;
31-60: the target maneuvers with the CA model. Other parameters are consistent with previous simulations
Simulation results:
Simulation analysis:
From the tracking trajectory graph and tracking error curve, the IMM algorithm has a good tracking effect on the trajectory of the target switching between multiple motion models.
Matlab simulation program:
由于某些原因，程序不便上传
需要的话加Q:1806831629,备注：交互式多模型卡尔曼滤波
Write at the end:
Written here, in fact, more than half of our tracking algorithm has been introduced. In the algorithm introduced above, we track only one target. However, in practice, we occasionally need to track multiple targets at the same time. In the next section, we will further introduce the topic of multi-target tracking.