# Vehicle Target Tracking Algorithm Based on Improved Strong Tracking Unscented Kalman Filter
## 3 Multidimensional Adaptive Factor-Based Strong Tracking UKF Algorithm
### Simulation Experiments and Analysis  
The simulation model measures the target using polar coordinates, and the measurement results are displayed on a bird' s-eye view plane. During the simulation process, MATLAB 2022a, along with a laptop computer equipped with an Intel i9-12900H processor, Intel, Santa Clara, CA, USA and an NVIDIA RTX 3060 graphics card, Nvidia, Santa Clara, CA, USA, were used as the hardware and software platform to verify the performance of the designed algorithm for high-speed tracking of a moving target under wide-ranging maneuvering conditions. To ensure the accuracy of the simulation, 200 Monte Carlo simulations were performed. The initial state of the target is set as \(x_{0}=[300\,\mathrm{m},70\,\mathrm{m}/\mathrm{s},0\,\mathrm{m}/\mathrm{s}^{ 2},200\,\mathrm{m}]^{T}\), with the radar located at a fixed position relative to the target. The target's initial position is \(P_{r}=[x_{0},y_{0}]^{T}=[0,0]\)). The observation period is \(T=1\,\mathrm{s}\), with a total simulation time of 175 s. The simulation introduces Gaussian noise with a mean of zero. The measurement noise covariance matrix is given by \(R_{k}=\mathrm{diag}([50^{2},0.1^{2}])\), and the measurement distance and angle errors are assumed to have biases of 50 m and \(0.1^{\circ}\), respectively. We used three models, CV, CA, and CT models, each with an initial probability of \(\mu_{0}=\left(\frac{1}{3},\frac{1}{3},\frac{1}{3}\right)^{T}\) and a Markov probability transfer matrix of \(P\):  
\[P= \begin{bmatrix}0.8&0.1&0.1\\ 0.1&0.8&0.1\\ 0.1&0.1&0.8\end{bmatrix}  \tag{25}\]  
The target movement patterns are shown in Table 1.  
In this simulation, we compared four algorithms, UKF [8], ST-UKF [9], AST-UKF [20], and MAST-UKF, to evaluate their tracking performance in complex traffic scenarios. UKF, as the benchmark method for nonlinear state estimation, was selected to verify the improvement of the adaptive mechanism on nonlinear tracking performance. ST-UKF and AST-UKF represent improved versions in terms of numerical stability and adaptive noise regulation, respectively. Compared with ST-UKF, the aim is to demonstrate that the multidimensional adaptive mechanism is more effective than the one-dimensional square-root improvement; compared with AST-UKF, it shows the superior generalization ability of multidimensional attenuation factors in handling complex motions (such as frequent switching between CV/CA/CT models). These comparisons enable the verification of the MAST-UKF's tracking performance on moving targets at high speed and wide-range maneuvering conditions. The experimental results are shown in Figure 2. It can be observed that the target's motion state changed at the 41 st second. First, during the turning process, MAST-UKF demonstrated the best tracking accuracy, followed by AST-UKF, ST-UKF, and finally, UKF. The specific reason is that MAST-UKF adjusts the state noise covariance by introducing multidimensional adaptive attenuation factors, which allows it to better adapt to inaccurate system state models and noise characteristics when the target state undergoes drastic changes, thereby improving tracking accuracy. In contrast, AST-UKF uses an adaptive attenuation factor with a strong tracking mechanism, which effectively adjusts the noise covariance. However, its ability to adapt to the system model during turning is slightly inferior to MAST-UKF, thus performing second best. ST-UKF improves accuracy by increasing the state noise covariance, and although it performs better than UKF, it still falls short of AST-UKF and MAST-UKF. The UKF algorithm has poor tracking accuracy during turning due to its fixed-noise covariance setting. After entering the straight section, both MAST-UKF and AST-UKF maintained good tracking performance. The UKF algorithm, influenced by the previous CT motion, exhibited fluctuations in tracking performance. Similarly, ST-UKF showed poor tracking due to delays in adjusting the attenuation factor when the model changed.