## 2 Materials and Methods
### Model for Assessing the Reliability of Measurements Using LSTM Networks
Figure 4: Target tracking in loss conditions using the Kalman filter. Figure 4 shows the true trajectory (blue line), measurements with losses (dots), and the Kalman filter estimate (green line). It is noticeable that even in the absence of measurements at individual cycles, the filter continues to predict using previous information. This demonstrates the basis of tracking dynamics and situations in which there is a need to estimate the reliability of measurements. Figure 5 shows the distribution of absolute values of Kalman filter innovations over the last 10 cycles. The visualization illustrates the level of noise and measurement instability. Higher concentration in high ranges signals a potential increase in error. This function is a source of features for the neural network and allows for the detection of 'anomalous' cycles. The graph in Figure 6. displays four features formed in the window:  
* the number of measurement losses;
* the average duration of losses;
* the proportion of losses in the window;
* the recovery factor (inverse duration of loss). Figure 5: Histogram of absolute innovations in a time window. Figure 6: Spider chart of measurement loss features. Normalized values assess the 'portrait' of the situation in the measurement channel. This set of features is fed into the input of the LSTM block to form a reliability forecast. Thus, a set of features describing the quality of measurements in the Kalman filter has been formed within the framework and the feasibility of their use as input data for a recurrent neural network has been substantiated. It is proposed to use an LSTM-type architecture to predict the reliability of measurements at the next cycle. The next stage is to build and train the corresponding neural network model, which will allow for the implementation of the intelligent adaptation of filtering in real time. To implement the module for predicting the reliability of measurements based on artificial intelligence, a recurrent neural network architecture of the LSTM type was built [21; 22], focused on processing sequences of formed features with a given time window. The main goal of the model is to form a probabilistic estimate \(P_{meas}(t+1)\) that reflects the expected reliability of measurements at the next cycle of support. The learning process consisted of the following steps:  
1. Feature preparation. Input vectors were built using internal filtering parameters such as innovations, covariance estimates, and measurement loss characteristics;
2. Labeling. Each training example was assigned a binary label indicating whether a measurement loss or critical noise event occurred in the next cycle;
3. Dataset simulation. Over 10,000 synthetic time series were generated covering various scenarios of measurement reliability;
4. Training setup. The LSTM model was trained using binary cross-entropy loss, Adam optimizer, and a validation split to prevent overfitting;
5. Evaluation. Model performance was evaluated based on its ability to detect transitions to unreliable states, using precision, recall, and visual comparison with reference trajectories. The neural network is implemented as a one-dimensional LSTM structure that accepts as input a feature vector with a length of N cycles. Each vector includes the following:  
* innovation value \(r(t)\);
* covariance estimate \(P(t\,|\,t-1)\);
* number of losses in the window;
* average length of gaps;
* binary histogram of absolute innovations. The network structure provides:  
* one LSTM layer with a hidden state dimension of 32;
* a normalization layer (BatchNormalization);
* a dense layer with sigmoid activation to form the initial estimate \(P_{meas}(t+1)\in[0;1]\). When forming the training sample, the learning process is carried out. Training is carried out on the basis of generated simulation data, in which various support scenarios are simulated as follows: normal conditions, noise, periodic loss of measurements, and intentional interference.