## 2 Materials and Methods
### Model for Assessing the Reliability of Measurements Using LSTM Networks  
One of the key aspects of adaptive tracking of targets in difficult conditions is the timely detection of the moment when measurements cease to be reliable, e.g., due to the increase in noise, interference, signal loss, or fragmented display of the object. Failure to detect such changes in real time leads to a decrease in the accuracy of the Kalman filter, the accumulation of errors, and the possible loss of the target. At the same time, early response allows for the filtering parameters to be reconfigured or for confidence to be shifted towards the GERT forecast. Therefore, predicting the reliability of the measurements is an important task assigned to the intelligent adaptive module. To increase the reliability of measurements, a forecasting method based on an artificial intelligence model using a recurrent neural network of the LSTM type is proposed. This approach was chosen due to the ability of LSTM to effectively work with time series, detect trends and dependencies in the history of input data, and form predictive estimates even in the presence of partial omissions. The following indicators available from the Kalman filter and related modules are used as input vectors for the neural network:  
* innovation value (difference between forecast and measurement);
* forecast error covariance;
* number of missed measurements over the last \(N\) cycles;
* average duration of the signal-free interval;
* histogram of absolute innovations over the time window. The specified input features for the measurement reliability prediction model do not require external sources or true target coordinates and can all be obtained within the framework of the already implemented support system, which ensures complete autonomy of the prediction module. In particular:  
* Kalman filter innovations are formed at each cycle as the difference between the actual measurement \(z(t)\) and the predicted value \(\hat{z}(t|t-1)\) \[r(t)=z(t)-\hat{z}(t|t-1)=z(t)-H\hat{x}(t|t-1),\] (6) where \(H\) is the observation matrix;
* the prediction error covariance (matrix \(P(t\,|\,t-1)\) is the basic filter parameter reflecting the degree of uncertainty before correction;
* the number of missed measurements is calculated as the number of cycles without an acceptable signal in a fixed time window;
* the average duration of the signal-free interval is determined as the average value of the lengths of sequences of zero cycles between valid measurements;
* a histogram of absolute innovations is formed over the last accumulated \(\,|\,r(t)\,|\,\) over the last \(N\) steps to assess the overall noise level or noise level of measurements. This allows us to organize model training in simulations and in operation, in order to implement online reliability prediction without external information, solely based on the dynamics of estimates and their derivative characteristics. The determined data are fed into the input of the LSTM block, which forms a forecast of the confidence level for the next measurement in the form of the probability \(P_{\textit{max}}(t+1)\). Values close to 1 indicate expected stable measurement; values close to 0 indicate potential loss or noise. The neural network can be trained offline, based on generated scenarios with simulations of various conditions (from ideal to critically noisy). The result of training is the ability of the model to recognize patterns that precede the loss of accuracy, even before it appears in the tracking algorithm. Based on the predicted value \(P_{\textit{max}}(t+1)\), the following are formed:
* decisions on changing the confidence in measurements in the Kalman filter (modification of the matrix \(R\)),
* adjustment of the weight coefficient \(\alpha(t)\) in the Kalman filter/GERT model estimation fusion block,
* activation of an alternative mode, for example, predictive tracking without updating. Figures 4-6 show an example of feature formation based on the Kalman filter in a window of the last 10 tracking cycles.