nfoursid

import numpy as np import pandas as pd from nfoursid.nfoursid import NFourSID from nfoursid.state_space import StateSpace from nfoursid.kalman import Kalman # 1. Define a state-space model (example parameters) A = np.array([[0.9, 0.1], [0, 0.9]]) B = np.array([[1], [0]]) C = np.array([[0.5, 0.5]]) D = np.array([[0]]) state_space_true = StateSpace(A, B, C, D) # 2. Simulate some data num_datapoints = 100 inputs = np.random.randn(num_datapoints, 1) * 0.1 # Small random inputs outputs = [] for i in range(num_datapoints): output_step = state_space_true.step(inputs[i].reshape(-1, 1), noise=np.random.randn(1, 1) * 0.05) outputs.append(output_step.flatten()) data = pd.DataFrame({ 'input_0': inputs.flatten(), 'output_0': np.array(outputs).flatten() }) # 3. Perform N4SID identification output_columns = ['output_0'] input_columns = ['input_0'] num_block_rows = 2 # See warnings regarding this parameter nfoursid_estimator = NFourSID( dataframe=data, output_columns=output_columns, input_columns=input_columns, num_block_rows=num_block_rows ) nfoursid_estimator.subspace_identification() # Essential before system_identification for proper order detection # Determine system order (e.g., from eigenvalue plot, assume 2 for this example) rank = 2 state_space_identified, covariance_matrix = nfoursid_estimator.system_identification(rank=rank) print("Identified State-Space A matrix:\n", state_space_identified.a) print("Identified State-Space C matrix:\n", state_space_identified.c) # 4. Use a Kalman filter for prediction/estimation kalman_filter = Kalman(state_space_identified, covariance_matrix) # Simulate a few steps with the Kalman filter filtered_outputs = [] for i in range(num_datapoints): kalman_filter.step(data[output_columns].iloc[i].values.reshape(-1,1), data[input_columns].iloc[i].values.reshape(-1,1)) filtered_outputs.append(kalman_filter.to_dataframe()['output_0']['filtered'].iloc[-1]) print("First 5 actual outputs:", data['output_0'].head().tolist()) print("First 5 filtered outputs:", filtered_outputs[:5])