diff --git a/tests/test_unit/test_fit_ellipse.py b/tests/test_unit/test_fit_ellipse.py
new file mode 100644
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+++ b/tests/test_unit/test_fit_ellipse.py
@@ -0,0 +1,134 @@
+import numpy as np
+
+from derotation.analysis.fit_ellipse import fit_ellipse_to_points
+
+
+def test_fit_ellipse_to_points_circular_pattern():
+    """
+    Test fit_ellipse_to_points with a circular pattern of points.
+    
+    This test verifies that the function correctly estimates the center of the
+    fitted ellipse when given a well-defined set of points arranged in a circle.
+    """
+    # Create a circular pattern of points centered at (128, 128)
+    center_x, center_y = 128, 128
+    radius = 50
+    angles = np.linspace(0, 2 * np.pi, 20, endpoint=False)
+    
+    # Generate points on the circle
+    x_points = center_x + radius * np.cos(angles)
+    y_points = center_y + radius * np.sin(angles)
+    points = np.column_stack([x_points, y_points])
+    
+    # Fit ellipse to the points
+    fitted_cx, fitted_cy, a, b, theta = fit_ellipse_to_points(points)
+    
+    # Verify that the fitted center is close to the expected center
+    assert np.isclose(fitted_cx, center_x, atol=5), \
+        f"Expected center_x close to {center_x}, got {fitted_cx}"
+    assert np.isclose(fitted_cy, center_y, atol=5), \
+        f"Expected center_y close to {center_y}, got {fitted_cy}"
+    
+    # For a circle, semi-major and semi-minor axes should be similar
+    assert np.isclose(a, b, rtol=0.2), \
+        f"For a circle, semi-axes should be similar: a={a}, b={b}"
+
+
+def test_fit_ellipse_to_points_horizontal_ellipse():
+    """
+    Test fit_ellipse_to_points with a horizontal elliptical pattern.
+    
+    This test verifies correct estimation of ellipse center for a
+    horizontally-oriented ellipse.
+    """
+    # Create a horizontal elliptical pattern
+    center_x, center_y = 200, 150
+    major_axis = 80
+    minor_axis = 40
+    angles = np.linspace(0, 2 * np.pi, 25, endpoint=False)
+    
+    # Generate points on the ellipse
+    x_points = center_x + major_axis * np.cos(angles)
+    y_points = center_y + minor_axis * np.sin(angles)
+    points = np.column_stack([x_points, y_points])
+    
+    # Fit ellipse to the points
+    fitted_cx, fitted_cy, a, b, theta = fit_ellipse_to_points(points)
+    
+    # Verify that the fitted center is close to the expected center
+    assert np.isclose(fitted_cx, center_x, atol=10), \
+        f"Expected center_x close to {center_x}, got {fitted_cx}"
+    assert np.isclose(fitted_cy, center_y, atol=10), \
+        f"Expected center_y close to {center_y}, got {fitted_cy}"
+
+
+def test_fit_ellipse_to_points_minimum_points():
+    """
+    Test fit_ellipse_to_points with minimum number of valid points.
+    
+    The function requires at least 5 valid points to fit an ellipse.
+    """
+    # Create exactly 5 points forming a simple pattern
+    points = np.array([
+        [100, 100],
+        [150, 100],
+        [150, 150],
+        [100, 150],
+        [125, 125],
+    ])
+    
+    # Should work with 5 points
+    fitted_cx, fitted_cy, a, b, theta = fit_ellipse_to_points(points)
+    
+    # Verify valid outputs
+    assert isinstance(fitted_cx, (int, float, np.number))
+    assert isinstance(fitted_cy, (int, float, np.number))
+    assert a > 0, "Semi-major axis should be positive"
+    assert b > 0, "Semi-minor axis should be positive"
+
+
+def test_fit_ellipse_to_points_raises_error_too_few_points():
+    """
+    Test that fit_ellipse_to_points raises an error with insufficient points.
+    """
+    # Create only 4 points (less than minimum required)
+    points = np.array([
+        [100, 100],
+        [150, 100],
+        [150, 150],
+        [100, 150],
+    ])
+    
+    # Should raise ValueError
+    try:
+        fit_ellipse_to_points(points)
+        assert False, "Expected ValueError for insufficient points"
+    except ValueError as e:
+        assert "Not enough valid points" in str(e)
+
+
+def test_fit_ellipse_to_points_with_nan_values():
+    """
+    Test that fit_ellipse_to_points correctly handles NaN values.
+    
+    The function should skip NaN points and still work if enough valid points remain.
+    """
+    # Create points with some NaN values
+    points = np.array([
+        [100, 100],
+        [150, 100],
+        [np.nan, np.nan],  # NaN point
+        [150, 150],
+        [100, 150],
+        [125, 125],
+        [np.nan, 200],  # Partial NaN
+    ])
+    
+    # Should work by ignoring NaN rows
+    fitted_cx, fitted_cy, a, b, theta = fit_ellipse_to_points(points)
+    
+    # Verify valid outputs
+    assert not np.isnan(fitted_cx), "Center x should not be NaN"
+    assert not np.isnan(fitted_cy), "Center y should not be NaN"
+    assert a > 0, "Semi-major axis should be positive"
+    assert b > 0, "Semi-minor axis should be positive"