diff --git a/src/components/detection/l_shape_fitting/robust_least_squares_detector.py b/src/components/detection/l_shape_fitting/robust_least_squares_detector.py
new file mode 100644
index 00000000..65469eb9
--- /dev/null
+++ b/src/components/detection/l_shape_fitting/robust_least_squares_detector.py
@@ -0,0 +1,384 @@
+"""
+robust_least_squares_detector.py
+
+Author: Shreyansh Shethia
+"""
+
+from asyncio.log import logger
+import sys
+import copy
+import itertools
+import numpy as np
+from collections import deque
+from pathlib import Path
+from math import pi, sin, cos
+from scipy.optimize import least_squares
+from math import sin, cos, atan2
+import matplotlib.pyplot as plt
+abs_dir_path = str(Path(__file__).absolute().parent)
+sys.path.append(abs_dir_path + "/../../search/kd_tree")
+
+from l_shape_fitting_detector import LShapeFittingDetector
+from kd_tree import KdTree
+from rectangle import Rectangle
+import numpy as np
+from scipy.optimize import least_squares
+from math import sin, cos, atan2
+from scipy.spatial.distance import pdist, squareform
+
+class FittingDataTracker:
+    """
+    Telemetry and performance tracking class for OBB fitting analysis.
+    
+    This class captures frame-by-frame metrics from both the geometric 
+    baseline and the optimized refinement stage. It facilitates the 
+    calculation of Root Mean Square Error (RMSE) and tracks the 
+    evolution of spatial parameters (cx, cy, theta) over time.
+    """
+    def __init__(self):
+        """
+        Initialize the tracker with Ground Truth placeholders and data storage.
+        """
+        self.gt_cx = 20.0      # replace with 
+        self.gt_cy = 0.0   # Example ground truth center y
+        self.data = {
+            "time": [], 
+            "rmse_geo": [], 
+            "rmse_opt": [], 
+            "theta_geo": [], 
+            "theta_opt": [],
+            "cx_geo": [], 
+            "cy_geo": [], 
+            "cx_opt": [], 
+            "cy_opt": []
+        }
+
+    def log(self, t, r_geo, r_opt, p_geo, p_opt):
+        """
+        Record performance metrics for the current simulation frame.
+
+        Calculates the instantaneous RMSE for both methods and logs the 
+        predicted pose and dimensions.
+
+        Args:
+            t (float/int): Current frame index or simulation time.
+            r_geo (numpy.ndarray): Residual vector from the geometric fit.
+            r_opt (numpy.ndarray): Residual vector from the optimized fit.
+            p_geo (list/tuple): Pose parameters from geometric fitting [cx, cy, theta, ...].
+            p_opt (list/tuple): Pose parameters from optimized fitting [cx, cy, theta, ...].
+        """
+        self.data["time"].append(t)
+        self.data["rmse_geo"].append(np.sqrt(np.mean(r_geo**2)))
+        self.data["rmse_opt"].append(np.sqrt(np.mean(r_opt**2)))
+        self.data["theta_geo"].append(np.degrees(p_geo[2]))
+        self.data["theta_opt"].append(np.degrees(p_opt[2]))
+        self.data["cx_geo"].append(p_geo[0])
+        self.data["cy_geo"].append(p_geo[1])
+        self.data["cx_opt"].append(p_opt[0])
+        self.data["cy_opt"].append(p_opt[1])
+
+    def plot(self):
+        """
+        Generate a multi-panel performance report using Matplotlib.
+
+        Produces:
+        1. An RMSE comparison plot to visualize fitting precision.
+        2. A two-panel plot comparing predicted Center-X and Center-Y 
+           against baseline geometric results.
+        """
+        if not self.data["time"]:
+            print("No data collected to plot.")
+            return
+
+        plt.figure(figsize=(10, 5))
+        plt.plot(self.data["time"], self.data["rmse_geo"], 'b--', label='Geometric RMSE')
+        plt.plot(self.data["time"], self.data["rmse_opt"], 'r-', label='Optimized RMSE')
+        plt.ylabel("RMSE [m]"); plt.legend(); plt.grid(True)
+
+        # Create a 2x1 plot specifically for Center Accuracy
+        fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(10, 10))
+        
+        # Plot 1: CX Accuracy
+        ax1.plot(self.data["time"], self.data["cx_geo"], 'b--', label='Geometric CX', alpha=0.5)
+        ax1.plot(self.data["time"], self.data["cx_opt"], 'r-', label='Optimized CX')
+        #ax1.axhline(y=self.gt_cx, color='g', linestyle='-', linewidth=2, label='Ground Truth CX')
+        ax1.set_ylabel("X Position [m]")
+        ax1.set_title("Center X: Ground Truth vs. Predictions")
+        ax1.legend(); ax1.grid(True)
+
+        # Plot 2: CY Accuracy
+        ax2.plot(self.data["time"], self.data["cy_geo"], 'b--', label='Geometric CY', alpha=0.5)
+        ax2.plot(self.data["time"], self.data["cy_opt"], 'r-', label='Optimized CY')
+        #ax2.axhline(y=self.gt_cy, color='g', linestyle='-', linewidth=2, label='Ground Truth CY')
+        ax2.set_ylabel("Y Position [m]")
+        ax2.set_xlabel("Frames")
+        ax2.set_title("Center Y: Ground Truth vs. Predictions")
+        ax2.legend(); ax2.grid(True)
+
+        plt.tight_layout()
+        plt.show()
+
+# Create the specific instance
+tracker = FittingDataTracker()
+
+class OptimizedLShapeDetector(LShapeFittingDetector):
+    def __init__(self, min_rng_th_m=3.0, rng_th_rate=0.1, change_angle_deg=1.0, lossfunc='huber', show_logger_debug=True):
+        """
+        Initialize the Robust L-Shape detector with Least-Squares optimization.
+        
+        Args:
+            min_rng_th_m (float): Minimum range threshold for clustering.
+            rng_th_rate (float): Range threshold rate.
+            change_angle_deg (float): Step size for the geometric orientation sweep.
+            lossfunc (str): Robust M-estimator to use ('huber', 'cauchy', etc.).
+            show_logger_debug (bool): Flag to print optimization results to console.
+        """
+        super().__init__(min_rng_th_m, rng_th_rate, change_angle_deg)
+        self.f_scale = 0.05  # Tight tolerance for the final polish
+        self.prev_rects = {}
+        self.lossfunc = lossfunc # Can be Cauchy, Huber, soft_l1, linear
+        self.show_logger_debug = show_logger_debug
+
+    def _calculate_residuals(self, params, points, weights):
+        """
+        Calculate the Signed Distance Field (SDF) residuals for the optimizer.
+        
+        This function transforms points into the local frame of the candidate box 
+        and calculates the distance of each point to the nearest rectangle edge.
+        
+        Args:
+            params (list): [cx, cy, theta, w, l]
+            points (numpy.ndarray): (2, N) array of LiDAR points in world frame.
+            weights (numpy.ndarray): (N,) array of weights for each point.
+            
+        Returns:
+            numpy.ndarray: Flattened residual vector scaled by weights.
+        """
+        cx, cy, theta, w, l = params
+        cos_t, sin_t = np.cos(theta), np.sin(theta)
+        
+        # Transform points to box-local frame
+        dx = cos_t * (points[0,:] - cx) + sin_t * (points[1,:] - cy)
+        dy = -sin_t * (points[0,:] - cx) + cos_t * (points[1,:] - cy)
+        
+        # Distance to box edges
+        err_x = np.abs(dx) - (w / 2.0)
+        err_y = np.abs(dy) - (l / 2.0)
+        
+        # Signed Distance Field (SDF) logic
+        res = np.sqrt(np.maximum(err_x, 0)**2 + np.maximum(err_y, 0)**2) + \
+              np.minimum(np.maximum(err_x, err_y), 0)
+
+        return np.concatenate([res * np.sqrt(weights)])
+
+    def _get_initial_guess(self, points_array):
+        """
+        Generate a high-quality initial guess using a hybrid geometric approach.
+        
+        1. Uses Yano's variance criterion to find the global orientation.
+        2. Uses the midpoint of the farthest-point pair for the spatial center.
+        3. Projects points onto the chosen axes to estimate initial dimensions.
+        
+        Args:
+            points_array (numpy.ndarray): (2, N) array of LiDAR points.
+            
+        Returns:
+            list: [cx, cy, theta_init, w_init, l_init] as an initial guess for the solver.
+        """
+        # points_array shape is (2, N)
+        points_t = points_array.T # (N, 2)
+        
+        # 1. Find Best Angle via Variance Criterion -- Global Heading Search
+        min_cost_angle = (-float("inf"), None)
+        for angle_rad in np.arange(0, np.pi/2 - self.CHANGE_ANGLE_RAD, self.CHANGE_ANGLE_RAD):
+            rotated_points = self._rotate_points(points_array, angle_rad)
+            cost = self._calculate_variance_criterion(rotated_points)
+            if min_cost_angle[0] < cost: 
+                min_cost_angle = (cost, angle_rad)
+        
+        theta_init = min_cost_angle[1]
+
+        # 2. Find the two farthest points (the diameter of the point cloud)
+        # and estimate center (cx, cy)
+        
+        if points_t.shape[0] > 2:
+            # Finding the absolute farthest pair
+            dists = pdist(points_t)
+            dist_matrix = squareform(dists)
+            i, j = np.unravel_index(np.argmax(dist_matrix), dist_matrix.shape)
+            p1, p2 = points_t[i], points_t[j]
+            
+            # Use the midpoint of these two as the center guess
+            cx, cy = (p1 + p2) / 2.0
+        else:
+            cx, cy = np.mean(points_array, axis=1)
+        
+        # 3. Box Dimensions (w, l) Estimation
+        cos_t, sin_t = np.cos(theta_init), np.sin(theta_init)
+        
+        # Local coordinates relative to the chosen center and angle
+        dx =  cos_t * (points_array[0,:] - cx) + sin_t * (points_array[1,:] - cy)
+        dy = -sin_t * (points_array[0,:] - cx) + cos_t * (points_array[1,:] - cy)
+        
+        # Now w and l are guaranteed to be aligned with the best angle
+        w = np.max(dx) - np.min(dx)
+        l = np.max(dy) - np.min(dy)
+        
+        return [cx, cy, theta_init, max(0.5, w), max(0.5, l)]  # Ensure minimum size to avoid degenerate boxes
+    
+    
+    def _calculate_rectangle(self, points_array):
+        """
+        Execute the full fitting pipeline: Initialization -> Optimization -> Logging.
+        
+        This is the main entry point for the detector, providing a polished OBB 
+        by refining the geometric guess with a non-linear Huber-weighted solver.
+        
+        Args:
+            points_array (numpy.ndarray): (2, N) array of clustered LiDAR points.
+            
+        Returns:
+            Rectangle: A specialized rectangle object containing the refined OBB parameters.
+        """
+        self.prev_rects = {}
+        
+        # --- STAGE 1: Get Initial Guess from L-Shape Fitting (Your Farthest-Point Logic) ---
+        init_guess = self._get_initial_guess(points_array)
+        
+        # --- STAGE 2: Domain for Optimization ---
+        theta_window = np.radians(2.0) # Small window is fine now because theta is good
+        lower = np.array([-np.inf, -np.inf, init_guess[2] - theta_window, init_guess[3]*0.9, init_guess[4]*0.9])
+        upper = np.array([np.inf, np.inf, init_guess[2] + theta_window, init_guess[3]*1.1, init_guess[4]*1.1])
+        
+        # Simple uniform weights
+        # TODO: Implement a New method for weights based on point distribution 
+        # This is because points closer to Lidar will have less noise and more denser distribution
+        weights = np.ones(points_array.shape[1])
+
+        # Calculate initial cost
+        res_before = self._calculate_residuals(init_guess, points_array, weights)
+        cost_before = 0.5 * np.sum(res_before**2) # Least squares cost is 0.5 * sum(r^2)
+        
+        try:
+            res = least_squares(
+                self._calculate_residuals, init_guess,
+                args=(points_array, weights),
+                bounds=(lower, upper),
+                loss=self.lossfunc, f_scale=.02
+            )
+            cx, cy, theta, w, l = res.x
+            self.prev_rects = res.x
+
+        except:
+            # Fallback to Initial Guess if optimization fails
+            cx, cy, theta, w, l = init_guess
+            self.prev_rects = init_guess
+ 
+        # --- STAGE 3: After Optimization: Logging for Analysis ---
+        if 'res' in locals():
+            # Calculate residuals after optimization
+            
+            final_params = res.x
+            res_after = self._calculate_residuals(final_params, points_array, weights)
+            cost_after = 0.5 * np.sum(res_after**2)
+            improvement = (cost_before - cost_after) / (cost_before + 1e-6) * 100
+            theta_diff = np.rad2deg(final_params[2] - init_guess[2])
+            tracker.log(len(tracker.data["time"]), res_before, res_after, init_guess, res.x)
+
+            # --- PRINT REPORT ---
+            if self.show_logger_debug:
+                print("-" * 30)
+                print(f"Optimization Report (Status: {res.message})")
+                print(f"  Cost:  {cost_before:.4f} -> {cost_after:.4f} ({improvement:.1f}% improvement)")
+                print(f"  Theta: {np.rad2deg(init_guess[2]):.2f}° -> {np.rad2deg(final_params[2]):.2f}° (Δ: {theta_diff:.2f}°)")
+                print("-" * 30)
+
+        else:
+            print("Optimization failed; using Initial Guess.")
+
+        # --- STAGE 4: Create Final Rectangle ---
+        cos_t, sin_t = cos(theta), sin(theta)
+        c1_mid = cx * cos_t + cy * sin_t
+        c2_mid = -cx * sin_t + cy * cos_t
+
+        return Rectangle(a=[cos_t, -sin_t, cos_t, -sin_t],
+                         b=[sin_t, cos_t, sin_t, cos_t],
+                         c=[c1_mid - w/2.0, c2_mid - l/2.0, c1_mid + w/2.0, c2_mid + l/2.0])
+    
+
+class DualLShapeDetector:
+    """
+    A comparative detector class that runs both geometric and optimized L-shape fitting.
+    
+    This class facilitates side-by-side visualization and performance analysis by 
+    encapsulating a standard LShapeFittingDetector and an OptimizedLShapeDetector. 
+    It is primarily used for validating the accuracy gains of non-linear optimization 
+    over traditional geometric search methods.
+    """    
+    def __init__(self, show_logger_debug=True):
+        """
+        Initialize the dual detector with both fitting pipelines.
+
+        Args:
+            show_logger_debug (bool): If True, enables console output for the 
+                                      optimized fitting stage.
+        """
+        self.geometric_detector = LShapeFittingDetector()
+        self.optimized_detector = OptimizedLShapeDetector(show_logger_debug=show_logger_debug)
+        self.latest_rectangles_list = []
+
+    def update(self, point_cloud):
+        """
+        Update both detection pipelines with the latest LiDAR point cloud data.
+
+        Processes the raw cluster through the geometric sweep first, followed 
+        by the optimized Huber-weighted polish. Results are aggregated into 
+        a single list for state management and visualization.
+
+        Args:
+            point_cloud (numpy.ndarray): The raw (2, N) LiDAR point cloud cluster.
+        """
+        # 1. Update both detectors
+        self.geometric_detector.update(point_cloud)
+        self.optimized_detector.update(point_cloud)
+
+        # 2. Combine results for the vehicle state if needed
+        # We show both in the list so they can both be drawn
+        self.latest_rectangles_list = (self.geometric_detector.latest_rectangles_list + 
+                                       self.optimized_detector.latest_rectangles_list)
+
+    def draw(self, axes, elems, x_m, y_m, yaw_rad):
+        """
+        Visualize the OBB results from both detectors on a 2D plot.
+
+        Renders the geometric fit as a thin blue line and the optimized fit 
+        as a thick red line to clearly distinguish the refinement polish.
+
+        Args:
+            axes (matplotlib.axes.Axes): The axes object for the current plot.
+            elems (list): A list of plot elements to be updated/cleared.
+            x_m (float): Current vehicle X position in world frame.
+            y_m (float): Current vehicle Y position in world frame.
+            yaw_rad (float): Current vehicle heading in radians.
+        """
+        def custom_draw(rect_obj, color_code, label_prefix, lw=2):
+            """Internal helper to handle homogeneous transformation and plotting."""
+            transformed_contour = rect_obj.contour.homogeneous_transformation(x_m, y_m, yaw_rad)
+            rect_plot, = axes.plot(transformed_contour.get_x_data(),
+                                   transformed_contour.get_y_data(),
+                                   color=color_code, ls='-', linewidth=lw, label=label_prefix)
+            elems.append(rect_plot)
+            
+            transformed_center = rect_obj.center_xy.homogeneous_transformation(x_m, y_m, yaw_rad)
+            center_plot, = axes.plot(transformed_center.get_x_data(),
+                                     transformed_center.get_y_data(),
+                                     marker='.', color=color_code)
+            elems.append(center_plot)
+
+        # Draw Geometric (Blue) - Thin line
+        for rect in self.geometric_detector.latest_rectangles_list:
+            custom_draw(rect, 'b', 'Geometric', lw=1.5)
+
+        # Draw Optimized (Red) - Thick line
+        for rect in self.optimized_detector.latest_rectangles_list:
+            custom_draw(rect, 'r', 'Optimized', lw=3.0)
\ No newline at end of file
diff --git a/src/simulations/perception/point_cloud_rectangle_fitting/point_cloud_robustLS_rectangle_fitting.gif b/src/simulations/perception/point_cloud_rectangle_fitting/point_cloud_robustLS_rectangle_fitting.gif
new file mode 100644
index 00000000..332b5693
Binary files /dev/null and b/src/simulations/perception/point_cloud_rectangle_fitting/point_cloud_robustLS_rectangle_fitting.gif differ
diff --git a/src/simulations/perception/point_cloud_rectangle_fitting/point_cloud_robustLS_rectangle_fitting.py b/src/simulations/perception/point_cloud_rectangle_fitting/point_cloud_robustLS_rectangle_fitting.py
new file mode 100644
index 00000000..a05c2c1b
--- /dev/null
+++ b/src/simulations/perception/point_cloud_rectangle_fitting/point_cloud_robustLS_rectangle_fitting.py
@@ -0,0 +1,99 @@
+"""
+point_cloud_robustLS_rectangle_fitting.py
+
+Author: Shreyansh Shethia
+"""
+
+# import path setting
+import numpy as np
+import sys
+from pathlib import Path
+import matplotlib.pyplot as plt
+
+abs_dir_path = str(Path(__file__).absolute().parent)
+relative_path = "/../../../components/"
+relative_simulations = "/../../../simulations/"
+
+sys.path.append(abs_dir_path + relative_path + "visualization")
+sys.path.append(abs_dir_path + relative_path + "state")
+sys.path.append(abs_dir_path + relative_path + "vehicle")
+sys.path.append(abs_dir_path + relative_path + "obstacle")
+sys.path.append(abs_dir_path + relative_path + "sensors")
+sys.path.append(abs_dir_path + relative_path + "sensors/lidar")
+sys.path.append(abs_dir_path + relative_path + "detection/l_shape_fitting")
+
+
+# import component modules
+
+from global_xy_visualizer import GlobalXYVisualizer
+from min_max import MinMax
+from time_parameters import TimeParameters
+from vehicle_specification import VehicleSpecification
+from state import State
+from four_wheels_vehicle import FourWheelsVehicle
+from obstacle import Obstacle
+from obstacle_list import ObstacleList
+from sensors import Sensors
+from sensor_parameters import SensorParameters
+from omni_directional_lidar import OmniDirectionalLidar
+from l_shape_fitting_detector import LShapeFittingDetector
+from robust_least_squares_detector import OptimizedLShapeDetector, DualLShapeDetector, tracker #RansacOptimizationDetector #RobustRectangleFittingDetector
+
+# flag to show plot figure
+# when executed as unit test, this flag is set as false
+show_plot = True
+# --- STEP 1: Define at the top ---
+
+def main():
+    """
+    Main process function
+    """
+    
+    # set simulation parameters
+    x_lim, y_lim = MinMax(-30, 30), MinMax(-30, 30)
+    navigation_gif_path = abs_dir_path + relative_simulations + "perception/point_cloud_rectangle_fitting/point_cloud_robustLS_rectangle_fitting.gif"
+    vis = GlobalXYVisualizer(x_lim, y_lim, TimeParameters(span_sec=20), gif_name=navigation_gif_path)
+
+    # create obstacle instances
+    obst_list = ObstacleList()
+    obst1 = Obstacle(State(x_m=-5.0, y_m=15.0, speed_mps=1.0), yaw_rate_rps=np.deg2rad(10), width_m=1.0)
+    obst_list.add_obstacle(obst1)
+    #obst2 = Obstacle(State(x_m=0.0, y_m=-15.0), length_m=10.0, width_m=5.0)
+    #obst_list.add_obstacle(obst2)
+    obst3 = Obstacle(State(x_m=20.0), yaw_rate_rps=np.deg2rad(15))
+    obst_list.add_obstacle(obst3)
+    #obst4 = Obstacle(State(x_m=-20.0, y_m=0.0), width_m=1.0)
+    #obst_list.add_obstacle(obst4)
+    obst6 = Obstacle(State(x_m=-15.0, y_m=-15.0), length_m=10.0, width_m=5.0)
+    obst_list.add_obstacle(obst6)
+    #obst7 = Obstacle(State(x_m=-15.0, y_m=15.0, yaw_rad = np.pi/4), length_m=10.0, width_m=5.0)
+    #obst_list.add_obstacle(obst7)
+    vis.add_object(obst_list)
+
+    # create vehicle instance
+    spec = VehicleSpecification(area_size=30.0) # spec instance
+    lidar = OmniDirectionalLidar(obst_list, SensorParameters(lon_m=spec.wheel_base_m/2)) # lidar instance
+    detector = DualLShapeDetector(show_logger_debug=True if show_plot else False) # detector instance 
+    vehicle = FourWheelsVehicle(State(color=spec.color), spec, sensors=Sensors(lidar=lidar), detector=detector) # set state, spec, lidar, detector as arguments
+    vis.add_object(vehicle)
+
+    # plot figure is not shown when executed as unit test
+    if not show_plot:
+        vis.not_show_plot()
+    else:
+        print("Simulation started. Close the simulation window to generate report after simulation.")
+
+    # ... Execute simulation ...
+    vis.draw()
+    if (show_plot and len(obst_list.get_list())==1):
+        # This only runs AFTER you close the simulation window
+        # If there are multiple obstacles, the plot gets too crowded to be useful
+        print("Generating post-simulation report...")
+        tracker.plot()
+
+    
+
+
+# execute main process
+if __name__ == "__main__":
+    main()
diff --git a/test/test_point_cloud_robustLS_rectangle_fitting.py b/test/test_point_cloud_robustLS_rectangle_fitting.py
new file mode 100644
index 00000000..b96abc45
--- /dev/null
+++ b/test/test_point_cloud_robustLS_rectangle_fitting.py
@@ -0,0 +1,17 @@
+"""
+Test of Object Detection simulation by Robust Rectangle Fitting algorithm
+
+Author: Shreyansh Shethia
+"""
+
+from pathlib import Path
+import sys
+import pytest
+
+sys.path.append(str(Path(__file__).absolute().parent) + "/../src/simulations/perception/point_cloud_rectangle_fitting")
+import point_cloud_robustLS_rectangle_fitting
+
+
+def test_simulation():
+    point_cloud_robustLS_rectangle_fitting.show_plot = False
+    point_cloud_robustLS_rectangle_fitting.main()