diff --git a/pyrecest/filters/piecewise_constant_filter.py b/pyrecest/filters/piecewise_constant_filter.py
new file mode 100644
index 000000000..ae925fd1c
--- /dev/null
+++ b/pyrecest/filters/piecewise_constant_filter.py
@@ -0,0 +1,145 @@
+import numpy as np
+from pyrecest.distributions.circle.piecewise_constant_distribution import PieceWiseConstantDistribution
+from pyrecest.distributions import AbstractCircularDistribution
+from scipy.integrate import nquad, quad
+from .abstract_circular_filter import AbstractCircularFilter
+
+
+class PiecewiseConstantFilter(AbstractCircularFilter):
+    def __init__(self, n):
+        # Constructor
+        # Parameters:
+        #   n (scalar)
+        #       number of discretization steps
+        assert np.isscalar(n)
+        self.set_state(PieceWiseConstantDistribution(np.ones(n) / n))
+
+    def set_state(self, new_state):
+        assert isinstance(new_state, AbstractCircularDistribution)
+        if isinstance(new_state, PieceWiseConstantDistribution):
+            self.pwc = new_state
+        else:
+            self.pwc = PieceWiseConstantDistribution(PieceWiseConstantDistribution.calculate_parameters_numerically(new_state.pdf, len(self.pwc.w)))
+
+    def predict(self, A):
+        # Prediction step based on transition matrix
+        # Parameters:
+        #   A (L x L matrix)
+        #       system matrix
+        w = self.pwc.w
+        w = np.matmul(A, w.T)
+        w = w.T / np.sum(w)
+        self.pwc = PieceWiseConstantDistribution(w)
+
+    def update(self, H, z):
+        # Measurement update based on measurement matrix
+        # Parameters:
+        #   H (Lw x L matrix)
+        #       measurement matrix 
+        #   z (scalar)
+        #       measurement 
+        # get the right column from H
+        assert H.shape[1] == len(self.pwc.w)
+        assert np.isscalar(z)
+        Lw = H.shape[0]
+        row = int(np.floor(1 + z / (2 * np.pi) * Lw))
+        w = self.pwc.w
+        w = H[row, :] * w
+        self.pwc = PieceWiseConstantDistribution(w)
+
+    def update_likelihood(self, likelihood, z):
+        # Updates assuming nonlinear measurement model given by a
+        # likelihood function likelihood(z, x) = f(z | x), where z is the
+        # measurement. The function can be created using the
+        # LikelihoodFactory.
+        #
+        # Parameters:
+        #   likelihood (function handle)
+        #       function from Z x [0, 2pi) to [0, infinity), where Z is
+        #       the measurement space containing z
+        #   z (arbitrary)
+        #       measurement
+        L = len(self.pwc.w)
+        tmp = np.zeros(L)
+        for i in range(L):
+            tmp[i] = quad(lambda x: likelihood(z, x), PieceWiseConstantDistribution.left_border(i, L), PieceWiseConstantDistribution.right_border(i, L))[0]
+        self.pwc = PieceWiseConstantDistribution(tmp * self.pwc.w)
+
+    def get_estimate(self):
+        return self.pwc
+
+
+    
+    @staticmethod
+    def calculateSystemMatrixNumerically(L, a, noiseDistribution):
+        # Obtains system matrix by 2d numerical integration from system
+        # function
+        # Parameters:
+        #   L (scalar)
+        #       number of discretization intervals
+        #   a (function handle)
+        #       system function x_k+1 = a(x_k,w_k), needs to be
+        #       vectorized
+        #   noiseDistribution (AbstractCircularDistribution)
+        #       noise (assumed to be defined on [0,2pi)
+        # Returns;
+        #   A (L x L matrix)
+        #       system matrix
+        assert isinstance(L, int)
+        assert isinstance(noiseDistribution, AbstractCircularDistribution)
+        assert callable(a)
+
+        A = np.zeros((L, L))
+        for i in range(L):
+            l1 = PieceWiseConstantDistribution.leftBorder(i, L)
+            r1 = PieceWiseConstantDistribution.rightBorder(i, L)
+            for j in range(L):
+                l2 = PieceWiseConstantDistribution.leftBorder(j, L)
+                r2 = PieceWiseConstantDistribution.rightBorder(j, L)
+                indicator = lambda x: np.where((l2 < x) & (x < r2), 1, 0)
+
+                def integrand(x, w):
+                    return noiseDistribution.pdf(w) * indicator(a(x, w))
+
+                A[j, i] = nquad(integrand, [[l1, r1], [0, 2 * np.pi]])[0] * L / 2 / np.pi
+
+        return A
+    
+    
+    @staticmethod
+    def calculateMeasurementMatrixNumerically(L, Lmeas, h, noiseDistribution):
+        # Obtains system matrix by 2d numerical integration from
+        # measurement function
+        # Parameters:
+        #   L (scalar)
+        #       number of discretization intervals for state
+        #   Lmeas (scalar)
+        #       number of discretization intervals for measurement
+        #   h (function handle)
+        #       system function z_k = h(x_k,v_k), needs to be
+        #       vectorized
+        #   noiseDistribution (AbstractCircularDistribution)
+        #       noise (assumed to be defined on [0,2pi)
+        # Returns;
+        #   H (Lmeas x L matrix)
+        #       measurement matrix
+        assert isinstance(L, int)
+        assert isinstance(Lmeas, int)
+        assert isinstance(noiseDistribution, AbstractCircularDistribution)
+        assert callable(h)
+
+        H = np.zeros((Lmeas, L))
+        for i in range(Lmeas):
+            l1 = PieceWiseConstantDistribution.leftBorder(i, Lmeas)
+            r1 = PieceWiseConstantDistribution.rightBorder(i, Lmeas)
+            for j in range(L):
+                l2 = PieceWiseConstantDistribution.leftBorder(j, L)
+                r2 = PieceWiseConstantDistribution.rightBorder(j, L)
+                indicator = lambda x: np.where((l1 < x) & (x < r1), 1, 0)
+
+                def integrand(x, v):
+                    return noiseDistribution.pdf(v) * indicator(h(x, v))
+
+                H[i, j] = nquad(integrand, [[l2, r2], [0, 2 * np.pi]])[0] * L / 2 / np.pi
+
+        return H