<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def batch_filter(self, zs, Rs=None, dts=None, UT=None, saver=None):
 """ Performs the UKF filter over the list of measurement in `zs`. Parameters zs : list-like list of measurements at each time step `self._dt` Missing measurements must be represented by 'None'. Rs : None, np.array or list-like, default=None optional list of values to use for the measurement error covariance R. If Rs is None then self.R is used for all epochs. If it is a list of matrices or a 3D array where len(Rs) == len(zs), then it is treated as a list of R values, one per epoch. This allows you to have varying R per epoch. dts : None, scalar or list-like, default=None optional value or list of delta time to be passed into predict. If dtss is None then self.dt is used for all epochs. If it is a list where len(dts) == len(zs), then it is treated as a list of dt values, one per epoch. This allows you to have varying epoch durations. UT : function(sigmas, Wm, Wc, noise_cov), optional Optional function to compute the unscented transform for the sigma points passed through hx. Typically the default function will work - you can use x_mean_fn and z_mean_fn to alter the behavior of the unscented transform. saver : filterpy.common.Saver, optional filterpy.common.Saver object. If provided, saver.save() will be called after every epoch Returns ------- means: ndarray((n,dim_x,1)) array of the state for each time step after the update. Each entry is an np.array. In other words `means[k,:]` is the state at step `k`. covariance: ndarray((n,dim_x,dim_x)) array of the covariances for each time step after the update. In other words `covariance[k,:,:]` is the covariance at step `k`. Examples -------- .. code-block:: Python # this example demonstrates tracking a measurement where the time # between measurement varies, as stored in dts The output is then smoothed # with an RTS smoother. zs = [t + random.randn()*4 for t in range (40)] (mu, cov, _, _) = ukf.batch_filter(zs, dts=dts) (xs, Ps, Ks) = ukf.rts_smoother(mu, cov) """

        #pylint: disable=too-many-arguments

        try:
            z = zs[0]
        except TypeError:
            raise TypeError('zs must be list-like')

        if self._dim_z == 1:
            if not(isscalar(z) or (z.ndim == 1 and len(z) == 1)):
                raise TypeError('zs must be a list of scalars or 1D, 1 element arrays')
        else:
            if len(z) != self._dim_z:
                raise TypeError(
                    'each element in zs must be a 1D array of length {}'.format(self._dim_z))

        z_n = np.size(zs, 0)
        if Rs is None:
            Rs = [self.R] * z_n

        if dts is None:
            dts = [self._dt] * z_n

        # mean estimates from Kalman Filter
        if self.x.ndim == 1:
            means = zeros((z_n, self._dim_x))
        else:
            means = zeros((z_n, self._dim_x, 1))

        # state covariances from Kalman Filter
        covariances = zeros((z_n, self._dim_x, self._dim_x))

        for i, (z, r, dt) in enumerate(zip(zs, Rs, dts)):
            self.predict(dt=dt, UT=UT)
            self.update(z, r, UT=UT)
            means[i, :] = self.x
            covariances[i, :, :] = self.P

            if saver is not None:
                saver.save()

        return (means, covariances)