def __init__(self, n, init_pdf, p_xt_xtp, p_yt_xt):
r"""Initialise particle filter.
:param int n: number of particles
:param init_pdf: either :class:`~pybayes.pdfs.EmpPdf` instance that will be used
directly as a posterior (and should already have initial particles sampled) or
any other probability density which initial particles are sampled from
:type init_pdf: :class:`~pybayes.pdfs.Pdf`
:param p_xt_xtp: :math:`p(x_t|x_{t-1})` cpdf of state in *t* given state in *t-1*
:type p_xt_xtp: :class:`~pybayes.pdfs.CPdf`
:param p_yt_xt: :math:`p(y_t|x_t)` cpdf of observation in *t* given state in *t*
:type p_yt_xt: :class:`~pybayes.pdfs.CPdf`
"""
if not isinstance(n, int) or n < 1:
raise TypeError("n must be a positive integer")
if not isinstance(init_pdf, Pdf):
raise TypeError("init_pdf must be an instance ot the Pdf class")
if not isinstance(p_xt_xtp, CPdf) or not isinstance(p_yt_xt, CPdf):
raise TypeError("both p_xt_xtp and p_yt_xt must be instances of the CPdf class")
dim = init_pdf.shape() # dimension of state
if p_xt_xtp.shape() != dim or p_xt_xtp.cond_shape() < dim:
raise ValueError("Expected shape() and cond_shape() of p_xt_xtp will "
+ "be (respectively greater than) {0}; ({1}, {2}) given.".format(dim,
p_xt_xtp.shape(), p_xt_xtp.cond_shape()))
self.p_xt_xtp = p_xt_xtp
if p_yt_xt.cond_shape() != dim:
raise ValueError("Expected cond_shape() of p_yt_xt will be {0}; {1} given."
.format(dim, p_yt_xt.cond_shape()))
self.p_yt_xt = p_yt_xt
if isinstance(init_pdf, EmpPdf):
self.emp = init_pdf # use directly
else:
self.emp = EmpPdf(init_pdf.samples(n))
class ParticleFilter(Filter):
r"""Standard particle filter implementation with resampling.
Specifying proposal density is currently unsupported, but planned; speak up if you want it!
Posterior pdf is represented using :class:`~pybayes.pdfs.EmpPdf` and takes following form:
.. math:: p(x_t|y_{1:t}) = \sum_{i=1}^n \omega_i \delta ( x_t - x_t^{(i)} )
"""
def __init__(self, n, init_pdf, p_xt_xtp, p_yt_xt):
r"""Initialise particle filter.
:param int n: number of particles
:param init_pdf: either :class:`~pybayes.pdfs.EmpPdf` instance that will be used
directly as a posterior (and should already have initial particles sampled) or
any other probability density which initial particles are sampled from
:type init_pdf: :class:`~pybayes.pdfs.Pdf`
:param p_xt_xtp: :math:`p(x_t|x_{t-1})` cpdf of state in *t* given state in *t-1*
:type p_xt_xtp: :class:`~pybayes.pdfs.CPdf`
:param p_yt_xt: :math:`p(y_t|x_t)` cpdf of observation in *t* given state in *t*
:type p_yt_xt: :class:`~pybayes.pdfs.CPdf`
"""
if not isinstance(n, int) or n < 1:
raise TypeError("n must be a positive integer")
if not isinstance(init_pdf, Pdf):
raise TypeError("init_pdf must be an instance ot the Pdf class")
if not isinstance(p_xt_xtp, CPdf) or not isinstance(p_yt_xt, CPdf):
raise TypeError("both p_xt_xtp and p_yt_xt must be instances of the CPdf class")
dim = init_pdf.shape() # dimension of state
if p_xt_xtp.shape() != dim or p_xt_xtp.cond_shape() < dim:
raise ValueError("Expected shape() and cond_shape() of p_xt_xtp will "
+ "be (respectively greater than) {0}; ({1}, {2}) given.".format(dim,
p_xt_xtp.shape(), p_xt_xtp.cond_shape()))
self.p_xt_xtp = p_xt_xtp
if p_yt_xt.cond_shape() != dim:
raise ValueError("Expected cond_shape() of p_yt_xt will be {0}; {1} given."
.format(dim, p_yt_xt.cond_shape()))
self.p_yt_xt = p_yt_xt
if isinstance(init_pdf, EmpPdf):
self.emp = init_pdf # use directly
else:
self.emp = EmpPdf(init_pdf.samples(n))
def bayes(self, yt, cond = None):
r"""Perform Bayes rule for new measurement :math:`y_t`; *cond* is ignored.
:param numpy.ndarray cond: optional condition that is passed to :math:`p(x_t|x_{t-1})`
after :math:`x_{t-1}` so that is can be rewritten as: :math:`p(x_t|x_{t-1}, c)`.
The algorithm is as follows:
1. generate new particles: :math:`x_t^{(i)} = \text{sample from }
p(x_t^{(i)}|x_{t-1}^{(i)}) \quad \forall i`
2. recompute weights: :math:`\omega_i = p(y_t|x_t^{(i)})
\omega_i \quad \forall i`
3. normalise weights
4. resample particles
"""
for i in range(self.emp.particles.shape[0]):
# generate new ith particle:
self.emp.particles[i] = self.p_xt_xtp.sample(self.emp.particles[i])
# recompute ith weight:
self.emp.weights[i] *= exp(self.p_yt_xt.eval_log(yt, self.emp.particles[i]))
# assure that weights are normalised
self.emp.normalise_weights()
# resample
self.emp.resample()
return True
def posterior(self):
return self.emp
